Critic thinking: Project Management

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17 Project Management L E A R N I N G O B J E C T I V E S After completing this chapter, you should be able to:

LO17.1 Describe the project life cycle.

LO17.2 Discuss the behavioral aspects of projects in terms of project personnel and the project manager.

LO17.3 Name the six key decisions in project management.

LO17.4 Explain the nature and importance of a work breakdown structure in project management.

LO17.5 Give a general description of PERT/CPM techniques.

LO17.6 Construct simple network diagrams.

LO17.7 Analyze networks with deterministic times.

LO17.8 Analyze networks with probabilistic times.

LO17.9 Describe activity “crashing” and solve typical problems.

LO17.10 Discuss the advantages of using PERT and potential sources of error.

LO17.11 Discuss the key steps in risk management.

17.1 Introduction, 732

17.2 Project Life Cycle, 732

17.3 Behavioral Aspects of Project Management, 733 The Nature of Projects, 734 Key Decisions in Project Management, 735 The Project Manager, 736 Behavioral Issues, 737 Project Champions, 737 Certification, 737 The Pros and Cons of Working on Projects, 737

17.4 Work Breakdown Structure, 739

17.5 Planning and Scheduling with Gantt Charts, 739

17.6 PERT and CPM, 740 The Network Diagram, 740 Network Conventions, 742

17.7 Deterministic Time Estimates, 743 17.8 A Computing Algorithm, 744

Activity-on-Arrow, 744 Activity-on-Node, 748 Computing Slack Times, 750

17.9 Probabilistic Time Estimates, 751 17.10 Determining Path

Probabilities, 754 17.11 Simulation, 756 17.12 Budget Control, 757

17.13 Time–Cost Trade-Offs: Crashing, 757

17.14 Advantages of Using PERT and Potential Sources of Error, 760

17.15 Critical Chain Project Management, 761

17.16 Other Topics in Project Management, 761

17.17 Project Management Software, 762

17.18 Operations Strategy, 763

17.19 Risk Management, 763 Cases: The Case of the Mexican

Crazy Quilt, 779 Time, Please, 781

C H A P T E R O U T L I N E

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Projects are a unique aspect of business operations that require a special management approach. Unlike many other aspects of business, which tend to operate more routinely, projects often have uncertainties and risks that tend to make managing them more challenging, such as the Hoover Dam bridge.

Examples of projects are many. Some are huge, such as building the space station, rescue and cleanup operations after major natural disasters, and hosting the Olympic games. Others are smaller in scope, but still quite involved, such as producing a major motion picture, putting on a Broadway play, or producing a music video. They involve a tremendous amount of planning and coordinating set design, set building, script writing, camera crews, directors, actors or hosts, costumes, advertising, and more to accomplish project objectives while meeting budget and time constraints.

Consider the Olympic Games. They involve much more than the festivities, the excitement, national pride, and compe- tition among athletes. They all involve a tremendous amount of planning, preparation, and coordinating work that needs to get done before and during the games. Athletes’ living quarters and training facilities must be provided, competition schedules must be developed, arrangements for televising events must be made, equipment and crews must be coordi- nated, transportation and hotel accommodations must be made, and many other activities that go on behind the scenes must be planned and managed so that everything goes off smoothly.

The Microsoft Corporation periodically releases new or updated software. Each release is the result of many people working countless hours writing code, testing programs, and revising code. Design, production, and marketing efforts also have to be coordinated. The reputation and profits of the company are closely related to successful software development.

Not all projects are successful, and the consequences of project failure can be costly, and even catastrophic. ERP installation projects (see Chapter 12) are expensive and time-consuming, and more than a few companies have termi- nated their projects after spending large sums of money.

This chapter introduces the basic concepts of project management. It includes a discussion of some behavioral aspects of project management, along with some of the difficulties project managers are apt to encounter. The main portion of the chap- ter is devoted to a description of graphical and computational methods that are used for planning and scheduling projects.

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17.1 INTRODUCTION

Managers typically oversee a variety of operations. Some of these involve routine, repeti- tive activities, but others involve nonroutine activities. Under the latter heading are projects: unique, one-time operations designed to accomplish a set of objectives in a limited time frame. Other examples of projects include constructing a shopping complex, merging two companies, putting on a play, and designing and running a political campaign. Examples of projects within business organizations include designing new products or services, designing advertising campaigns, designing information systems, reengineering a process, designing databases, software development, and designing Web pages.

Projects may involve considerable cost. Some have a long time horizon, and some involve a large number of activities that must be carefully planned and coordinated. Most are expected to be completed based on time, cost, and performance targets. To accomplish this, goals must be established and priorities set. Tasks must be identified and time estimates made. Resource requirements also must be projected and budgets prepared. Once under way, progress must be monitored to assure that project goals and objectives will be achieved.

The project approach enables an organization to focus attention and concentrate efforts on accomplishing a narrow set of performance objectives within a limited time and budget framework. This can produce significant benefits compared with other approaches that might be considered. Even so, projects present managers with a host of problems that differ in many respects from those encountered with more routine activities. The problems of planning and coordinating project activities can be formidable for large projects, which typically have thou- sands of activities that must be carefully planned and monitored if the project is to proceed according to schedule and at a reasonable cost.

Projects can have strategic importance for organizations. For example, good project man- agement can be instrumental in successfully implementing an enterprise resource planning (ERP) system or converting a traditional operation to a lean operation. And good project management is very important when virtual teams are used.

Table 17.1 provides an overview of project management.

17.2 PROJECT LIFE CYCLE

The size, length, and scope of projects vary widely according to the nature and purpose of the project. Nevertheless, all projects have something in common: They go through a life cycle, which typically consists of five phases.

1. Initiating. This begins the process by outlining the expected costs, benefits, and risks associated with a project. It includes defining the major project goals and choosing a project manager

2. Planning. This phase provides details on deliverables, scope of the project, budget, schedule and milestones, performance objectives, resources needed, a quality plan, and a plan for handling risks. The accompanying documents generated in the planning phase will be used in the executing and monitoring phases to guide activities and monitor progress. Members of the project team are chosen.

3. Executing. In this phase the actual work of the project is carried out. The project is managed as activities are completed, resources are consumed, and milestones are reached. Management involves what the Project Management Institute (www.pmi.org) refers to as the nine management areas: project integration, scope, human resources, communications, time, risk, quality, cost, and procurement.

4. Monitoring and Controlling. This phase occurs at the same time as project execution. It involves comparing actual progress with planned progress and undertakes correc- tive action if needed, and monitoring any corrective action to make sure it achieves the desired effect.

Projects Unique, one-time operations designed to accomplish a specific set of objectives in a limited time frame.

LO17.1 Describe the proj- ect life cycle.

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5. Closing. This phase ends the project. It involves handing off the project deliverables, obtaining customer acceptance, documenting lessons learned, and releasing resources.

It should be noted that the phases can overlap, so that one phase may not be fully complete before the next phase begins. This can reduce the time necessary to move through the life cycle, perhaps generating some competitive advantage and cost saving. Although subsequent decisions in an earlier phase may result in waste for some portion of the activity in a following phase, careful coordination of activities can minimize that risk.

Figure 17.1 illustrates the phases in a project life cycle.

17.3 BEHAVIORAL ASPECTS OF PROJECT MANAGEMENT

Project management differs from management of more traditional activities mainly because of its limited time framework and the unique set of activities involved, which gives rise to a host of unique problems. This section describes more fully the nature of projects and their behavioral implications. Special attention is given to the role of the project manager.

LO17.2 Discuss the behav- ioral aspects of projects in terms of project personnel and the project manager.

What is project management? A team-based approach for managing projects. How is it different from general operations management? 1. Limited time frame 2. Narrow focus, specific objectives 3. Less bureaucratic

Why is it used? 1. Special needs that don’t lend themselves to functional management 2. Pressures for new or improved products or services, cost reduction

What are the key metrics? 1. Time 2. Cost 3. Performance objectives

What are the key success factors? 1. Top-down commitment 2. A respected and capable project manager 3. Enough time to plan 4. Careful tracking and control 5. Good communications

What are the major administrative issues? 1. Executive responsibilities:

a. Project selection b. Selection of a project manager c. Organizational structure (To whom will the project manager report?)

2. Organizational alternatives: a. Manage within functional unit b. Assign a coordinator c. Use a matrix organization with a project leader

What are the main tools? 1. Work breakdown structure: An initial planning tool that is needed to develop a list of activities, activity

sequences, and a realistic budget 2. Network diagram: A “big picture” visual aid that is used to estimate project duration, identify activities

that are critical for timely project completion, identify areas where slack time exists, and develop activ- ity schedules

3. Gantt charts: A visual aid used to plan and monitor individual activities 4. Risk management: Analyses of potential failures or problems, assessment of their likelihood and conse-

quences, and contingency plans

TABLE 17.1 Overview of project management

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The Nature of Projects As projects go through their life cycle, a variety of skill requirements are involved. The circumstances are analogous to constructing a house. Initially an idea is presented and its feasibility is assessed, then plans must be drawn up and approved by the owner and pos- sibly a town building commission or other regulatory agency. Then a succession of activi- ties occurs, each with its own skill requirements, starting with the site preparation, then laying the foundation, erecting the frame, roofing, constructing exterior walls, wiring and plumbing, installing kitchen and bathroom fixtures and appliances, interior finishing work, and painting and carpeting work. Similar sequences occur on large construction projects, in R&D work, in the aerospace industry, and in virtually every other instance where projects are being carried out.

Projects typically bring together people with diverse knowledge and skills, most of whom remain associated with the project for less than its full life. Some people go from project to project as their contributions become needed, and others are “on loan,” either on a full-time or part-time basis, from their regular jobs. The latter is usually the case when a special project exists within the framework of a more traditional organization. However, some organizations are involved with projects on a regular basis; examples include consulting firms, architects, writers and publishers, and construction firms. In those organizations, it is not uncommon for some individuals to spend virtually all of their time on projects.

Some organizations use a matrix organization that allows them to integrate the activities of a variety of specialists within a functional framework. For instance, they have certain people who prepare proposals, others who concentrate exclusively on engineering, others who devote their efforts to marketing, and so on.

In a matrix organization, functional and project managers share workers and facilities. Project managers negotiate with functional managers for people to work on a project. Those selected will be temporarily assigned to the project manager. However, they are still respon- sible to their functional manager. They may work part-time or full-time on the project. When their work is done, they return to their functional department.

A matrix organization works quite well with people who can function with two managers. It can create synergy when people from various functional areas are brought together to work on a project. However, some people do not function well under such a structure, and may be stressed working in that environment. Matrix organizations typically do not allow long-term working relationships to develop. Furthermore, using multiple managers for one employee may result in uncertainty regarding employee evaluation and accountability.

FIGURE 17.1 Project life cycle Initiating

Goals Specifications Feasibility Tasks Responsibilities

Schedules Budgets Resources Risks Sta�ng

Status reports Changes Quality Manage Monitor and control

Train customer Transfer documents Release resources Reassign sta� Lessons learned

Le ve

l o f

e �

o rt

Planning Execution and

Monitoring and Controlling Closing

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Key Decisions in Project Management Much of the success of projects depends on key managerial decisions over a sequence of steps:

• Deciding which projects to implement. • Selecting the project manager. • Selecting the project team. • Planning and designing the project. • Managing and controlling project resources. • Deciding if and when a project should be terminated.

Deciding Which Projects to Implement. This involves determining the criteria that will be used to decide which projects to pursue. Typical factors include budget, availability of appropriate knowledge and skill personnel, and cost–benefit considerations. Of course, other factors may override these criteria, factors such as availability of funds, safety issues, govern- ment-mandated actions, and so on.

Selecting the Project Manager. The project manager is the central person in the project. The following section on project managers discusses this topic.

Selecting the Project Team. The team can greatly influence the ultimate success or fail- ure of a project. Important considerations include not only a person’s knowledge and skill base, but also how well the person works with others (particularly those who have already been chosen for the project), enthusiasm for the project, other projects the person is involved in, and how likely those other projects might be to interfere with work on this project.

Planning and Designing the Project. Project planning and design require decisions on project performance goals, a timetable for project completion, the scope of the project, what work needs to be done, how it will be done, if some portions will be outsourced, what resources will be needed, a budget, and when and how long resources will be needed.

Managing and Controlling Project Resources. This involves managing personnel, equipment, and the budget; establishing appropriate metrics for evaluating the project; moni- toring progress; and taking corrective action when needed. Also necessary are designing an

LO17.3 Name the six key decisions in project management.

The U2 360 Tour was named after the 360-degree staging and audience configuration it used for shows. To accommodate this, the stage set made use of a massive four-legged supporting rig that was nicknamed “The Claw.” The tour crew consisted of 137 touring crews supplemented by over 120 hired locally. Moving the massive set from venues took as long as 3½ days. First, sound and light equipment was packed into the fleet of trucks during the four hours following the concert; the remainder of the time was spent deconstructing the steel structures.

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information system and deciding what project documents should be generated, their contents and format, when and by whom they will be needed, and how often they should be updated.

Deciding If and When a Project Should Be Terminated. Sometimes it is better to ter- minate a project than to invest any more resources. Important considerations here are the like- lihood of success, termination costs, and whether resources could be better used elsewhere.

