OM007

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 1/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

325

326

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 2/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

CHAPTER 13 Project Management

Learning Objectives

▪ Describe the need for project management and its use for administrative and clinical

operations.

▪ Review the information sources for project management in various health services

operations.

▪ Evaluate projects with PERT/CPM techniques.

▪ Recognize risk in project completion, and develop probabilistic methods.

▪ Describe the concept of project compression.

▪ Evaluate the cost/benefit of project compression.

Health care managers typically oversee a variety of operations intended to deliver health

services. Besides those, health care managers may work on projects that are unique and

nonroutine, designed to accomplish a specified set of objectives in a limited time. Projects

can be viewed as temporary endeavors undertaken to create new products and services

(Klastorin, 2004; p. 3). Typical examples of such nonroutine projects are moving a hospital

to a new location by a certain date or renovating an outpatient facility to meet changing

demand patterns. Projects like these have considerable costs. They involve a large number

of activities that must be carefully planned and coordinated to achieve the desired results,

and may take a long time to complete (Stevenson, 2002; pp. 766–767 and Kerzner, 2004; pp.

179–180).

327

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 3/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

Project management is an approach for handling these unique, one‐time endeavors that may have long or short time horizons, significant costs, and significant effects on the

organization's operation. Since these projects include many separate activities, planning

and coordination are essential to complete them on time, within cost constraints, and with a

high quality result.

Most projects are expected to be completed within time, cost, and performance guidelines,

meaning that goals must be established and priorities set. Tasks must be identified and time

estimates made. Resource requirements for the entire project have to be projected. Budgets

have to be prepared. Once under way, progress must be monitored to make sure that project

goals and objectives are met. Through the project approach, the organization focuses

attention and concentrates efforts on accomplishing a narrow set of objectives within a

limited time and budget.

Project management can be handled by assigning existing staff to the project for its

duration. However, problems arise if the project manager lacks expertise or continues to

have responsibility for other assignments, and also later when the individual or team must

be reintegrated into routine operations. For these and other reasons, often independent

consultants are hired to take over project management for the health care providers.

Whether projects are managed internally or externally, however, it is still important for the

managers in health care organizations to understand project management concepts, in

order to successfully manage internal projects and to understand the information presented

to them by outside consultants.

The Characteristics of Projects

Projects have phases: planning, execution of planned activities, and phase‐out. Those phases are known as a project's life cycle, and typically consist of four stages:

1. Formulation and Analysis: The organization recognizes the need for a project (for

example, the need to replace a health care facility with a more modern one) or

responds to a request for a proposal from a potential customer or client (for example,

expanding health care services to secure a new third‐party contract). The expected costs, benefits, and risks of undertaking the project must be analyzed at this stage.

2. Planning: At this stage, details of how the work will flow are hammered out and

estimates are made of necessary human resources, time, and cost.

3. Implementation: The project is undertaken; most of the time and resources for a project

are consumed at this stage.

327

328

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 4/36

4. Termination: The project is completed; tasks include reassigning personnel and dealing

with leftover and excess materials and equipment.

During the project's life cycle, a project brings together people with expertise and diverse

skills, who each become associated with only a portion of the project, rather than

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 5/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

its full scope. Their involvement relates to their specialized skills. To manage these diverse,

skilled personnel is a challenge that is the responsibility of the project manager.

The Project Manager

The central figure in a project is the project manager, who bears the ultimate responsibility

for its organization and completion. A project manager must be able to communicate

effectively among project team members and coordinate their activities to accomplish the

objectives.

Once the project is underway, the project manager oversees a range of support activities.

Both time constraints and costs must be managed so that the project is completed within the

projected time frame and budget. Open channels of communication must be maintained so

that everybody has the information they need to do their work. The quality of the work

done must be assessed constantly to ensure that performance objectives are realized.

Workflow must be managed so that activities are accomplished in the necessary sequence.

Meanwhile, the project manager must also communicate with external constituencies such

as regulatory boards, potential patients, subcontractors, and so on. Finally, it is important to

direct and motivate the diverse people working on the project, as well as coordinate their

activities (Stevenson, 2002; p. 769).