The Project Manager The project manager has many duties. In the planning stage, the project manager must prepare a scope statement that spells out the deliverables and goals, determine required skills and resources needed, develop a schedule and budget, and develop plans for managing the scope, the schedule, the budget, and quality and risk.

The project manager bears the ultimate responsibility for the success or failure of the proj- ect. He or she must be capable of working through others to accomplish the objectives of the project. The project manager is responsible for effectively managing each of the following:

1. The work, so that all of the necessary activities are accomplished in the desired sequence, and performance goals are met.

2. The human resources, so that those working on the project have direction and motivation. 3. Communications, so that everybody has the information needed to do the work. 4. Quality, so that performance objectives are realized. 5. Time, so that the project is completed on schedule. 6. Costs, so that the project is completed within budget. 7. Scope, so the project stays within the prescribed scope, and “scope creep” doesn’t occur

without commensurate changes to the schedule (if needed) and the budget.

Several of these responsibilities are often portrayed in what is known as a “project management triangle.”

To effectively manage a project, a project manager must employ a certain set of skills. The skills include the ability to motivate and direct team members; make trade-off decisions; expedite the work when necessary; put out fires; and monitor time, budget, and technical details. For projects that involve fairly well-defined work, those skills will often suffice. However, for projects that are less well defined, and thus have a higher degree of uncertainty, the project manager also must employ strong leadership skills. These include the ability to adapt to chang- ing circumstances that may involve changes to project goals, technical require- ments, and project team composition. As a leader, the project manager not only must be able to deal with these issues; he or she also must recognize the need for change, decide what changes are necessary, and work to accomplish them.

The job of project manager can be both difficult and rewarding. The man- ager must coordinate and motivate people who sometimes owe their allegiance to other managers in their functional areas. In addition, the people who work on a project frequently possess specialized knowledge and skills that the project man-

ager lacks. Nevertheless, the manager is expected to guide and evaluate their efforts. Project managers often must function in an environment that is beset with uncertainties. Even so, budgets and time constraints are usually imposed, which can create additional pressures on project personnel. Finally, the project manager may not have the authority needed to accom- plish all the objectives of the project. Instead, the manager sometimes must rely on persuasion and the cooperation of others to realize project goals.

Ethical issues often arise in connection with projects. Examples include the temptation to understate costs or to withhold information in order to get a project approved, pressure to alter or make misleading statements on status reports, falsifying records, compromising work- ers’ safety, and approving substandard work. It is the responsibility of managers at all levels to maintain and enforce ethical standards. Moreover, employees often take their cue from

The Project Management Triangle

Performance Objectives

Schedule

Quality

C os

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managers’ behavior, so it is doubly important for managers to model ethical behavior. The Project Management Institute (PMI) has a website (www.pmi.org) that includes a code of eth- ics for project managers, in addition to other useful information about project management.

The position of project manager has high visibility. The rewards of the job of project man- ager come from the creative challenges of the job, the benefits of being associated with a successful project (including promotion and monetary compensation), and the personal satis- faction of seeing it through to its conclusion.

Behavioral Issues Project metrics related to cost, schedule, and quality are important indicators of how well a project is doing. Behavioral metrics are also important, and should not be overlooked. People make the project happen. However, behavioral issues can interfere with the success of a proj- ect if they are not carefully managed. Decentralized decision making, the stress of achiev- ing project milestones on time and within budget, and surprises can contribute to behavioral problems.

Because project work is often based on team efforts, workers are usually evaluated on the basis of the team’s overall contribution relative to project metrics, and not on an individual basis. The team must be able to function as a unit, so interpersonal skills are very important, as are coping skills. And conflict resolution can be an important part of a project manager’s job. Some problems can be avoided by the project manager by carefully selecting team mem- bers when possible; leadership; motivation; maintaining an environment of integrity, trust, and professionalism; and being supportive of team efforts.

Project Champions Some companies make use of project champions. These are people, usually within the com- pany, who promote and support the project. They can be instrumental in facilitating the work of the project manager by “talking up” the project to other managers who might be asked to share resources with the project team as well as employees who might be asked to work on parts of the project. The work that a project champion does can be critical to the success of a project, so it is important for team members to encourage and communicate with the project champion.

Certification The Project Management Institute (PMI) administers a globally recognized, examination- based professional certification program. The certification program maintains ISO 9001 cer- tification in Quality Management Systems. There are two levels of certification: Associate and Project Management Professional. Candidates for the Associate and Professional levels must meet specific education and experience requirements and agree to adhere to a code of professional conduct. The Project Management Professional must demonstrate an ongoing professional commitment to the field of project management by satisfying PMI’s Continuing Certification Requirements Program.1

The Pros and Cons of Working on Projects People are selected to work on special projects because the knowledge or abilities they pos- sess are needed. In some instances, however, their supervisors may be reluctant to allow them to interrupt their regular jobs, even on a part-time basis, because it may require training a new person to do a job that will be temporary. Moreover, managers don’t want to lose the out- put of good workers. The workers themselves are not always eager to participate in projects because it may mean working for two bosses who impose differing demands, it may disrupt friendships and daily routines, and it presents the risk of being replaced on the current job. Furthermore, there may be fear of being associated with an unsuccessful project because of the adverse effect it might have on career advancement. In too many instances, when a major project is phased out and the project team disbanded, team members tend to drift away from

Project champions A person who promotes and supports a project.

1www.pmi.org.

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the organization for lack of a new project and the difficulty of returning to former jobs. This tendency is more pronounced after lengthy projects and is less likely to occur when a team member works on a part-time basis.

In spite of the potential risks, people are attracted by the potential rewards of being involved in a project. One is the dynamic environment that surrounds a project, often a marked contrast to the staid environment of a routine in which some may feel trapped. Some individuals seem to thrive in more dynamic environments; they welcome the challenge of working under pres- sure and solving new problems. Then, too, projects may present opportunities to meet new people and to increase future job opportunities, especially if the project is successful. In addi- tion, association with a project can be a source of status among fellow workers. Finally, work- ing on projects frequently inspires a team spirit, increasing morale and motivation to achieve successful completion of project goals.

Bob Weinstein Not many people can eloquently describe the changing role of project managers as well as Jonathan Gispan, who teaches the skill to managers at the Lockheed Martin Corporation division in King of Prussia, PA. Gispan spent 38 years of his career working at GE Aerospace as a project manager.

Project managers have never been more critical, according to this veteran techie. The function’s core responsibilities haven’t changed, but the players and playing field are very different than they were five years ago.

Gispan views the project manager as the focal point of a com- plex relationship matrix that includes customers, workers, vendors and bosses. “Project managers make things happen,” he says. “Not only do they manage a project from start to finish, they also manage the people who make it happen.”

The job requires a jack-of-all-trades who can both understand a problem and solve it. “Project managers must successfully man- age the total life cycle of a project,” says Gispan. “The job requires a super-organized person who knows how to get a project com- pleted quickly and inexpensively and boasts the advanced com- munication skills necessary to work closely with vendors, project teams, and senior management.”

Project managers have always had to deal with changing rela- tionships. The big change, according to Gispan, is the speed of change, which has made the project manager’s job more difficult. “The changes taking place now are faster and more dramatic than in the past,” he says. “Customers are less inclined to give you money for development work, for example. They’d rather save money by using off-the-shelf capabilities. Budgets that used to be reasonably substantial and healthy are now tight.”

Gispan adds that corporate mergers and consolidations have complicated the picture. Project managers must deal with com- plex, often labyrinthine decision-making structures. Getting quick decisions requires work and persistence.

Further complicating the situation is a high worker attrition rate. “A decade ago, the attrition rate was about 3 percent; today it has jumped to almost 10 percent,” Gispan explains. “It means project managers have to constantly put together new teams.”

READING PROJECT MANAGERS HAVE NEVER BEEN MORE CRITICAL

Through it all, the project manager must be clear-headed and keep a tight rein on projects. It sounds intimidating, yet Gispan sees it as a positive. “The current marketplace keeps you on your toes,” he says. “Even though everything is changing at what seems like an overwhelming pace, it is best to view change as a motivator that allows you to keep pace with technology and get better at your job. The idea is not merely to cope with change but to thrive in it. It is more of an attitude than anything else.”

What does it take to be a project manager? “You need a good technical base,” says Karen Nichols, project manager at EWP Engi- neering, Inc., a consulting engineering company in Salt Lake City, UT. “That translates to at least five to seven years in the trenches.”

That’s for starters. “But you also need to know how the busi- ness side of the equation works,” says Nichols. “This is tough for some technical people because it requires the ability to under- stand how the two different sides of the business mesh. Project managers must also be familiar with accounting methods as well as sales and marketing strategies. In short, they must know how to manage a project so it makes a profit.”

If you think you have what it takes, ask to work with a project manager. “It won’t take you long to find out whether you have an aptitude and natural feel for the work,” says Nichols. “Not everyone is happy—or capable of—juggling many balls in the air at once.”

Once you get your feet wet, you can move up quickly, adds Gispan. “After you’ve proven to management that you’re orga- nized and can manage several tasks, it won’t be long before you are managing everything associated with a program. Get good at it and you’ll move up the ranks from project manager to general manager where you are running several company businesses.”

And, don’t be confused by job titles. Each company has its own unique title for the project manager role. Whatever the title, a proj- ect manager is easy to spot. “It’s the person who negotiates with all the key players and makes things happen,” says Gispan. “Tech- nology companies would perish without them.”

Source: Bob Weinstein, “Project Managers Have Never Been More Critical,” Roch- ester Democrat and Chronicle, February 18, 1999. Copyright © 1999 Rochester Democrat and Chronicle. Reprinted by permission.

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17.4 WORK BREAKDOWN STRUCTURE

Because large projects usually involve a very large number of activities, planners need some way to determine exactly what will need to be done so that they can realistically estimate how long it will take to complete the various elements of the project and how much it will cost. They often accomplish this by developing a work breakdown structure (WBS), which is a hierarchical listing of what must be done during the project. This methodology establishes a logical frame- work for identifying the required activities for the project (see Figure 17.2). The first step in developing the work breakdown structure is to identify the major elements of the project. These are the Level 2 boxes in Figure 17.2. The next step is to identify the major supporting activi- ties for each of the major elements—the Level 3 boxes. Then, each major supporting activity is broken down into a list of the activities that will be needed to accomplish it—the Level 4 boxes. (For purposes of illustration, only a portion of the Level 4 boxes are shown.) Usually there are many activities in the Level 4 lists. Large projects involve additional levels, but Figure 17.2 gives you some idea of the concept of the work breakdown structure.

Developing a good work breakdown structure can require substantial time and effort due to the uncertainties associated with a project and/or the size of the project. Typically the por- tion of time spent on developing the work breakdown structure greatly exceeds the time spent on actually developing a project schedule. The importance of a work breakdown structure is underscored by the fact that the activity list that results serves as the focal point for planning and doing the project. Moreover, the work breakdown structure is the basis for developing time and cost estimates.

17.5 PLANNING AND SCHEDULING WITH GANTT CHARTS

The Gantt chart (see Chapter 16) is a popular visual tool for planning and scheduling simple projects. It enables a manager to initially schedule project activities and then to monitor prog- ress over time by comparing planned progress to actual progress. Figure 17.3 illustrates a Gantt chart for a bank’s plan to establish a new direct marketing department. To prepare the chart, the vice president in charge of the project had to first identify the major activities that would be required. Next, time estimates for each activity were made, and the sequence of activities was determined. Once completed, the chart indicated which activities were to occur, their planned duration, and when they were to occur. Then, as the project progressed, the manager was able to see which activities were on schedule and which were behind schedule.

LO17.4 Explain the nature and importance of a work breakdown structure in project management.

Work breakdown structure (WBS) A hierarchical listing of what must be done during a project.

FIGURE 17.2 Schematic of a work breakdown structure

Level 1

Level 2

Level 3

Level 4

Project

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However, Gantt charts fail to reveal certain relationships among activities that can be cru- cial to effective project management. For instance, if one of the early activities in a project suffers a delay, it would be important for the manager to be able to easily determine which later activities would result in a delay. Conversely, some activities may safely be delayed with- out affecting the overall project schedule. The Gantt chart does not directly reveal this. On more complex projects, it is often used in conjunction with a network diagram, defined in the following section, for scheduling purposes.

17.6 PERT AND CPM

PERT (program evaluation and review technique) and CPM (critical path method) are two of the most widely used techniques for planning and coordinating large-scale projects. By using PERT or CPM, managers are able to obtain:

1. A graphical display of project activities 2. An estimate of how long the project will take 3. An indication of which activities are the most critical to timely project completion 4. An indication of how long any activity can be delayed without delaying the project

Although PERT and CPM were developed independently, they have a great deal in com- mon. Moreover, many of the initial differences between them have disappeared as users bor- rowed certain features from one technique for use with the other. For practical purposes, the two techniques now are the same; the comments and procedures described will apply to CPM analysis as well as to PERT analysis of projects.

The Network Diagram One of the main features of PERT and related techniques is their use of a network (or pre- cedence) diagram to depict major project activities and their sequential relationships. There are two slightly different conventions for constructing these network diagrams. Under one convention, the arrows designate activities; under the other convention, the nodes designate activities. These conventions are referred to as activity-on-arrow (AOA) and activity-on- node (AON). Activities consume resources and/or time. The nodes in the AOA approach

LO17.5 Give a general description of PERT/CPM techniques.

Activity-on-node(AON) Network diagram convention in which nodes designate activities.

PERT Program evaluation and review technique, for planning and coordinating large projects.

CPM Critical path method, for planning and coordinating large projects.

Network (precedence) diagram Diagram of project activities that shows sequen- tial relationships by use of arrows and nodes.

Activity-on-arrow (AOA) Network diagram convention in which arrows designate activities.

FIGURE 17.3 Gantt chart for bank example

Start 2 4 6 8 10 12 14 16 18 20

Locate new facilities

Activity Weeks after start

Interview prospective sta�

Hire and train sta�

Select and order furniture

Remodel and install phones

Furniture received and set up

Move in/ startup

Start 2 4 6 8 10 12 14 16 18 20

Weeks after start

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represent the activities’ starting and finishing points, which are called events. Events are points in time. Unlike activities, they consume neither resources nor time. The nodes in an AON diagram represent activities.

Both conventions are illustrated in Figure 17.4, using the bank example that was depicted in the Gantt chart in Figure 17.3. Compare the two. In the AOA diagram, the arrows represent activities and they show the sequence in which certain activities must be performed (e.g., Inter- view precedes Hire and train); in the AON diagram, the arrows show only the sequence in which certain activities must be performed while the nodes represent the activities. Activities in AOA networks can be referred to in either of two ways. One is by their endpoints (e.g., activity 2-4) and the other is by a letter assigned to an arrow (e.g., activity c). Both methods are illustrated in this chapter. Activities in AON networks are referred to by a letter (or number) assigned to a node. Although these two approaches are slightly different, they both show sequential relationships—something Gantt charts do not. Note that the AON diagram has a starting node, S, which is actually not an activity but is added in order to have a single starting node.

Despite these differences, the two conventions are remarkably similar, so you should not encounter much difficulty in understanding either one. In fact, there are convincing argu- ments for having some familiarity with both approaches. Perhaps the most compelling is that both approaches are widely used. Moreover, a contractor doing work for the organization may be using the other approach, so employees of the organization who deal with the contractor on project matters would benefit from knowledge of the other approach. However, any particular organization would typically use only one approach, and employees would have to work with that approach.

Of particular interest to managers are the paths in a network diagram. A path is a sequence of activities that leads from the starting node to the ending node. For example, in the AOA diagram, the sequence 1-2-4-5-6 is a path. In the AON diagram, S-1-2-6-7 is a path. Note that in both diagrams there are three paths. One reason for the importance of paths is that they reveal sequential relationships. The importance of sequential relationships cannot be over- stated: If one activity in a sequence is delayed (i.e., late) or done incorrectly, the start of all following activities on that path will be delayed.

Another important aspect of paths is the length of a path: How long will a particular sequence of activities take to complete? The length (of time) of any path can be determined by summing the expected times of the activities on that path. The path with the longest time is of particular interest because it governs project completion time. In other words, expected project duration equals the expected time of the longest path. Moreover, if there are any delays along the longest path, there will be corresponding delays in project completion time. Attempts to shorten project completion must focus on the longest sequence of activities. Because of its influence on project completion time, the longest path is referred to as the critical path, and its activities are referred to as critical activities.

Activities Project steps that consume resources and/or time.

Events The starting and finishing of activities, desig- nated by nodes in the AOA convention.

Path A sequence of activities that leads from the starting node to the finishing node.

Critical path The longest path; determines expected project duration.

Critical activities Activities on the critical path.

FIGURE 17.4 A simple project network diagram

Activity-on-arrow (AOA) diagram

Lo ca

fac ilit

ies

Interview Hir

e a nd

tra in

Remodel

Ord er

furn itur

e Fu rn

itu re

se tu

Move in S

Move in

Hire and train

Locate facilities

Order furniture

Remodel

Interview

Furniture setup

Activity-on-node (AON) diagram

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Paths that are shorter than the critical path can experience some delays and still not affect the overall project completion time as long as the ultimate path time does not exceed the length of the critical path. The allowable slippage for any path is called slack, and it reflects the difference between the length of a given path and the length of the critical path. The criti- cal path, then, has zero slack time.

Network Conventions Developing and interpreting network diagrams requires some familiarity with networking conventions. Table 17.2 illustrates some of the most basic and most common features of net- work diagrams. This will provide sufficient background for understanding the basic concepts associated with precedence diagrams and allow you to solve typical problems.

A special feature that is sometimes used in AOA networks to clarify relationships is a dummy activity. In order to recognize the need to use a dummy activity using the AOA approach when presented with a list of activities and the activities each precedes, examine the “Immediate Predecessor” list. Look for instances where multiple activities are listed, such as a, b in the following list. If a or b appears separately in the list (as b does in the fol- lowing table), a dummy will be needed to clarify the relationship (see the last diagram in Table 17.2).

Activity Immediate

Predecessor

a —

b —

c a, b

d b

Here are two more AOA conventions:

For reference purposes, nodes are numbered typically from left to right, with lower num- bers assigned to preceding nodes and higher numbers to following nodes:

Slack Allowable slippage for a path; the difference between the length of a path and the length of the critical path.

LO17.6 Construct simple network diagrams.

b d

5 1

Starting and ending arrows are sometimes used during development of a network for increased clarity:

End

b d

5 1

Start

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17.7 DETERMINISTIC TIME ESTIMATES

The main determinant of the way PERT and CPM networks are analyzed and interpreted is whether activity time estimates are probabilistic or deterministic. If time estimates can be made with a high degree of confidence that actual times are fairly certain, we say the estimates are deterministic. If actual times are subject to variation, we say the estimates are probabilistic. Probabilistic time estimates must include an indication of the extent of probable variation.

This section describes analysis of networks with deterministic time estimates. A later sec- tion deals with probabilistic times.

One of the best ways to gain an understanding of the nature of network analysis is to con- sider a simple example.

LO17.7 Analyze networks with deterministic times.

Deterministic Time estimates that are fairly certain.

Probabilistic Estimates of times that allow for variation.

TABLE 17.2 Network conventions

a b c

a c

Dummy activity

b c

AOA AONInterpretation

Activities must be completed in sequence: first a, then b, and then c.

Both a and b must be completed before c can start.

Activity a must be completed before b or c can start.

Both a and b must be completed before c or d can start.

Use a dummy activity to clarify relationships:

1. To separate two activities that have the same starting and ending nodes.

2. When activities share some, but not all, preceding activities. Here, activity c is preceded by activities a and b, while activity d is only preceded by activity b.

(No dummy needed)

ba c

Identifying the Critical Path, Computing Project Duration and Slack Times for Deterministic Times

Given the additional information on the bank network of Figure 17.4 shown in Figure 17.5, determine the following.

a. The length of each path b. The critical path c. The expected length of the project d. The amount of slack time for each path

E X A M P L E 1

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17.8 A COMPUTING ALGORITHM

Many real-life project networks are much larger than the simple network illustrated in the pre- ceding example; they often contain hundreds or even thousands of activities. Because the nec- essary computations can become exceedingly complex and time-consuming, large networks are generally analyzed by computer programs instead of manually. Planners use an algorithm to develop four pieces of information about the network activities:

ES, the earliest time activity can start, assuming all preceding activities start as early as possible. EF, the earliest time the activity can finish. LS, the latest time the activity can start and not delay the project. LF, the latest time the activity can finish and not delay the project.

Once these values have been determined, they can be used to find:

1. Expected project duration 2. Slack time 3. The critical path

Activity-on-Arrow The three examples that follow illustrate how to compute those values using the precedence diagram of Example 1.

screenCam tutorial

S O L U T I O N

FIGURE 17.5 AOA diagram

8 w ee

Lo cat

5 6

6 we eks

Orde r

furnit ure

11 weeksRemodel

3 w eeks

Setup

1 week

Move in

9 w ee

Hir e a

nd tra

in 4 weeksInterview

screenCam tutorial

a. As shown in the following table, the path lengths are 18 weeks, 20 weeks, and 14 weeks. b. Path 1–2–5–6 is the longest path (20 weeks), so it is the critical path. c. The expected length of the project is equal to the length of the critical path (i.e., 20

weeks). d. We find the slack for each path by subtracting its length from the length of the criti-

cal path, as shown in the last column of the table. (Note: It is sometimes desirable to know the slack time associated with activities. The next section describes a method for obtaining those slack times.)

Path Length (weeks) Slack

1–2–4–5–6 8 + 6 + 3 + 1 = 18 20 − 18 = 2

1–2–5–6 8 + 11 + 1 = 20* 20 − 20 = 0

1–3–5–6 4 + 9 + 1 = 14 20 − 14 = 6 *Critical path length.

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S O L U T I O N

Computing Earliest Starting and Finishing Times Compute the earliest starting time and earliest finishing time for each activity in the dia- gram shown in Figure 17.5.

E X A M P L E 2

ES EFt

Begin by placing brackets at the two ends of each starting activity:

We want to determine and place in the brackets for each activity the earliest starting time, ES, and the earliest finishing time, EF, for every activity, and put them in brackets, as follows:

This permits calculation of the EF times for these activities: EF2-4 = 8 + 6 = 14; EF2-5 = 8 + 11 = 19; and EF3-5 = 4 + 9 = 13.

The EF time for an activity becomes the ES time for the next activity to follow it in the diagram. Hence, because activity 1-2 has an EF time of 8, both activities 2-4 and 2-5 have ES times of 8. Similarly, activity 3-5 has an ES time of 4.

Do this for all activities, beginning at the left side of the precedence diagram and moving to the right side.

Once ES has been determined for each activity, EF can be found by adding the activity time, t, to ES: ES + t = EF.

Use an ES of 0 for all starting activities. Thus, activities 1-2 and 1-3 are assigned ES values of 0. This permits computation of the EF for each of these activities:

EF1-2 = 0 + 8 = 8 and EF1-3 = 0 + 4 = 4

5 6

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Computation of earliest starting and finishing times is aided by two simple rules:

1. The earliest finish time for any activity is equal to its earliest start time plus its expected duration, t:

EF = ES + t (17−1)

2. ES for activities at nodes with one entering arrow is equal to EF of the entering arrow. ES for activities leaving nodes with multiple entering arrows is equal to the largest EF of the entering arrow.

The ES for activity 4-5 is the EF time of activity 2-4, which is 14. Using this value, we find the EF for activity 4-5 is 17; EF4-5 = 14 + 3 = 17.

Then the EF for the last activity, 5-6, is 20; EF5-6 = 19 + 1 = 20. Note that the latest EF is the project duration. Thus, the expected length of the project is 20 weeks.

In order to determine the ES for activity 5-6, we must realize that activity 5-6 cannot start until every activity that precedes it is finished. Therefore, the largest of the EF times for the three activities that precede activity 5-6 determines ES5-6. Hence, the ES for activity 5-6 is 19.

5 6

68 14

5 6

68 14

3 14

5 6

68 14

3 14

19 20 1

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Computation of the latest starting and finishing times is aided by the use of two rules: 1. The latest starting time for each activity is equal to its latest finishing time minus its

expected duration: EF = ES − t (17–2)

2. For nodes with one leaving arrow, LF for arrows entering that node equals the LS of the leaving arrow. For nodes with multiple leaving arrows, LF for arrows entering that node equals the smallest LS of leaving arrows.

Finding ES and EF times involves a forward pass through the network; finding LS and LF times involves a backward pass through the network. Hence, we must begin with the EF of the last activity and use that time as the LF for the last activity. Then we obtain the LS for the last activity by subtracting its expected duration from its LF.

(Note: For an AON diagram, if a starting node or ending node does not have a time associated with it, ignore that node.)

Forward Pass For each path, start at the left side of the diagram and work toward the right side. For each beginning activity: ES = 0. For each activity: ES + Activity time = EF. For the following activity: ES = EF of preceding activity.

Note: If an activity has multiple immediate preceding activities, set its ES equal to the largest EF of its immediate predecessors.

Backward Pass For each path, start at the right side of the diagram and work toward the left side.

Use the largest EF as the LF for all ending activities.

For each activity: LS = LF – Activity time. For the preceding activity: LF = LS of following activity.

Note: If an activity has multiple immediately following activi- ties, set the activity’s LF equal to the smallest LS of the following activities.

R U L E S F O R T H E C O M P U T I N G A LG O R I T H M

Computing the Latest Finishing and Starting Times Compute the latest finishing and starting times for the precedence diagram developed in Example 2.

E X A M P L E 3

S O L U T I O N LS ES

LF EF

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We must add the LS and LF times to the brackets on the diagram.

Begin by setting the LF time of the last activity equal to the EF of that activity. Thus, LF5-6 = EF5-6 = 20 weeks Obtain the LS time for activity 5-6 by subtracting the activity time, t, from the LF time: LS5-6 = LF5-6 − t = 20 − 1 = 19 Mark these values on the diagram:

5 6

68 14

3 14

19 19

20 20

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Activity-on-Node The computing algorithm is performed in essentially the same manner in the AON approach. Figure 17.6 shows the node diagram, and Figures 17.7A, B, and C illustrate the computing algorithm.