Managing Teams and Relationships on Projects

A project manager's job has its share of headaches as well as rewards. Personnel who are

loyal to their bosses in their own functional areas have to be motivated by the project

manager towards the project's unique goals. Since the team members report both to the

project manager and to their functional bosses, the task of managing personnel with two or

more bosses can be challenging indeed, especially with the dynamic and intelligent

workforce in health care. Supervisors often are reluctant to allow their employees to

interrupt their normal responsibilities to work on a project because their absence

necessitates training replacements. Training costs may be incurred for a replacement who

will work only over the project's life span, until the incumbent employee returns. In any

case, supervisors are reluctant to lose the output of valuable employees. The employees

themselves are not always eager to participate in projects because of the potential strains of

working under two bosses in a matrix type of organization. From the employee's

perspective, working on a project may disrupt daily routines and personal relationships. It

also raises a risk of being replaced in the original position.

328

329

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 6/36

Another potential strain arises from the fact that the personnel who work on a project

frequently possess specialized clinical knowledge and skills that the project manager lacks.

Yet, the project manager is expected to guide their efforts and evaluate their performance.

Apart from all these particular challenges, the environment in which project managers in

health care facilities work is constantly changing and filled with uncertainties, in spite of

which they must meet budgets and time constraints.

A project manager can, however, anticipate important rewards from adapting to and

overcoming the unique challenges of the job: the career benefits of being associated

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 7/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

with a successful project and the personal satisfaction of seeing it through to its conclusion.

Many people embrace the dynamic environment of a project as a welcome diversion from

routine tasks. They welcome the challenge of working under pressure and solving new

problems. Projects may also present opportunities to meet new people and increase future

job opportunities through networking. Project participants can point to a successful project

as a source of status among their fellow workers. Finally, projects frequently generate a

team spirit that increases the satisfaction of achieving project goals (Stevenson, 2002 pp.

770–772).

Although project managers aim to have smooth operations, conflicts can occur in various

areas: (A) priorities in scheduling and sequencing the tasks; (B) among the team members;

(C) budget and costs; and (D) other administrative and technical issues.

Planning and Scheduling Projects

Planning a project starts once its objectives have been established and the project manager

and major players of the team have been identified. For planning and scheduling the project

there are useful methodologies available. The Gantt chart, the Program Evaluation and

Review Technique (PERT), and the Critical Path Method (CPM) give project managers

graphic displays of project activities and allow calculation of a time estimate for the project.

Activities are project steps that consume resources and time. The crucial activities that

require special attention to ensure on‐time completion of the project can be identified, as well as the limits for how long others’ start can be delayed.

The Gantt Chart

The Gantt chart is useful for scheduling project activities in the planning stage and then

monitoring them by comparing their actual progress to planned progress. We will illustrate

a Gantt chart, launching a new radiation oncology service, with the list of necessary

activities and their duration, in Exhibit 13.1.

The Gantt chart depicts the duration of this project as sixty‐four weeks; however, not all the activities occur at the beginning. For example, contractor selection—activity C—does not

start until land has been acquired and a radiation oncologist hired—activity B. For certain

decisions, the input of key personnel for the new service must be considered; dependency

relationships exist among the activities. Some activities cannot start until after others are

finished. Yet certain activities can be carried out parallel with others. For example, activities

D and E can be carried out during the same time frame. What other activities in this

329

330

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 8/36

example can be carried out simultaneously? Since a Gantt chart displays the information on

a time scale, project managers can report the activities to their internal and external

constituencies during their implementation. They also can monitor the work of the

subcontractors for conformity to the schedule.

The Gantt chart's display of the schedule of activities is based on their sequential

relationships, and those are identified during the formulation phase of the project. They are

called dependency or precedence relationships. The activity precedence relationships for

the example of the radiation oncology facility are identified in Table 13.1.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 9/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

EXHIBIT 13.1. Gantt Chart for Launching a New Radiation Oncology Service.

This table displays the crucial information that structures the project, so that an activity

cannot be started until after a previously necessary activity has been done. Similarly, those

activities that can be performed simultaneously are identified.

Table 13.1 shows that activities A and B start around the same time and are followed by

activity C. Activities D and E follow activity C and also should start at around the same time.

Those two activities are followed by activities F and G, which should start simultaneously.

Finally, activities F and G lead to activity H, the last activity, which will complete the project.

330

331

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 10/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

TABLE 13.1. Activity Precedence Relationships.

An obvious advantage of a Gantt chart is its simplicity, which makes it a very popular

management tool. However, Gantt charts cannot depict other chronological relationships

among the activities that also affect whether the project is done on time and successfully.

For example, a Gantt chart cannot show a health care manager how a delay in one of the

early activities will affect later activities. Conversely, some activities may be safely delayed

without affecting the overall project schedule, but the health care manager cannot see that

from a Gantt chart. This tool is most useful, then, for simple projects or for the early

planning on more complex projects.

PERT and CPM

331

332

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 11/36

Program Evaluation and Review Technique (PERT) and the Critical Path Method (CPM) are

tools for planning and coordinating large projects. Project managers can graph the project

activities, estimate the project's duration, identify the activities most critical to its on‐time completion, and calculate how long any activity can be delayed without delaying the project

(Stevenson, 2002; p. 775).

PERT and CPM were developed independently in the late 1950s. Initially, PERT was

developed by the U.S. government and private contractors in order to speed up weapons

development, because it was believed then that the Soviet Union was ahead of the United

States in their missile programs. CPM was developed by Du Pont and Remington Rand

Corporation to plan and coordinate maintenance projects in chemical plants (Stevenson,

2002; pp. 770–772). PERT considers the probabilistic nature of

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 12/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

completion times. CPM is used mostly for deterministic problems. Both methods, however,

have common features for scheduling project tasks. For instance, the project manager must

use the precedence information to visualize a network of activities, which can be

accomplished in a couple of ways.

The Network

A network is a diagram of project activities and their precedence relationships, as shown

with arrows and nodes. An activity represented by an arrow is called activity on arc

(arrow), or AOA. An activity also can be represented by a node (a circle) and is then called

an activity on node, or AON. Although in practice both representations are used, most

project management computer programs are designed using an AON network because of its

simplicity. To represent certain precedence relationships in AOA networks, a dummy arc

with no time (or resource) must be used, which certainly may confuse nontechnical users.

Figure 13.1 illustrates the conventions used for activity on arc and activity on node

networks. Three activities, A, B, and C are to be completed for the project. Activities A and B

start and finish at the same time; activity C cannot start until A and B have been finished. In

Figure 13.1, diagram (a) shows the conceptualization of these activities; diagram (b)

represents the activity on arc (AOA); and diagram (c) represents the activity on node (AON).

The activities in the AOA diagram show the consumption of resources and time. Nodes that

appear in the AOA approach represent the beginnings and completions of activities, which

are called events; since events are points in time,

332

333

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 13/36

FIGURE 13.1. Network Representations.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 14/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

they do not consume resources or time. However, when the events are represented by

nodes in the AON diagram, they do represent resource and time consumption.

Most computer programs identify activities by their endpoints; so without dummy

variables, activities sharing the same endpoints could not be separated, even if they had

quite different expected durations. The AON approach usually uses more nodes, but it

eliminates the need for dummy activities. In practice, both approaches are used; neither is

more effective than the other. Most PERT/CPM computer programs can process either

method. Often the choice depends on personal preference or established procedures.

However, the AON convention is probably simpler for nontechnical users and is used in this

text.

Projects are analyzed on the basis of the information that is available. If activity times and

resource consumption are fairly certain, a deterministic analysis called the critical path

method would be appropriate. On the other hand, if the activity times and resources are

subject to variation, that leads also to variation in the project's completion, so in that case a

probabilistic approach must be used.

Critical Path Method (CPM)

Let us consider the radiation oncology example presented earlier to illustrate the CPM

method. Figure 13.2 displays the network diagram of this project using the activity on node

convention and the precedence relationship displayed in Table 13.1.