5 6

68 14

8 8

19 19

10 4

19 13

3 1614

1917

19 19

20 20

The LS time of 19 for activity 5-6 now becomes the LF time for each of the activities that precedes activity 5-6. This permits determination of the LS times for each of those activities: Subtract the activity time from the LF to obtain the LS time for the activity. The LS time for activity 3-5 is 19 − 9 = 10.

The LF for activity 1-2 is the smaller of the two LS times of the activities that 1-2 precedes. Hence, the LF time for activity 1-2 is 8. The reason you use the smaller time is that activity 1-2 must finish at a time that permits all following activities to start no later than their LS times.

Once you have determined the LF time of activity 1-2, find its LS time by subtracting the activity time of 8 from the LF time of 8. Hence, the LS time is 0.

Next, the LS for activity 4-5, which is 16, becomes the LF for activity 2-4, and the LS for activity 3-5, which is 10, becomes the LF for activity 1-3. Using these values, you find the LS for each of these activities by subtracting the activity time from the LF time.

5 6

6 0

10 4

6 10 8

16 14

8 8

19 19

10 4

19 13

3 1614

1917

19 19

20 20

5 6

0 0

8 8

6 0

10 4

6 10 8

16 14

8 8

19 19

10 4

19 13

3 1614

1917

19 19

20 20

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FIGURE 17.7A AON diagram with brackets added

FIGURE 17.7B Forward pass

119

94 13

118 19

314 17

8 14

80 8

tES EF

40 4

FIGURE 17.6 AON diagram

3 Move in

Hire and train

Locate facilities

Order furniture

Remodel

Interview

Estimated activity completion time

in weeks

Furniture setup

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Computing Slack Times The slack time can be computed in either of two ways:

Slack = LS − ES or LF − EF (17−3) The critical path using this computing algorithm is denoted by activities with zero slack

time. Thus, the table in Example 4 indicates that activities 1-2, 2-5, and 5-6 are all critical activities, which agrees with the results of the intuitive approach demonstrated in Example 1.

Knowledge of slack times provides managers with information for planning the allocation of scarce resources and for directing control efforts toward those activities that might be most susceptible to delaying the project. In this regard, it is important to recognize that the activ- ity slack times are based on the assumption that all of the activities on the same path will be started as early as possible and not exceed their expected times. Furthermore, if two activities are both on the same path (e.g., activities 2-4 and 4-5 in the preceding example) and have the same slack (e.g., two weeks), this will be the total slack available to both. In essence, the activities have shared slack. Hence, if the first activity uses all the slack, there will be zero slack for all following activities on that same path.

FIGURE 17.7C Backward pass

1 19 19

20 20

9 10 4 13

11 8 8

19 19

3 16 14 17

6 10 8 14

8 0 0

8 8

t LS ES EF

4 6 0 4

As noted earlier, this algorithm lends itself to computerization. A computer printout for this problem would appear something like the one shown in Table 17.3.

S O L U T I O N

Computing Slack Times Compute slack times for the preceding example.

E X A M P L E 4

Either the starting times or the finishing times can be used. Suppose we choose the starting times. Using ES times computed in Example 2 and LS times computed in Example 3, slack times are:

Activity LS ES (LS − ES)

Slack

1-2 0 0 0 1-3 6 0 6 2-4 10 8 2 2-5 8 8 0 3-5 10 4 6 4-5 16 14 2 5-6 19 19 0

Activities that have a slack of zero are on the critical path. Hence, the critical path is 1−2−5−6.

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17.9 PROBABILISTIC TIME ESTIMATES

The preceding discussion assumed that activity times were known and not subject to varia- tion. While that condition exists in some situations, there are many others where it does not. Consequently, those situations require a probabilistic approach.

The probabilistic approach involves three time estimates for each activity instead of one:

1. Optimistic time: The length of time required under optimum conditions; represented by to 2. Pessimistic time: The length of time required under the worst conditions; represented by tp 3. Most likely time: The most probable amount of time required; represented by tm Managers or others with knowledge about the project can make these time estimates.

The beta distribution is generally used to describe the inherent variability in time esti- mates (see Figure 17.8). Although there is no real theoretical justification for using the beta distribution, it has certain features that make it attractive in practice: The distribution can be symmetrical or skewed to either the right or the left according to the nature of a particular activity; the mean and variance of the distribution can be readily obtained from the three time estimates listed above; and the distribution is unimodal with a high concentration of probabil- ity surrounding the most likely time estimate.

Of special interest in network analysis are the average or expected time for each activity, te, and the variance of each activity time, σ 2 . The expected time of an activity, te, is a weighted average of the three time estimates:

t e = t 0 + 4 t m + t p ___________

6 (17–4)

LO17.8 Analyze networks with probabilistic times.

Optimistic time The length of time required under optimal conditions.

Pessimistic time The length of time required under the worst conditions.

Most likely time The most probable length of time that will be required.

Beta distribution Used to describe the inherent variabil- ity in activity time estimates.

SCHEDULE

EARLY LATE

Activity Time ES EF LS LF Slack

1-2 8.00 0.00 8.00 0.00 8.00 0.00

1-3 4.00 0.00 4.00 6.00 10.00 6.00

2-4 6.00 8.00 14.00 10.00 16.00 2.00

2-5 11.00 8.00 19.00 8.00 19.00 0.00

3-5 9.00 4.00 13.00 10.00 19.00 6.00

4-5 3.00 14.00 17.00 16.00 19.00 2.00

5-6 1.00 19.00 20.00 19.00 20.00 0.00

THE CRITICAL PATH SEQUENCE IS:

SNODE FNODE TIME

1 2 8.00

2 5 11.00

5 6 1.00

20.00

TABLE 17.3 Computer printout

FIGURE 17.8 A beta distribution is used to describe probabilistic time estimates

Activity start

Optimistic time

Most likely time (mode)

Pessimistic time

te tptmto

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The expected duration of a path (i.e., the path mean) is equal to the sum of the expected times of the activities on that path:

Path mean = ∑ of expected times of activities on the path (17–5)

The standard deviation of each activity’s time is estimated as one-sixth of the difference between the pessimistic and optimistic time estimates. (Analogously, nearly all of the area under a normal distribution lies within three standard deviations of the mean, which is a range of six standard deviations.) We find the variance by squaring the standard deviation. Thus,

σ 2 = [ ( t p − t 0 ) ________

6 ]

or ( t p − t 0 ) 2 ________

36 (17–6)

The size of the variance reflects the degree of uncertainty associated with an activity’s time: The larger the variance, the greater the uncertainty.

It is also desirable to compute the standard deviation of the expected time for each path. We can do this by summing the variances of the activities on a path and then taking the square root of that number; that is,

σ path = √ _____________________________

∑ ( Variances of activities on path ) (17–7) Example 5 illustrates these computations.

Computing Expected Activity Times and Variances, and the Expected Duration and Standard Deviation of Each Path

The network diagram for a project is shown in the accompanying figure, with three time estimates for each activity. Activity times are in weeks. Do the following:

a. Compute the expected time for each activity and the expected duration for each path. b. Identify the critical path. c. Compute the variance of each activity and the variance and standard deviation of each

path.

E X A M P L E 5

3-4-5 3-5-7 5-7-9

AON diagram

d e f

1-3-4 2-4-6 2-3-5

a b c

2-3-6 4-6-8 3-4-6

g h i

FinishStart

3-4-5 d

3-5-7 e

5-7-9 f

2-4-6 b

4-6-8 h

1-3 -4

2-3-6 g

2-3-5 c

3-4 -6

Most likely time

Optimistic time

Pessimistic time

AOA diagram

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Knowledge of the expected path times and their standard deviations enables a manager to compute probabilistic estimates of the project completion time, such as these:

The probability that the project will be completed by a specified time. The probability that the project will take longer than its scheduled completion time.

These estimates can be derived from the probability that various paths will be completed by the specified time. This involves the use of the normal distribution. Although activity times are represented by a beta distribution, the path distribution is represented by a normal distribution. The central limit theorem tells us that the summing of activity times (random variables) results in a normal distribution. This is illustrated in Figure 17.9. The rationale for using a normal distribution is that sums of random variables (activity times or means) will tend to be normally distributed, regardless of the distributions of the variables. The normal tendency improves as the number of random variables increases. However, even when the number of items being summed is fairly small, the normal approximation provides a reason- able approximation to the actual distribution.

FIGURE 17.9 Activity distributions and the path distribution

Normal

Path

Beta

mean meanmeanmean

Activity

=++ Beta

Activity

Beta

Activity

S O L U T I O N

b. The path that has the longest expected duration is the critical path. Because path d–e–f has the largest path total, it is the critical path.

a. TIMES t

e =

t 0 + 4 t m + t p ___________ 6

Path Activity to tm tp Path Total

a–b–c a 1 3 4 2.83 b 2 4 6 4.00 10.00 c 2 3 5 3.17

d–e–f d 3 4 5 4.00 e 3 5 7 5.00 16.00 f 5 7 9 7.00

g–h–i g 2 3 6 3.33 h 4 6 8 6.00 13.50 i 3 4 6 4.17

c. TIMES σ 2 act =

( t p − t 0 ) 2 ________

36 σ 2 path σ path

Path Activity to tm tp

a–b–c a 1 3 4 (4 − 1)2/36 = 9/36 b 2 4 6 (6 − 2)2/36 = 16/36 34/36 5 0.944 0.97 c 2 3 5 (5 − 2)2/36 = 9/36

d–e–f d 3 4 5 (5 − 3)2/36 = 4/36 e 3 5 7 (7 − 3)2/36 = 16/36 36/36 5 1.00 1.00 f 5 7 9 (9 − 5)2/36 = 16/36

g–h–i g 2 3 6 (6 − 2)2/36 = 16/36 h 4 6 8 (8 − 4)2/36 = 16/36 41/36 5 1.139 1.07 i 3 4 6 (6 − 3)2/36 = 9/36

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17.10 DETERMINING PATH PROBABILITIES

The probability that a given path will be completed in a specified length of time can be deter- mined using the following formula:

z = Specified time − Path mean

_______________________ Path standard deviation

(17–8)

The resulting value of z indicates how many standard deviations of the path distribution the specified time is beyond the expected path duration. The more positive the value, the better. (A negative value of z indicates that the specified time is earlier than the expected path duration.) Once the value of z has been determined, it can be used to obtain the probability that the path will be completed by the specified time from Appendix B, Table B. Note that the probability is equal to the area under the normal curve to the left of z, as illustrated in Figure 17.10.

If the value of z is +3.00 or more, the path probability is close to 100 percent (for z = +3.00, it is .9987). Hence, it is very likely the activities that make up the path will be completed by the specified time. For that reason, a useful rule of thumb is to treat the path probability as being equal to 100 percent if the value of z is +3.00 or more.

Rule of thumb: If the value of z is +3.00 or more, treat the probability of path completion by the specified time as 100 percent.

A project is not completed until all of its activities have been completed, not only those on the critical path. It sometimes happens that another path ends up taking more time to complete than the critical path, in which case the project runs longer than expected. Hence, it can be risky to focus exclusively on the critical path. Instead, one must consider the possibility that at least one other path will delay timely project completion. This requires determining the prob- ability that all paths will finish by a specified time. To do that, find the probability that each path will finish by the specified time, and then multiply those probabilities. The result is the probability that the project will be completed by the specified time.

It is important to note the assumption of independence. It is assumed that path duration times are independent of each other. In essence, this requires two things: Activity times are independent of each other, and each activity is only on one path. For activity times to be independent, the time for one must not be a function of the time of another; if two activities were always early or late together, they would not be considered independent. The assumption of independent paths is usu- ally considered to be met if only afew activities in a large project are on multiple paths. Even then, common sense should govern the decision of whether the independence assumption is justified.

Independence Assumption that path duration times are independent of each other; requiring that activity times be independent, and that each activity is on only one path.

FIGURE 17.10 The path probability is the area under a normal curve to the left of z

Probability of completing

the path by the specified time

Expected path duration

Specified time

Computing the Probability that a Project Will and Will Not Be Completed by a Specified Time

Using the information from Example 5, answer the following questions:

a. Can the paths be considered independent? Why? b. What is the probability that the project can be completed within 17 weeks of its start? c. What is the probability that the project will be completed within 15 weeks of its start? d. What is the probability that the project will not be completed within 15 weeks of its start?

E X A M P L E 6

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S O L U T I O N a. Yes, the paths can be considered independent, since no activity is on more than one path and you have no information suggesting that any activity times are interrelated.

b. To answer questions of this nature, you must take into account the degree to which the path distributions “overlap” the specified completion time. This overlap concept is illustrated in the accompanying figure, which shows the three path distributions, each centered on that path’s expected duration, and the specified completion time of 17 weeks. The shaded portion of each distribution corresponds to the probability that the part will be completed within the specified time. Observe that paths a–b–c and g–h–i are well enough to the left of the specified time, so that it is highly likely that both will be finished by week 17, but the critical path overlaps the specified completion time. In such cases, you need consider only the distribution of path d–e–f in assessing the probability of completion by week 17.