One of the main features of a network diagram is that it shows the sequence in which

activities must be performed. On AON networks, it is customary to add a start node

preceding the activities to mark the start of the project, and an end node to mark its

conclusion. Figure 13.2 shows that activities A and B must be completed before activity C

can begin, and activities D and E cannot be started until activity C is finished. In ensuing

sections, activities F and G cannot start before activities E and D are finished. Finally,

activity H can start once activities F and G are finished.

333

334

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 15/36

FIGURE 13.2. AON Network Diagram for Radiation Oncology.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 16/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

A path is a sequence of activities that leads from the start node to the end node. The

radiation oncology project has eight paths, as follows:

1) A‐C‐D‐F‐H 2) A‐C‐D‐G‐H 3) A‐C‐E‐F‐H 4) A‐C‐E‐G‐H 5) B‐C‐D‐F‐H 6) B‐C‐D‐G‐H 7) B‐C‐E‐F‐H 8) B‐C‐E‐G‐H

The length of time for any path is found by summing the times of the activities on that path.

The time lengths for these eight paths, using times from Exhibit 13.1, are calculated and

shown in Table 13.2.

The critical path, or the path with the longest time, is the most important: it defines the

expected project duration. Paths that are shorter than the critical path could

334

335

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 17/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

encounter some delays without affecting the overall project completion time, as long as the

highest possible path time is defined by the length of the critical path.

TABLE 13.2. Path Lengths for the Radiation Oncology Project.

In this example, path 8 (B‐C‐E‐G‐H) is the critical path, with a total project completion time of sixty‐four weeks. All activities on the critical path are known as critical activities.

The path sequences given in the above example would not be apparent in a computer

program. In order for a program to identify paths, an algorithm is used to develop four

critical pieces of information about the network activities:

ES: the earliest time an activity can start, if all preceding activities started as early as

possible

335

336

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 18/36

LS: the latest time the activity can start and not delay the project

EF: the earliest time the activity can finish

LF: the latest time the activity can finish and not delay the project

Figure 13.3 shows that nomenclature, which this text uses to display those four times in a

network diagram.

By computing the ES, LS, EF, and LF, one can determine the expected project duration,

critical path activities, and slack time.

FIGURE 13.3. Activity Start and Finish Times.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 19/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

Computing ES and EF Times

Two simple rules compute the earliest start and finish times:

1. The earliest finish time (EF) for any activity is equal to its earliest start time plus its

expected duration, t:

2. The earliest start time (ES) for activities at nodes with one entering arrow is equal to the

earliest finish time (EF) of the entering arrow (the preceding activity). ES for activities

leaving nodes with multiple entering arrows is equal to the largest EF of the entering

arrow.

Computing LS and LF Times

The two rules for computing the latest starting and finishing times are as follows:

1. The latest starting time (LS) for each activity is equal to its latest finishing time minus its

expected duration:

2. For nodes with one leaving arrow, the latest finish time (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 the leaving arrows.

To find ES and EF times, move forward from left to right through the network; to find LS

and LF times, move backward from right to left through the network. Begin with the EF of

the last activity and use that time as the LF for the last activity. The LS for the last activity is

found by subtracting its expected duration from its LF. Figure 13.4 shows the calculated ES,

LS, EF, and LS times for each activity. All project management software reports these values;

nevertheless, the reader is encouraged to calculate a few to gain practical experience.

The allowable slippage of time for an activity, as well as for a path, is called slack. The slack

for an activity is the difference between the latest start time and the earliest start time. It

can also be computed by taking the difference between the latest finish time and the earliest

finish time. Slack for a path is the difference between its length and the length of the critical

336

337

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 20/36

path. The critical path has zero slack: all activities must start and finish at their allotted

times. Formally, two ways to compute slack time are:

or

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 21/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

FIGURE 13.4. Excel Setup and Solution to the Radiation Oncology Project, CPM Version.