To find the probability for a path you must first compute the value of z using For- mula 17–8 for the path. For example, for path d–e–f, we have:

z = 17 − 16

_______ 1.00

= + 1.00

Turning to Appendix B, Table B, with z = + 1.00, you will find that the area under the curve to the left of z is .8413. The computations are summarized in the following table. Note: If the value of z exceeds + 3.00, treat the probability of completion as being equal to 1.000.

17 weeks

Path

a–b–c

d–e–f

g–h–i

1.00

10.0

1.00

13.5

16.0

Weeks

Path z =

17 − Expected path duration __________________________

Path standard deviation

Probability of Completion in 17 Weeks

a–b–c 17 − 10

______ 0.97

= +7.22 1.00

d–e–f 17 − 16

______ 1.00

= +1.00 .8413

g–h–i 17 − 13.5

________ 1.07

= +3.27 1.00

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P ( Finish by week 17 ) = P(Path a–b–c finish) × P ( Path d–e–f finish ) × P ( Path g–h–i finish)

1.00

.8413

1.00 = .8413

c. For a specified time of 15 weeks, the z values are

Path z =

15 − Expected path duration __________________________

Path standard deviation

Probability of Completion in 15 Weeks

a–b–c 15 − 10.00

__________ .97

= +5.15 1.00

d–e–f 15 − 16.00

__________ 1.00

= − 1.00 .1587

g–h–i 15 − 13.50

__________ 1.07

= +1.40 .9192

Paths d–e–f and g–h–i have z values that are less than +3.00. From Appendix B, Table B, the area to the left of z = –1.00 is .1587, and the area

to the left of z = +1.40 is .9192. The path distributions are illustrated in the figure. The joint probability of all finishing before week 15 is the product of their probabili- ties: 1.00(.1587)(.9192) = .1459.

d. The probability of not finishing before week 15 is the complement of the probability obtained in part c: 1 − .1459 = .8541.

15 weeks

Path

a–b–c

d–e–f

g–h–i

1.00

10.0

.9192

13.5

16.0

Weeks

.1587

17.11 SIMULATION

We have examined a method for computing the probability that a project would be completed in a specified length of time. That discussion assumed that the paths of the project were independent; that is, the same activities are not on more than one path. If an activity were on more than one path and it happened that the completion time for that activity far exceeded its expected time, all paths that included that activity would be affected and, hence, their times would not be independent. Where activities are on multiple paths, one must consider if the

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preceding approach can be used. For instance, if only a few activities are on multiple paths, particularly if the paths are much shorter than the critical path, that approach may still be reasonable. Moreover, for purposes of illustration, as in the text problems and examples, the paths are treated as being independent when, in fact, they may not be.

In practice, when dependent cases occur, project planners often use simulation. It amounts to a form of repeated sampling wherein many passes are made through the project network. In each pass, a randomly selected value for each activity time is made based on the characteristics of the activity’s probability distribution (e.g., its mean, standard deviation, and distribution type). After each pass, the expected project duration is determined by adding the times along each path and designating the time of the longest path as the project duration. After a large number of such passes (e.g., several hundred), there is enough information to prepare a frequency distribution of the project duration times. Planners can use this distribution to make a probabilistic assessment of the actual project duration, allowing for some activities that are on more than one path. Prob- lem 19 in the simulation supplement to Chapter 18 located on the text website illustrates this.

17.12 BUDGET CONTROL

Budget control is a critical aspect of a project. Costs can exceed budget for a number of rea- sons, and unless corrective action is taken, serious cost overruns can occur, possibly putting the project in jeopardy. Cost overruns can occur for various reasons. One possibility is that initial estimates might have been overly optimistic. Another is that unforeseen events such as weather or supplier issues, work or parts that were substandard and had to be remedied, or some other event added costs.

Table 17.4 illustrates the project cost status for a hypothetical project that is in progress. For this project, the first three activities have been completed. Activity A was $1,000 under budget, Activity B was right at its budgeted amount, and Activity C was over budget by $3,500. The remaining activities are incomplete, but each has a projected cost and a projected difference. Unless there is a change during the remaining life of the project, the cost overrun is projected to be $4,000. The project manager will have to decide if that amount is accept- able, or whether corrective action should be initiated. Although managers’ intuitive feeling may be to focus on the activities that are over budget, they would likely review all activities to see where potential savings are possible. Of course, the project cost status would be updated, usually on a daily or weekly basis, to keep the project manager informed.

17.13 TIME–COST TRADE-OFFS: CRASHING

Estimates of activity times for projects usually are made for some given level of resources. In many situations, it is possible to reduce the length of a project by injecting additional resources. The impetus to shorten projects may reflect efforts to avoid late penalties, to

LO17.9 Describe activity “crashing” and solve typi- cal problems.

Activity Budgeted

Cost Percent

Complete Actual or

Projected Cost (Over/Under)

Actual—Budget

A $25,000 100% $24,000 $1,000

B 15,000 100 15,000 0

C 22,000 100 25,500 −3,500 D 10,000 75 10,500 −500 E 30,000 50 29,000 1,000

F 20,000 40 22,000 −2,000 G 8,000 25 8,000 0

−$4,000

TABLE 17.4 Project cost status for a hypothetical project

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take advantage of monetary incentives for timely or early completion of a project, or to free resources for use on other projects. In new product development, shortening may lead to a strategic benefit: beating the competition to the market. In some cases, however, the desire to shorten the length of a project merely reflects an attempt to reduce the costs associated with running the project, such as facilities and equipment costs, supervision, and labor and personnel costs. Managers often have various options at their disposal that will allow them to shorten, or crash, certain activities. Among the most obvious options are the use of additional funds to support additional personnel or more efficient equipment, and the relaxing of some work specifications. Hence, a project manager may be able to shorten a project by increasing direct expenses to speed up the project, thereby realizing savings on indirect project costs. The goal in evaluating time–cost trade-offs is to identify activities that will reduce the sum of the project costs.

In order to make a rational decision on which activities, if any, to crash and on the extent of crashing desirable, a manager needs certain information:

1. Regular time and crash time estimates for each activity 2. Regular cost and crash cost estimates for each activity 3. A list of activities that are on the critical path

Activities on the critical path are potential candidates for crashing, because shortening noncritical activities would not have an impact on total project duration. From an economic standpoint, activities should be crashed according to crashing costs: Crash those with the low- est crash costs first. Moreover, crashing should continue as long as the cost to crash is less than the benefits derived from crashing. Figure 17.11 illustrates the basic cost relationships.

Crashing analysis requires estimates of regular and crash times and costs for each activity, path lengths, and identification of critical activities. The general procedure for crashing is:

1. Crash the project one period at a time. 2. Crash the least expensive activity that is on the critical path. 3. When there are multiple critical paths, find the sum of crashing the least expensive

activity on each critical path. If two or more critical paths share common activities, compare the least expensive cost of crashing a common activity shared by critical paths with the sum for the separate critical paths.

Crash Shortening activity durations.

Workers demolish the south side of the Mulholland overpass on the 405 freeway during the 53-hour total freeway closure. The bridge was demolished as part of a $1 billion project to add carpool lanes and to make other improvements along the route from Orange County to San Francisco.

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FIGURE 17.11 Crashing activities* *Crashing activities reduce indirect project costs and increase direct costs; the optimum amount of crashing results in minimizing the sum of these two types of costs.

Total cost

Cumulative cost of crashing

Expected project costs

Sh ort

en Sho

rten

CRASH

Shorten

Optimum Project length 0

C o

screenCam tutorial

S O L U T I O N

Optimal Project Crashing Using the following information, develop the optimal time–cost solution. Project costs are $1,000 per day.

Activity Normal Time

Crash Time

Cost per Day to Crash

a 6 6 — b 10 8 $500 c 5 4 300 d 4 1 700 e 9 7 600 f 2 1 800

E X A M P L E 7

mhhe.com/stevenson13e

a. Determine which activities are on the critical path, its length, and the length of the other path: Path Length

a–b–f 18 c–d–e–f 20 (critical path)

b. Rank the critical path activities in order of lowest crashing cost, and determine the number of days each can be crashed. Note: Available days = Normal time – Crash time. Activity Cost per Day to Crash Available Days

c $300 1 e 600 2 d 700 3 f 800 1

4 d

9 e

5 c

10 b

6 a

2 f

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An important benefit of the sequential crashing procedure just described is that it provides the ability to quote different budget costs for different project times.

17.14 ADVANTAGES OF USING PERT AND POTENTIAL SOURCES OF ERROR

PERT and similar project scheduling techniques can provide important services for the proj- ect manager. Among the most useful features are these:

1. Use of these techniques forces the manager to organize and quantify available informa- tion and to recognize where additional information is needed.

2. The techniques provide a graphic display of the project and its major activities. 3. They identify (a) activities that should be closely watched because of the potential for

delaying the project and (b) other activities that have slack time and so can be delayed without affecting project completion time. This raises the possibility of reallocating resources to shorten the project.

LO17.10 Discuss the advantages of using PERT and potential sources of error.

c. Begin shortening the project, one day at a time, and check after each reduction to see which path is critical. (After a certain point, another path may equal the length of the shortened critical path.) Thus:

(1) Shorten activity c one day at a cost of $300. The length of the critical path now becomes 19 days.

(2) Activity c cannot be shortened any more. Shorten activity e one day at a cost of $600. The length of path c–d–e–f now becomes 18 days, which is the same as the length of path a–b–f.

(3) The paths are now both critical; further improvements will necessitate shortening both paths.

The remaining activities for crashing and their costs are:

Path Activity Crash cost per day

a–b–f a No reduction possible b $500 f 800

c–d–e–f c No further reduction possible d $700 e 600 f 800

At first glance, it would seem that crashing f would not be advantageous, because it has the highest crashing cost. However, f is on both paths, so shortening f by one day would shorten both paths (and hence, the project) by one day for a cost of $800. The option of shortening the least expensive activity on each path would cost $500 for b and $600 for e, or $1,100. Thus shorten f by one day. The project duration is now 17 days.

(4) At this point, no additional improvement is feasible. The cost to crash b is $500 and the cost to crash e is $600, for a total of $1,100, and that would exceed the indirect project costs of $1,000 per day.

(5) The crashing sequence is summarized as follows: LENGTH AFTER CRASHING n DAYS:

Path n = 0 1 2 3

a–b–f 18 18 18 17 c–d–e–f 20 19 18 17 Activity crashed c e f Cost $300 $600 $800

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No analytical technique is without potential errors. Among the more important sources of errors are the following:

1. When developing the project network, managers may unwittingly omit one or more important activities.

2. Precedence relationships may not all be correct as shown. 3. Time estimates may include a fudge factor; managers may feel uncomfortable about

making time estimates because they appear to commit themselves to completion within a certain time period.

4. There may be a tendency to focus solely on activities that are on the critical path. As the project progresses, other paths may become critical. Furthermore, major risk events may not be on the critical path.

17.15 CRITICAL CHAIN PROJECT MANAGEMENT

Critical chain project management (CCPM) is an approach to project management that includes an emphasis on the resources required to execute project tasks. It was developed by Eli Goldratt, who also developed the theory of constraints (see Chapter 16). Goldratt identifies cer- tain aspects of projects that he believes managers need to be aware of to better manage projects:

1. Time estimates are often pessimistic and with attention can be made more realistic (i.e., shortened).

2. When activities are finished ahead of schedule, that fact may go unreported, so managers may be unaware of resources that could potentially be used to shorten the critical path.

The critical chain of a project is analogous to the critical path of a network. However, the critical chain approach takes into account not only sequential task relationships, but also resource constraints that can result in tasks being delayed when they must wait for a resource that is being used on another task.

A key feature of the critical chain approach is the use of various buffers. Feeding (time) buffers are positioned at points in the network where noncritical sections of the network feed into the critical chain path to reduce the risk of delaying critical chain activities. Their pur- pose is to insulate the critical chain from variation in noncritical chains’ activities. Not every intersection will require a time buffer; only those sections that have a relatively small degree of slack time will provide benefit from a time buffer. A project (time) buffer at the end of the project is used to reduce the risk that time variations on the critical chain will interfere with timely project completion. Capacity (resource) buffers are used when multiple projects are ongoing to help manage the impact of variation of resource requirements among projects.

Regular updates of activity status relative to planned completion times can enable the proj- ect manager to see where actual or potential problems can arise, as well as where buffers can be reduced or eliminated, to reconfigure buffers.

17.16 OTHER TOPICS IN PROJECT MANAGEMENT

This section touches briefly on several other project management topics, including Six-Sigma projects, virtual project teams, and managing multiple projects.

One increasingly popular use of project management is for Six-Sigma projects. Although Six-Sigma projects tend to have a narrow focus, they still involve all of the typical elements and requirements of general project management. Six-Sigma projects are discussed in more detail in Chapter 9.

As companies globalize operations, they are increasingly using virtual project teams. All the basic elements of a project are present, but some or all of the team members are geographically

Virtual project teams Some or all of the team members are geographically separated.

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separated. Recent advances in communication technology have made this feasible. A key ben- efit is the ability to tap into human talents and perspectives that would otherwise be difficult or impossible to use. A key disadvantage can be the inability to realize synergies that can arise from closer contact among team members. Also, there are risks if there are language or cultural differences among team members, so communications have to be managed more carefully.