The four algorithms discussed previously can be used to find the critical path of a network

diagram. Any activities with zero slack time are on the critical path. Knowledge of slack

times lets project managers plan with more flexibility as well as detail for how to allocate

scarce resources. They can focus efforts on those critical path activities that have the

greatest potential for delaying the project. It is important to recognize that activity slack

times are calculated on the assumption that all the activities on the same path will start as

early as possible and not exceed their expected durations. Figure 13.4 depicts the Excel

solutions to the example of the radiation oncology project.

Probabilistic Approach

Many real‐life project networks are much larger than the simple network illustrated in the preceding example; they often contain hundreds or even thousands of activities. Because

337

338

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 22/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

the necessary computations can become exceedingly complex and time‐consuming, large networks are usually analyzed by computer programs rather than manually.

Often situations arise when health care managers cannot estimate activity times with

certainty. Such situations require a probabilistic approach, which uses three time estimates

for each activity instead of one:

1. Optimistic time (o): the length of time required under the best conditions.

2. Pessimistic time (p): the length of time required under the worst conditions.

3. Most likely time (m): the most probable length of time required.

These time estimates can be made by health care managers or by others knowledgeable

about the project: contractors, subcontractors, and other professionals who have completed

similar tasks or project components. They also could provide time and cost estimates for

each task they are familiar with. Care should be taken to make the estimates as realistic as

possible. The values can then be used to find the average or expected time for each activity

t , and the variance of each activity time, σ2. That calculation uses a beta distribution,

where the expected time (mean) is computed as a weighted average of the three time

estimates:

The standard deviation of each activity's time is estimated as one‐sixth of the difference between the pessimistic and the optimistic time estimates. The variance is then found by

squaring the standard deviation:

The size of the variance reflects the degree of uncertainty about an activity's time; the larger

the variance, the greater the uncertainty. After completing the average time estimates and

the variances for each activity, the analysis returns to the paths in the project network, since

completing a project on time depends on the path completion times. The completion time

for any path is a simple sum of all activity time estimates:

The standard deviation of the expected time for each path can also be computed, by

summing the variances of the activities on a path and then taking the square root of that

338

339

e

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 23/36

number:

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 24/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

Once the probabilistic expected path times and their standard deviations are determined, a

health care manager can calculate the probability that the project will be completed by a

specified time, as well as the probability that it will take longer. Probabilistic estimates in

network diagrams are based on the assumption that the duration time of a path is a random

variable that is normally distributed around the expected path time. That follows from the

fact that activity times (random variables) are being summed and that sums of random

variables tend to be normally distributed when the number of items (here, project

activities) is large, as is frequently the case with PERT projects. Even when the number of

items is relatively small, the normal distribution provides a reasonable approximation of

the actual distribution.

For probabilistic time estimates, it is assumed that path duration times are independent of

each other, meaning activity times are independent of each other and that each activity is

on only one path. The reason for using the independence assumption is simple: finding the

probability of when an individual path will be completed makes sense only if that path's

activities are independent of other paths. In a large project with many paths, the

independence assumption is considered to be met if only a few activities are shared among

paths. Project managers use common sense to decide whether the independence

assumption is justified.

One final, important point before looking at a probabilistic network example: sometimes a

path other than the critical path takes longer to complete, making the project run longer

than expected. Therefore, it can be risky to focus exclusively on the critical path. Health

care managers must always consider the possibility that at least one other path will delay

the overall completion of the project beyond the expected time. They therefore should

compute the probability that all paths will finish by a specified time. To do that, find the

probability for each path finishing by its specified time and multiply the resulting

probabilities to find the joint probability of timely completion.

The probabilistic PERT concepts are illustrated in Example 13.1 using the earlier radiation

oncology case adapted to probabilistic time outcomes.

339

340

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 25/36

Example 13.1

In planning for a new radiation oncology clinic, project managers determined that due to

the nature of some of the activities, time estimates vary. After consulting with experts in

each of the activity areas, they have calculated the optimistic, pessimistic, and most likely

time estimates, in weeks, as shown in Table 13.3.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 26/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

TABLE 13.3. Probabilistic Time Estimates for Radiation Oncology Clinic.

The network diagram for this project was shown in Figure 13.2, and the paths and activities

for each path were shown in Table 13.2. In order to calculate project completion time

probabilities, first we must calculate the expected time and variance for each activity and

path. Table 13.4 displays the calculations for each activity and path: the means (t ) and

standard deviations (s) for all eight possible paths for the project. Given this information,

the health care project manager can develop probabilistic estimates for the completion of

the project, for various specified opening times or target dates (t ). The expected completion

times of paths (t ) vary from forty‐six (ACDFH) to sixty‐four (BCEGH) weeks. Therefore, in calculating the project completion probabilities for a target date, all paths must be

considered, especially those closest to the critical path.

340

341

e

s

path

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 27/36

Although we computed each activity's mean and variance using a beta distribution, path

means and variances, on the other hand, are normally distributed (having many activities

approximates to normality by invoking the central limit theorem). The critical path in this

example is path 8 (BCEGH), which has the longest expected completion time. Besides that,

the expected time can go beyond sixty‐four weeks because of variation (standard deviation of approximately five weeks). That is, if sixty‐four weeks is the average completion time (t ), that indicates 50 percent completion probability under the normal curve. For an additional

five weeks (one standard deviation, or

e

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 28/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 29/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

z = 1), or specifically by week sixty‐nine (t ), the project completion probability can be improved to 84 percent. Figure 13.5 illustrates this concept. Completion probability nears

100 percent when the standard deviate z is 3.5 or more.

TABLE 13.4. Calculation of Expected Time and Standard Deviations on Each Path for the Radiation Oncology Clinic.

341

343 s

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 30/36

Again, note that each path's expected duration time is assumed to be independent, that is,

each activity is on one path, and activity times are independent of each other. However, if a

few activities are on multiple paths, we can assume a weak independence.

Table 13.5 depicts the calculation of z‐values for each path in the example, for sixty‐five weeks as the targeted completion time. As can be observed, paths 1 through 4 have z‐values

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 31/36

greater than 2.5, so those paths should have no significance for completion of other paths.

To observe the impact of the remaining four paths (5 through 8), we can calculate the

probabilities, as shown in Figure 13.6.

The last step in the analysis is the computation of joint probability, that is, we are interested

in the joint effect of all the paths on the completion of the project. This is a simple

multiplication of the completion probabilities of the significant paths (paths 5 through 8).

The probability of completion of this project within sixty‐five weeks is:

P (completion by sixty‐fifth week) = .9082 ×.7881×.7852×.5793 = .3255 or 32.5 percent.

FIGURE 13.5. Project Completion Probabilities by the Specified Time.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 32/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

TABLE 13.5. Path Completion Probabilities.

343

344

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 33/36

FIGURE 13.6. Completion Probabilities for Sixty - Five Weeks.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 34/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

Similarly, one can compute the probability of completion for other target days such as sixty‐ six, sixty‐seven, and seventy weeks.

P (completion by sixty‐sixth week) = .9345 × .8365×.8389 × .6700 = .4394 or 43.9 percent.

P (completion by sixty‐seventh week) = .9545 × .8770×.8830 × .7486 = .5533 or 55.3 percent.

P (completion by seventieth week) = .9871 × .9573×.9625 × .8869 = .8066 or 80.7 percent.

The Case of a Dominant Critical Path

If a critical path is dominant (no other paths are significant for completion probabilities),

then joint probabilities need not be calculated. In such a case, software programs can

calculate the completion probabilities for any number of targeted completion times. The

Excel solution to the probabilistic radiation oncology project is shown in Figure 13.7. Figure

13.7 also depicts the solution for P (completion by the sixty‐fifth week) as 58% and the completion time for target probability of 95% as about seventy‐two weeks.

344

345

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 35/36

FIGURE 13.7. Excel Setup and Solution to the Probabilistic Radiation Oncology Project.

Source: Screen shots reprinted by permission from Microsoft Corporation.

10/17/2018 Book Excerpt: Quantitative Methods in Health Care Management - OM007: Project Management

https://tempolearning.brightspace.com/d2l/le/content/6954/viewContent/6629/View 36/36

PRINTED BY: [email protected]. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

345

346