The existence of multiple projects can create added layers of pressure and complexity to project management. Resources often need to be shared across projects, and problems on one project may create issues for other projects, and can require reassessing priorities. When multiple projects are ongoing within an organization, resources needed for one project may be in use on another project, which could delay the project waiting for the resources to become available. Hence, it is important for managers to cross-check project schedules to avoid such conflicts. Project management software can help avoid conflicts when there are shared resources. In a related issue, project slippage can occur as a project nears completion if resources are transferred to new projects too quickly.

17.17 PROJECT MANAGEMENT SOFTWARE

Technology has had a number of benefits for project management. Among those benefits are the use of computer-aided design (CAD) to produce updated prototypes on construction and product-development projects; software such as Lotus Notes to keep team members who are in separate locations in close contact; and the ability for remote viewing of projects, allowing those in different locations a firsthand view of progress and problems.

There are a variety of specialized software programs available to help manage projects. As an example, let’s consider Microsoft Project.2 It can be used to effectively create schedules, estimate costs, and track progress. Users can:

• Assign resources. Assign resources to tasks and adjust them as necessary. • Compare project plan versions. Track version changes in project plans. • Evaluate changes. Evaluate the impact of schedule and resources changes. • Track performance. Track progress and monitor variances between target and actual

project goals such as cost, start date, and finish date, and maintain historical records.

Microsoft Project facilitates communication by enabling users to share a project plan with others in the organization, generate predefined reports, format and print custom reports, and easily present project status.

Microsoft Project can be customized to accommodate specific needs by allowing choice of data to display in a project schedule, the custom fields, and modification of formulas, toolbars, and reports. Microsoft Project is an integral part of the Microsoft Office System, making it easy to use products like Microsoft Office PowerPoint and Microsoft Office Visio to present project status.

There are many advantages to using a project management software package. Among them are the following:

• It imposes a methodology and a common project management terminology. • It provides a logical planning structure. • It can enhance communication among team members. • It can flag the occurrence of constraint violations. • It automatically formats reports. • It can generate multiple levels of summary reports and detailed reports. • It enables what-if scenarios. • It can generate various chart types, including basic Gantt charts.

2www.microsoft.com/office/project/prodinfo/standard/overview.mspx.

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One thing to keep in mind is that project management is more than choosing the right software. There is much that a project manager must do. Recall the key decisions that were discussed early in the chapter.

17.18 OPERATIONS STRATEGY

Projects can present both strategic opportunities and strategic risks, so it is critical for man- agement to devote adequate attention and resources to projects.

Projects are often used in situations that have some degree of uncertainty, which can result in delays, budget overruns, and failure to meet technical requirements. To minimize the impact of these possibilities, management must ensure that careful planning, wise selection of project managers and team members, and monitoring of the project occur.

Computer software and tools such as PERT can greatly assist project management. How- ever, care must be taken to avoid focusing exclusively on the critical path. The obvious reason is that as the project progresses, other paths may become critical. But another, less obvious, reason is that key risk events may not be on the critical path. Even so, if they occur, they can have a major impact on the project.

It is not uncommon for projects to fail, either completely or partially. When that happens, it can be beneficial to examine the probable reasons for the failure, and decide what possible decisions or actions, if any, might have contributed to the failure. These become “lessons learned” that may be applicable to future projects to decrease the likelihood of failure.

17.19 RISK MANAGEMENT

Risks are inherent in projects. They relate to the occurrence of events that can have undesir- able consequences, such as delays, increased costs, and an inability to meet technical speci- fications. In some instances, there is the risk that events will occur that will cause a project to be terminated. Although careful planning can reduce risks, no amount of planning can eliminate chance events due to unforeseen, or uncontrollable, circumstances.

The probability of occurrence of risk events is highest near the beginning of a project and lowest near the end. However, the cost associated with risk events tends to be lowest near the beginning of a project and highest near the end. (See Figure 17.12.)

Good risk management entails identifying as many potential risks as possible, analyzing and assessing those risks, working to minimize the probability of their occurrence, and estab- lishing contingency plans (and funds) for dealing with any that do occur. Much of this takes

LO17.11 Discuss the key steps in risk management.

FIGURE 17.12 Risk event probability and cost

Project life cycle

Cost to overcome occurrence of risk event

Probability of occurrence of a risk event

High

Low

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place before the start of a project, although it is not unusual for this process to be repeated during the project as experience grows and new information becomes available.

The first step is to identify the risks. Typically, there are numerous sources of risks, although the more experience an organization has with a particular type of work, the fewer and more identifiable the risks. Everyone associated with the project should have responsibility for the task of identifying risks. Brainstorming sessions and questionnaires can be useful in this regard.

Once risks have been identified, each risk must be evaluated to determine its probability of occurrence and the potential consequences if it does occur. Both quantitative and qualitative approaches have merit. Managers and workers can contribute to this effort, and experts might be called on. Experience with previous projects can be useful. Many tools might be applied, including scenario analysis, simulation, and PERT (described earlier in the chapter).

Risk reduction can take a number of forms. Much depends on the nature and scope of a project. “Redundant” (backup) systems can sometimes be used to reduce the risk of failure. For example, an emergency generator could supply power in the event of an electrical failure. Another approach is frequent monitoring of critical project dimensions with the goal of catching and eliminating problems in their early stages, before they cause extensive damage. Risks can sometimes be transferred, say by outsourcing a particular component of a project. Risk-sharing is another possibility. This might involve partnering, which can spread risks among partners; this approach may also reduce risk by enlarging the sphere of sources of ideas for reducing the risk.

A project leader may have to contend with multiple risks that have different costs and dif- ferent probabilities of occurring. A simple matrix such as the one illustrated in Figure 17.13 can be used to put the risks into perspective.

Events in the upper right-hand quadrant (events 3 and 4) have the highest probability of occurring, and also high costs. They should be given the greatest attention. Conversely, events in the lower left-hand quadrant (events 2 and 5) have relatively low probabilities and low costs, so they should be given the least attention. Events in the other two quadrants (events 6 and 1) should get moderate attention due either to high cost (event 6) or high probability of occurrence (event 1).

FIGURE 17.13 A risk matrix

1.000 0

$100

Probability of occurring

Cost

Event Probability Cost

1 .85 $18

2 .30 20

3 .55 68

4 .85 77

5 .10 30

6 .30 87

Projects are composed of a unique set of activities established to realize a given set of objectives in a limited time span. Projects go through a life cycle that involves definition, planning, execution, and delivery/termination. The nonroutine nature of project activities places a set of demands on the project manager that are different in many respects from those the manager of more routine operations activities experiences, both in planning and coordinating the work and in the human problems encountered. Ethi- cal conduct and risk management are among the key issues project managers must deal with.

PERT and CPM are two commonly used techniques for developing and monitoring projects. Although each technique was developed independently and for expressly different purposes, time and practice have erased most of the original differences, so that now there is little distinction between the two. Either provides the manager with a rational approach to project planning and a graphical display of project activities. Both depict the sequential relationships that exist among activities and reveal to managers which activities must be completed on time to achieve timely project completion. Managers can use that information to direct their attention toward the most critical activities.

SUMMARY

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activities, 741 activity-on-arrow (AOA), 740 activity-on-node (AON), 740 beta distribution, 751 CPM, 740 crash, 758 critical activities, 741 critical path, 741 deterministic, 743

KEY TERMS events, 741 independence, 754 most likely time, 751 network (precedence)

diagram, 740 optimistic time, 751 path, 741 PERT, 740

pessimistic time, 751 probabilistic, 743 project champion, 737 projects, 732 slack, 742 virtual project teams, 761 work breakdown structure

(WBS), 739

Two slightly different conventions can be used for constructing a network diagram. One designates the arrows as activities; the other designates the nodes as activities.

The task of developing and updating project networks quickly becomes complex for projects of even moderate size, so computer software is important. Among the advantages of using project management software are the provision for a logical planning structure, enhanced communication, and automatically formatted charts and reports.

In some instances, it may be possible to shorten, or crash, the length of a project by shortening one or more of the project activities. Typically, such gains are achieved by the use of additional resources, although in some cases, it may be possible to transfer resources among project activities. Generally, projects are shortened to the point where the cost of additional reduction would exceed the benefit of additional reduction, or to a specified time.

1. Projects are unique, limited duration sets of tasks designed to accomplish a set of objectives. 2. The key project metrics are cost, time, and performance. 3. Table 17.1 and Figure 17.1 provide valuable insights into the nature of projects and project

management. 4. The project manager and the project team can be major factors in achieving project goals. 5. Work breakdown structures, Gantt charts, and precedence diagrams are useful tools for managing

projects.

KEY POINTS

The following table contains information related to the major activities of a research project. Use the information to do the following:

a. Draw a precedence diagram using AOA. b. Find the critical path. c. Determine the expected length of the project.

Activity Immediate

Predecessor Expected

Time (days)

a — 5 c a 8 d c 2 b a 7 e — 3 f e 6 i b, d 10 m f, i 8 g — 1 h g 2 k h 17 end k, m

Problem 1

SOLVED PROBLEMS

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Problem 2

a. In constructing networks, these observations can be useful. (1) Activities with no predecessors are at the beginning (left side) of the network. (2) Activities with multiple predecessors are located at path intersections.

Complete the diagram in sections. Go down the activity list in order to avoid overlooking any activities.

Solution

Here are some additional hints for constructing a precedence diagram. (1) Use pencil. (2) Start and end with a single node. (3) Avoid having paths cross each other. (4) Have activities go from left to right. (5) Use only one arrow between any pair of nodes.

b. and c.

Path Length (days)

a–c–d–i–m* 5 + 8 + 2 + 10 + 8 = 33† a–b–i–m 5 + 7 + 10 + 8 = 30 e–f–m 3 + 6 + 8 = 17 g–h–k 1 + 2 + 17 = 20 *Critical path. †Expected project duration.

Using the computing algorithm, determine the slack times for the following AOA diagram. Identify the activities that are on the critical path.

e 3

a 5

g 1

b 7

c 8

d 2

h 2

k 17

m 8

i 10

f 6

AOA diagram

g h

End

a c

e f

Yes No

AON diagram

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4 1

This is accomplished in a two-step process. First, determine the earliest starting times and earliest finishing times, working from left to right, as shown in the following diagram.

The bracket at the left of each activity will eventually be filled in with the earliest and latest start- ing times, and the bracket at the right end of each activity will be filled in with the earliest and latest finishing times:

SolutionThe task of determining ES, EF, LS, and LF times can be greatly simplified by setting up two brack- ets for each activity, as illustrated:

LS ES

LF EF

2 4

10 0

9 9 14

14 17

Thus, activity 1-2 can start at 0. With a time of 4, it can finish at 0 + 4 = 4. This establishes the earliest start for all activities that begin at node 2. Hence, 2-5 and 2-4 can start no earlier than time 4. Activity 2-5 has an early finish of 4 + 6 = 10, and activity 2-4 has an early finish of 4 + 2 = 6. At this point, it is impossible to say what the earliest start is for 4-5; that will depend on which activity, 3-4 or 2-4, has the latest EF. Consequently, it is necessary to compute ES and EF along the lower path. Assuming an ES of 0 for activity 1-3, its EF will be 9, so activity 3-4 will have an ES of 9 and an EF of 9 + 5 = 14.

Considering that the two activities entering node 4 have EF times of 6 and 14, the earliest that activity 4-5 can start is the larger of these, which is 14. Hence, activity 4-5 has an ES of 14 and an EF of 14 + 3 = 17.

Now compare the EFs of the activities entering the final node. The larger of these, 17, is the expected project duration.

The LF and LS times for each activity can now be determined by working backward through the network (from right to left). The LF for the two activities entering node 5 is 17—the project dura- tion. In other words, to finish the project in 17 weeks, these last two activities must both finish by that time.

In the case of activity 4-5, the LS necessary for an LF of 17 is 17 − 3 = 14. This means that both activities 2-4 and 3-4 must finish no later than 14. Hence, their LF times are 14. Activity 3-4 has an LS time of 14 − 5 = 9, making the LF of activity 1-3 equal to 9, and its LS equal to 9 − 9 = 0.

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Solution Standard deviations cannot be added, but variances can be added. Square each standard deviation to obtain its variance, and then add the resulting variances to obtain the path variance:

Standard Deviation Variance

1.50 2.25

0.80 0.64

1.30 1.69

4.58 (path variance) The square root of the path variance is the path standard deviation:

√ ____

4.58 = 2.14 (path standard deviation)

Problem 3 A path in a network has three activities. Their standard deviations are 1.50, 0.80, and 1.30. Find the path standard deviation.

The slack time for any activity is the difference between either LF and EF or LS and ES. Thus,

Activity LS ES Slack or LF EF Slack

1-2 7 0 7 11 4 7 2-5 11 4 7 17 10 7 2-4 12 4 8 14 6 8 1-3 0 0 0 9 9 0 3-4 9 9 0 14 14 0 4-5 14 14 0 17 17 0

The activities with zero slack times indicate the critical path. In this case the critical path is 1−3−4−5. When working problems of this nature, keep in mind the following:

∙ The ES time for leaving activities of nodes with multiple entering activities is the largest EF of the entering activities.

∙ The LF for an entering activity for nodes with multiple leaving activities is the smallest LS of the leaving activities.

Activity 2-4, with an LF time of 14, has an LS time of 14 − 2 = 12. Activity 2-5 has an LF of 17 and therefore an LS of 17 − 6 = 11. Thus, the latest activity 2-5 can start is 11, and the latest 2-4 can start is 12 in order to finish by week 17. Since activity 1-2 precedes both of these activities, it can finish no later than the smaller of these, which is 11. Hence, activity 1-2 has an LF of 11 and an LS of 11 − 4 = 7.

The ES, EF, LF, and LS times are shown on the following network.

11 4

17 107

11 4

0 0

9 9 9

9 14 14

14 14

17 17

124

14 6

Expected times in weeks and variances for the major activities of an R&D project are depicted in the following table. Determine the probability that project completion time will be:

a. 50 weeks or less b. More than 50 weeks

Problem 4

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Compute the mean and standard deviation for each path:

Path Expected Time (weeks) Standard Deviation (weeks)

Top 16 + 11 + 24 = 51 √ ___________

.69 + .69 + .11 = 1.22 Middle 5 + 18 + 26 = 49 √

___________ .00 + .25 + .11 = .60

Bottom 5 + 10 + 14 + 12 = 41 √ _______________

.00 + .25 + .36 + .11 = .85 a. Compute the z for each path for the length specified. For any path that has a z of + 3.00 or more,

treat its probability of completion before the specified time as 1.00. Use

z = 50 − t path ________

σ path

The probability that each path will be completed in 50 weeks or less is shown in the corre- sponding diagram. (Probabilities are from Appendix B, Table B.) The probability that the project will be completed in 50 weeks or less depends on all three paths being completed in that time. Because z for the bottom path is greater than + 3.00, it is treated as having a probability of com- pletion in 50 weeks of 100 percent. It is less certain that the other two paths will be completed in that time. The probability that both will not exceed 50 is the product of their individual prob- abilities of completion. Thus, .2061(.9525)(1.00) = .1963.

b. The probability that the project will exceed 50 weeks is the complement of this number, which is 1.000 − .1963 = .8037. (Note that it is not the product of the path probabilities.)

Path Activity Mean Variance

A 16 .69 Top B 11 .69

C 24 .11 D 5 0

Middle E 18 .25 F 26 .11 D 5 0

Bottom G 10 .25 H 14 .36 I 12 .11

Solution

.2061

–.82 50

z scale

Weeks

z =

T = 50 weeks

50 – 51 1.22

= –.82

z = 50 – 49 .60

= 1.67

z = 50 – 41 .85

= 10.59

z scale

Weeks

1.67

10.59

z scale

Weeks

.9525

100%

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Costs for a project are $12,000 per week for as long as the project lasts. The project manager has sup- plied the cost and time information shown. Use the information to:

a. Determine an optimum crashing plan b. Graph the total costs for the plan

Activity

Crashing Potential (weeks)

Cost per Week to Crash

a 3 $11,000 b 3 3,000 first week,

$ 4,000 others c 2 6,000 d 1 1,000 e 3 6,000 f 1 2,000

Problem 5

a. (1) Compute path lengths and identify the critical path:

Path Duration (weeks)

a–b 24 (critical path)

c–d 19

e–f 23

(2) Rank critical activities according to crash costs:

Activity Cost per Week to Crash

b $ 3,000

a 11,000

Activity b should be shortened one week since it has the lower crashing cost. This would reduce indirect costs by $12,000 at a cost of $3,000, for a net savings of $9,000. At this point, paths a–b and e–f would both have a length of 23 weeks, so both would be critical.

(3) Rank activities by crashing costs on the two critical paths:

Path Activity Cost per Week to Crash

a–b b $ 4,000

a 11,000

e–f f 2,000

e 6,000

Choose one activity (the least costly) on each path to crash: b on a–b and f on e–f, for a total cost of $4,000 + $2,000 = $6,000 and a net savings of $12,000 − $6,000 = $6,000.

(4) Check to see which path(s) might be critical: a–b and e–f would be 22 weeks in length, and c–d would still be 19 weeks.

Solution

13 weeks c

10 we

ek s

15 weekse

6 weeks d

8 w ee

14 weeksb

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(5) Rank activities on the critical paths:

Path Activity Cost per Week to Crash

a–b b $ 4,000

a 11,000

e–f e 6,000

f (no further crashing possible)

Crash b on path a–b and e on e–f for a cost of $4,000 + $6,000 = $10,000, for a net savings of $12,000 − $10,000 = $2,000.

(6) At this point, no further improvement is possible: paths a–b and e–f would be 21 weeks in length, and one activity from each path would have to be shortened. This would mean activ- ity a at $11,000 and e at $6,000 for a total of $17,000, which exceeds the $12,000 potential savings in costs.

b. The following table summarizes the results, showing the length of the project after crashing n weeks:

Path n = 0 1 2 3

a–b 24 23 22 21

c–d 19 19 19 19

e–f 23 23 22 21

Activity crashed b b,f b,e

Crashing costs ($000) 3 6 10

A summary of costs for the preceding schedule would look like this:

Project Length

Cumulative Weeks

Shortened

Cumulative Crashing

Costs ($000) Indirect

Costs ($000) Total

Costs ($000)

24 0 0 24(12) = 288 288

23 1 3 23(12) = 276 279

22 2 3 + 6 = 9 22(12) = 264 273

21 3 9 + 10 = 19 21(12) = 252 271

20 4 19 + 17 = 36 20(12) = 240 276

The graph of total costs is as follows:

290

280

270

260

Project duration (weeks)

T o

ta l c

o st

20 21 22 23 24

276

271 273

279

288

Crash

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1. A project manager may need two skill sets—those of a manager and those of a leader. Explain. 2. Explain the term project champion and list some ways to keep a champion involved with the project. 3. List the steps in risk management. 4. Give some examples of ethical issues that may arise on projects. What can a project manager do to

minimize such issues? 5. What are the key advantages of using project management software? 6. What is a work breakdown structure, and how is it useful for project planning? 7. Identify the term being described for each of the following:

a. A sequence of activities in a project. b. The longest time sequence of activities in a project. c. Used when two activities have the same starting and finishing points. d. The difference in time length of any path and the critical path. e. The statistical distribution used to describe variability of an activity time. f. The statistical distribution used to describe path variability. g. Shortening an activity by allocating additional resources.

8. List the main advantages of PERT. List the main limitations. 9. Why might a probabilistic estimate of a project’s completion time based solely on the variance of

the critical path be misleading? Under what circumstances would it be acceptable? 10. Define each of these terms, and indicate how each is determined.

a. Expected activity time. b. Variance of an activity time. c. Standard deviation of a path’s time.

11. Why might a person wish to be involved with a critical path activity? What are some of the reasons one might have for not wanting this association?

12. What are some of the potential benefits of working on a special project in one’s firm? What are some of the risks?

13. What are some aspects of the project manager’s job that make it more demanding than the job of a manager working in a more routine organizational framework?

14. What is the main benefit of a project organization over more traditional forms of operations man- agement for project work?

DISCUSSION AND REVIEW QUESTIONS

1. Project management techniques have been used successfully for a wide variety of efforts, including the many NASA space missions, huge construction projects, implementation of major systems such as ERP, production of movies, development of new products and services, theatrical productions, and much more. Why not use them for managing the operations function of any business?

2. Give three examples of unethical conduct involving projects and the ethical principle each one violates.

CRITICAL THINKING EXERCISES

1. For each of the following network diagrams, determine both the critical path and the expected proj- ect duration. The numbers on the arrows represent expected activity times. a. AOA diagram

PROBLEMS

1. What trade-offs are associated with time and cost estimates for a proposed project? 2. Who needs to be involved in assessing the cost of a project? 3. Name and explain briefly two ways that technology has had an impact on project management.

TAKING STOCK

2 4 7

5 8

4 6 9

102

113

12 1

4 3

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b. AON diagram

8 9

9 2

c. AOA diagram

133

11 14

8 4 7

2 5

7 14

13 161 3

10 11

d. AON diagram

C F

EStart

End

7 8

5 7 6

2. Chris received new word processing software for her birthday. She also received a check, with which she intends to purchase a new computer. Chris’s college instructor assigned a paper due next week. Chris decided that she will prepare the paper on the new computer. She made a list of the activities she will need to do and their estimated times. a. Arrange the activities into two logical sequences. b. (1) Construct an AOA network diagram. (2) Construct an AON diagram. c. Determine the critical path and the expected duration time.

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d. What are some possible reasons for the project to take longer than the expected duration?

Estimated Time (hrs.) Activity (abbreviation)

0.8 Install software (Inst)

0.4 Outline the paper (Out)

0.2 Submit paper to instructor (Sub)

0.6 Choose a topic (Ch)

0.5 Use grammar-checking routine and make corrections (Ck)

3.0 Write the paper using the word-processing software (Write)

2.0 Shop for a new computer (Sh)

1.0 Select and purchase computer (Sel)

2.0 Do library research on chosen topic (Lib)

3. Prepare a Gantt chart for each of the following in the style of the chart shown in section 17.5. a. The bank location problem (see Figure 17.4). Hint: Use the early start (ES) times given in Table 17.3. b. Solved Problem number 2.

4. a. Develop a list of activities and their immediate predecessors similar to the lists in this problem for this diagram:

b. Construct an activity-on-arrow precedence diagram for each of the following cases. Note that each case requires the use of a dummy activity.

c. Construct an AON diagram for each case.

(1) Activity Immediate

Predecessor (2) Activity Immediate

Predecessor

A — J —

B — K —

C — L J

D A M L

E B N J

F B P N

G C Q —

H F R K

I F, G S Q

K D, E V R, S, T

End H, I, K T Q

W T

End M, P, V, W

5. For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project. a. Problem 1a. b. Problem 1b.

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6. Reconsider the network diagram of Problem 1a. Suppose that after 12 weeks, activities 1-2, 1-3, and 2-4 have been finished; activity 2-5 is 75 percent finished; and activity 3-6 is half finished. How many weeks after the original start time should the project be finished?

7. Three recent college graduates have formed a partnership and have opened an advertising firm. Their first project consists of activities listed in the following table. a. Draw the precedence diagram. b. What is the probability that the project can be completed in 24 days or less? In 21 days or less? c. Suppose it is now the end of the seventh day and that activities A and B have been completed

while activity D is 50 percent completed. Time estimates for the completion of activity D are 5, 6, and 7. Activities C and H are ready to begin. Determine the probability of finishing the project by day 24 and the probability of finishing by day 21.

TIME IN DAYS

Activity Immediate

Predecessor Optimistic Most Likely Pessimistic

A — 5 6 7 B — 8 8 11 C A 6 8 11 D — 9 12 15 E C 5 6 9 F D 5 6 7 G F 2 3 7 H B 4 4 5 I H 5 7 8 End E, G, I

d. The partners have decided that shortening the project by two days would be beneficial, as long as it doesn’t cost more than about $20,000. They have estimated the daily crashing costs for each activity in thousands, as shown in the following table. Which activities should be crashed, and what further analysis would they probably want to do?

Activity First Crash Second Crash

C $ 8 $10 D 10 11 E 9 10 F 7 9 G 8 9 H 7 8 I 6 8

8. The new director of special events at a large university has decided to completely revamp gradu- ation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Gradua- tion day is 16 weeks from now. Assuming the project begins now, what is the probability that the project will be completed before a. Graduation time? b. The end of week 15? c. The end of week 13?

Path Expected Duration

(weeks) Variance

A 10 1.21

B 8 2.00

C 12 1.00

D 15 2.89

E 14 1.44

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9. Construct a network diagram for the information in the following table. Use either AOA or AON (see Example 5 for either type). What is the probability that the project will take more than 10 weeks to complete if the activity means and standard deviations are as shown below? Times are in weeks.

Path Activity Mean Standard Deviation

A C 5 1.3 D 4 1.0

B E 8 1.6

10. The project described in the following table is scheduled to be completed in 11 weeks. Construct a network diagram using AOA or AON (see Example 5 for either type). Then answer the follow- ing questions:

a. If you were the manager of this project, would you be concerned? Explain. b. If there is a penalty of $5,000 a week for each week the project is late, what is the probability

of incurring a penalty of at least $5,000?

Path Activity Estimated Time

(weeks) Standard

Deviation (wks.)

A C 4 0.70 D 6 0.90

B E 3 0.62 F 9 1.90

11. The following precedence diagram reflects three time estimates in weeks for each activity. Determine:

a. The expected completion time for each path and its variance. b. The probability that the project will require more than 49 weeks. c. The probability that the project can be completed in 46 weeks or less.

9-10-12

8-8-8

3 8

1 2 5-6-7

8-10-14 6 11

7-10-12

10 -1

1- 12

6- 6-

10 .5-

13 -15

5-7-10

14- 18-

13-13-13

10 -12-14

11- 12

-13

12. A project manager has compiled a list of major activities that will be required to install a com- puter information system in her firm. The list includes estimated completion times for activities and precedence relationships.

Activity Immediate

Predecessor Estimated

Times (weeks)

A — 2-4-6

D A 6-8-10

E D 7-9-12

H E 2-3-5

F A 3-4-8

G F 5-7-9

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Activity Immediate

Predecessor Estimated

Times (weeks)

B — 2-2-3 I B 2-3-6 J I 3-4-5 K J 4-5-8 C — 5-8-12 M C 1-1-1 N M 6-7-11 O N 8-9-13

End H, G, K, O a. Construct a network diagram. You can use either AOA or AON (see Example 5). b. If the project is finished within 26 weeks of its start, the project manager will receive a bonus

of $1,000; and if the project is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus.

13. Here is a list of activity times for a project as well as crashing costs for its activities. Determine which activities should be crashed and the total cost of crashing if the goal is to shorten the proj- ect by three weeks as cheaply as possible. First construct a network diagram. You can use either an AOA or an AON (see Example 5).

Path Activity Duration (weeks) First Crash Second Crash

Top A 5 $8 $10 B 6 7 9 C 3 14 15

Middle D 3 9 11 E 7 8 9 C 3 14 15

Bottom F 5 10 15 G 5 11 13 H 5 12 14

14. The project manager of a task force planning the construction of a domed stadium had hoped to be able to complete construction prior to the start of the next college football season. After reviewing construction time estimates, it now appears that a certain amount of crashing will be needed to ensure project completion before the season opener. Given the following time and cost estimates, determine a minimum-cost crashing schedule that will shave five weeks off the project length. Note: No activity can be crashed more than two weeks.

CRASHING COSTS ($000)

Activity Immediate Predecessor Normal Time (weeks) First Week Second Week

A — 12 $15 $20 B A 14 10 10 C — 10 5 5 D C 17 20 21 E C 18 16 18 F C 12 12 15 G D 15 24 24 H E 8 — — I F 7 30 — J I 12 25 25 K B 9 10 10 M G 3 — — N H 11 40 — P H, J 8 20 20

End K, M, N, P

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15. A construction project has indirect costs totaling $40,000 per week. Major activities in the project and their expected times in weeks are shown in this precedence diagram.

4 1

6 10

12 9

Crashing costs for each activity are:

CRASHING COSTS ($000)

Activity First Week Second Week Third Week

1-2 $18 $22 $ — 2-5 24 25 25 5-7 30 30 35 7-11 15 20 —

11-13 30 33 36 1-3 12 24 26 3-8 — — — 8-11 40 40 40 3-9 3 10 12 9-12 2 7 10

12-13 26 — — 1-4 10 15 25 4-6 8 13 — 6-10 5 12 —

10-12 14 15 —

a. Determine the optimum time–cost crashing plan. b. Plot the total-cost curve that describes the least expensive crashing schedule that will reduce the

project length by six weeks. 16. Chuck’s Custom Boats (CCB) builds luxury yachts to customer order. CCB has landed a contract

with a mysterious New York lawyer (Mr. T). Relevant data are shown on the next page. The com- plication is that Mr. T wants delivery in 32 weeks or he will impose a penalty of $375 for each week his yacht is late. Note: No activity can be crashed more than two weeks.

CRASHING COSTS

Activity Immediate Predecessor Normal Time (weeks) 1st Week 2nd Week

K — 9 $410 $415 L K 7 125 — N K 5 45 45 M L 4 300 350 J N 6 50 — Q J, M 5 200 225 P Q 8 — — Y Q 7 85 90 Z P 6 90 —

End Y, Z

Develop a crashing schedule.

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17. Given the following table, construct a network diagram, either AOA or AON. Times are in days. a. Determine the expected duration of the project. b. Compute the probability that the project will take at least 18 days.

Path Activity Time Estimates

A 4-5-6 Top B 7-8-10

C 3-5-9 D 7-8-11

Bottom E 2-3-4 F 1-4-6

18. Create a risk matrix in the style of Figure 17.13 for this project. Use a vertical scale of $0 to $80. Which event should the project manager be most concerned about?

Event Probability Cost ($000)

1 .25 15 2 .35 25 3 .20 55 4 .80 10 5 .10 77 6 .40 55 7 .60 50

19. Create a risk matrix for this project:

Event Cost ($000) Probability

Equipment breakdown 40 .20 Vendor is late with key segment 200 .60 Subcontractor has labor issues 140 .30 Weather problems 15 Unknown Funding delays 50 .40 to .60 Testing delays 20 .40

Explain your reasoning for your placement of the events Weather problems and Funding delays.

“The mission of the project which you will head is to get our new Mexican subsidiary ready for take-over by Mexican managers. My hope is that you will be able to do this in about two years,” explained Robert Linderman, president of Linderman Industries, Inc., to Carl Conway, newly appointed manager for “Operation Mexicano.” Conway had been hired specifically for this assign- ment because of his experience in managing large defense proj- ects in the aerospace industry.

“The first thing that I will have to do is put a project team together,” said Conway. “I imagine that you have in mind my draw- ing people from the functional divisions.”

“Yes, I have already sent memoranda to the division manag- ers informing them that you will be asking for some of their key people to work under you for about two years,” said Linderman.

CASE THE CASE OF THE MEXICAN CRAZY QUILT

“In addition, I have advised them to be prepared to process work orders from Operation Mexicano with the personnel and equip- ment of their organizations. Later on in the project’s life, you will begin to get Mexican personnel, both managers and technicians, into your organization. These people will have Mexican supervi- sors, but until the mission is accomplished, they also will report to you. I will have to admit that you are going to have some com- plex authority relationships, especially as you personally will be responsible to the president of the subsidiary, Felix Delgado, as well as to me.”

Conway began to make his plans for the project team. The plant building was available and empty in Mexico City, and it was important to get equipment purchased and installed as soon as possible. A plant layout would have to be prepared, but before

(continued)

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that could be done there would have to be a manufacturing plan. Therefore, he needed to recruit an industrial engineer, a produc- tion planner, and an equipment buyer. They, in turn, would have to build their own staffs.

He made an appointment with Sam Sargis, corporate manager of industrial engineering. “I have had a preliminary talk with Bob Cates about his joining Operation Mexicano, and he is quite inter- ested,” Carl said. “Will you release him to me?”

“Why, I’m grooming Cates to take over my job when I retire,” replied Sargis. “He is my best man. Let me pick someone else for you, or better still, you just tell me what industrial engineering work you want done, and I will have it done for you.”

“Sorry, I want Cates,” said Carl firmly. “And besides, you are not due to retire for five years. This will be good experience for him.”

For production planning, Carl had in mind Bert Mill, an older man with extensive experience in managing production operations, but Mill rejected his offer. “I talked it over with my wife,” he said, “and we feel that at my age I shouldn’t take a chance on not having a job to come back to when Operation Mexicano is finished.”

Carl next talked to Emil Banowetz, who was assistant to Jim Burke, the vice president for manufacturing, and Banowetz decided that he would like to join the project team. However, Burke told Conway that if Banowetz were forcibly taken away from him, he would give Mr. Linderman his resignation, so Carl decided to back down. He finally accepted a man that Burke recommended.

Filling the equipment buyer’s slot was easy. The director of procurement phoned Carl and said that a senior buyer, Humberto Guzman, had requested permission to ask for the assignment, and that he strongly recommended him. Guzman has been purchasing agent for a large mining company in Mexico for about 10 years.

Carl had about the same experiences in getting the people he wanted for the functions of engineering, quality control, cost, mar- keting, and advertising as he did for the first three positions; in other words, he won some confrontations with the division man- agers and lost some. For personnel, he got Dr. Juan Perez, who was slated to be personnel director of the subsidiary company, to affiliate temporarily with the project team.

The first brush that Project Mexicano had in getting a functional division to do work for it came when Carl’s engineering man, Frank Fong, reported to him that the engineering vice president, who was formerly Fong’s boss, refused to authorize top priority to the chang- ing of dimensions in the production drawings to the metric system. Carl had to take this issue to Linderman, who ruled in his favor. The defeated vice president, of course, did not take kindly to the decision.

The next incident revolved around Carl’s desire to have a pilot run of products made with metric measurements for shipment to Mexico. The purpose was to test the market acceptance of the Linderman articles. Jim Burke stated flatly that there was no way that his production workers could be trained to work with metric drawings. Carl quickly saw that this was an issue that he was not going to win, so he had his buyer, Guzman, work with the newly appointed manufacturing manager for the subsidiary in getting a run of the products subcontracted in Mexico City.

Bob Cates made a special trip from Mexico City to present Carl with an interesting problem. The Mexican industrial engineer, whom Bob was supposed to be training, had his own ideas about plant layout. When they differed from Bob’s as they usually did, he would take his complaint directly to Felix Delgado, the president of the Mexican subsidiary. Because Delgado’s competence was primar- ily in finance, he would not know how to decide the argument and would simply table it. Carl took examples of some of the disagree- ments to Bob’s former boss, Sam Sargis, who quite unexpectedly ruled against Bob’s proposed methods. Carl saw that there was bad feeling by Sargis against Bob for leaving his department, which boded ill for Bob’s return. To solve the immediate problem, however, Carl asked Dr. Perez to try to reconcile the situation in Mexico City.

Despite these problems, and many more of a similar nature, Project Mexicano was successful, and the transition to Mexican management was made in just a little over two years. By a curious twist, through Dr. Perez’s intercession Felix Delgado became very impressed by Bob Cates and convinced him to accept the job of director of industrial engineering for the Mexican company. Hum- berto Guzman also stayed on to head the procurement operation.

Other members of the project team were not so fortunate. Linderman Industries was laying off personnel when the project ended, and only the project production man was able to get a job in the company at as high a level as the one he had when he joined the team. The cost expert elected to leave Linderman because he said the glamour of Project Mexicano had spoiled him for any routine job.

Carl Conway had a difficult decision of his own to make. Rob- ert Linderman said that he was extremely pleased with his perfor- mance and that something good would open up in the company for him soon. In the meantime, there was a staff assignment avail- able for him. Carl had seen enough project managers in the aero- space industry who had figuratively rotted on staff assignments when their projects were completed to be somewhat wary.

Questions 1. Was Linderman Industries’ adoption of project organization an

appropriate one for getting the Mexican subsidiary started? 2. In consideration of Robert Linderman’s letting the division

managers know that the project manager would be asking for some of their key people, why would Conway have any dif- ficulty in getting the ones he wanted?

3. Would you expect that many people would turn down a chance to join a project organization, as Bert Mill did?

4. Why would Conway take his problem with the engineering vice president to Linderman and have it resolved in his favor, yet back down in two disputes with the manufacturing vice president?

5. What could Linderman Industries have done to assure good jobs for the people coming off Project Mexicano, including Carl Conway, the project manager?

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Chatfield, Carl, and Timothy D. Johnson. Microsoft Project (2013) Step by Step. Redmond, WA: Micro- soft Press, 2013.

Goldratt, Eliyahu. Critical Chain. Great Barrington, MA: North River Press, 1997.

HBR Guide to Project Management. Watertown, MA: Harvard Business School Publishing Corporation, 2012.

Heagney, Joseph. Fundamentals of Project Manage- ment, 4th ed. New York: American Management Association, 2012.

Heldman, Kim. Project Management Jump Start, 3rd ed. New York: Wiley, 2011.

SELECTED BIBLIOGRAPHY AND FURTHER READINGS

Horine, Gregory M. Project Management: Absolute Beginner’s Guide, 3rd ed. Indianapolis: Que Pub- lishing, 2013.

Project Management Body of Knowledge, 5th ed. [A Guide to the Project Management Body of Knowl- edge]: PMBOK(R) Guide by Project Management Institute. Newtown Square, PA: Project Manage- ment Institute, 2013.

Wysoki, Robert K. Effective Project Management: Tra- ditional, Agile, Extreme, 6th ed. New York: Wiley, 2012.

B. “Smitty” Smith is a project manager for a large consumer electron- ics corporation. Although she has been with the company only four years, she has demonstrated an uncanny ability to bring projects in on time, meet technical specifications, and be close to budget. Her latest assignment is a project that will involve merging two existing technologies. She and her team have almost finished developing the proposal that will be presented to a management committee for approval. All that remains to be done is to develop a time estimate for the project. The team has to construct a network diagram for the project. It has three paths. The expected durations and standard deviations for the paths are listed in the following table.

CASE TIME, PLEASE

Path Expected Duration (weeks)

Standard Deviation

A 10 4

B 14 2

C 13 2

What project durations (in weeks) should Smitty include in the pro- posal for these risks of not delivering the project on time: 5 percent, 10 percent, 15 percent? What are the pros and cons of quoting proj- ect times aggressively? Conservatively?

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17 Project Management

Introduction
Project Life Cycle
Behavioral Aspects of Project Management
Reading: Project Managers Have Never Been More Critical
Work Breakdown Structure
Planning and Scheduling with Gantt Charts
Pert and Cpm
Deterministic Time Estimates
A Computing Algorithm
Probabilistic Time Estimates
Determining Path Probabilities
Simulation
Budget Control
Time–Cost Trade-offs: Crashing
Advantages of Using Pert and Potential Sources of Error
Critical Chain Project Management
Other Topics in Project Management
Project Management Software
Operations Strategy
Risk Management
Summary
Key Points
Key Terms
Solved Problems
Discussion and Review Questions
Taking Stock
Critical Thinking Exercises
Problems
Case The Case of the Mexican Crazy Quilt
Time, Please
Selected Bibliography and Further Readings