QSO 420 ( week 4)

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◀ C h a p t e r t w e n t y-t h r e e ▶

Challenging and engaging Questions and exercises

Logic problems are a unique way of learning how to apply project management princi- ples to project situations. They are enjoyable and entertaining. Include these problems in your project management studies to enhance the learning experience.

▶ how to Solve Logic problems

To solve logic problems, the wording in the clues must be read carefully. All of the necessary information is provided in the clues, and trial-and-error solutions are not necessary. The problems can be solved with simple logic. In some cases, grids are pro- vided. Below is the technique for solving the grid problems.

◾ Sample Logic problem

Three married couples live in three different cities and each couple has a different num- ber of children. The husbands are Alfred, Dirk, and Mickey. The wives are Annette, Barbara, and Cathy, but they are not necessarily married to the husbands according to the order of the husbands’ names. The three cities in which the couples live are Boston, Chicago, and Denver, and the numbers of children are one, two, and three. In completing the table below, we will use a “•” to signify “yes” and an “X” to signify “No.”

Clues

1. Barbara and Mickey are a couple but do not live in Chicago.

2. One of the couples, which does not include Annette, lives in Boston with their three children.

3. Alfred and his wife live in Denver; they have more than one child.

4. Cathy’s husband’s first name begins with an initial that appears later in the alpha- bet than Cathy’s first name initial

For additional problems, see Kerzner, H., Logic Problems for Project Managers (Hoboken, NJ: John Wiley & Sons, 2006).

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◾ explanation

From clue 1, Barbara and Mickey are husband and wife. So, a “•” can be placed at the intersection and the other cells have an “X.” Likewise, because they do not live in Chicago, we can place an “X” in that location as well, and any other locations that relate Barbara or Mickey to Chicago. This is shown in the figure below.

With clue 2, we can signify a “Yes” in the box that signifies the intersection of Boston and three children, and also a “No” for the Annette location in that column. This is shown below.

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Using clue 3, we can place a “Yes” in the intersection of Alfred and Denver, and the corresponding cells will then have a “No” response. We can also elimi- nate the one child cell from the Alfred row and the Denver column. The result is shown below.

Now notice that in the cells that relate husbands and cities, we know that Dirk must reside in Chicago and Mickey must reside in Boston. Also, Mickey must live in Boston with three children. The results are shown below.

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We also know from this figure that the city in which the couple has two children is Denver. This is represented in the figure below.

Now using clue 4, we know that Cathy cannot be married to Alfred. Therefore, we can complete the figure as shown below.

We now know the solution to the problem:

■ Alfred and Annette live in Denver with two children.

■ Mickey and Barbara live in Boston with three children.

■ Dirk and Cathy live in Chicago with one child.

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Sometimes, you may have to go back over the clues a second or third time to extract more information. However, guessing is never required and logic must prevail.

For other types of logic problems, the difficulty is in knowing which clue or clues to start with. Since this may be more complex, hints are provided to assist you.

Now it’s your turn to demonstrate your decision-making skills. Good luck!

▶ Logic problem #1: types of Contracts

In the figure below are six different contract types for six different project managers. From the clues under the figure, determine the contract type for each project manager and their position in the figure. Knowledge of each type of contract is essential to solve the problem.

Project Manager: Jane, Richard, Paul, Frank, Tim, Alice

Contract Type: Cost plus percentage of cost (CPPC), firm fixed price (FFP), cost plus incentive fee (CPIF), fixed price incentive fee (FPIF), cost plus fixed fee (CPFF), time and materials (T & M)

Clues:

1. The contract type that today is illegal in the government is located in position 4 in the diagram.

2. Tim’s project has a contract that contains a “ceiling” and “floor” on profits.

3. Alice’s contract is in an even-numbered position in the diagram.

4. The two incentive-type contracts are located in different rows in the figure and hor- izontally adjacent to only one other contract and both of the adjacent contracts are for projects managed by female project managers.

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5. Frank’s project, which is not in position 3, and Richard’s project are not adjacent to each other either horizontally or vertically, and are located in different rows.

6. The contract type with the maximum risk exposure to the seller is to the right (as you look at the figure) and next to the cost-plus contract, where the fee is defined as a dollar value rather than as a percentage, and above the contract type that con- tains a “point of total assumption” term.

▶ Logic problem #2: the Mysterious network Diagram

A project manager discovers that his team has neglected to complete the network dia- gram for the project. The network diagram is shown below. However, the project man- ager has some information available, specifically that each activity, labeled A–G, has a different duration between one and seven weeks. Also, the slack time for each of the activities is known as shown below.

Duration (weeks): 1, 2, 3, 4, 5, 6, 7 Slack time (weeks): 0, 0, 0, 2, 4, 4, 7

Using the clues provided below, determine the duration of each activity as well as the early start, early finish, latest start, and latest finish times for each activity.

Clues

1. Activity E is on the critical path.

2. The early start time (ES) for Activity F is five weeks.

3. The duration of Activity B is seven weeks.

4. Activity D has four weeks of slack, but Activity F has the greatest amount of slack.

5. The early finish time (EF) for Activity G is 17 weeks.

6. The latest finish time (LF) for Activity E is 13 weeks.

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Activity Duration Early Start Early Finish Latest Start Latest Finish

▶ Logic problem #3: the Incomplete Status report

As a continuation of Logic Problem #2, you also discover that the status report for your project is somewhat incomplete. The status report is shown below. From the clues provided, complete the status report.

Clues

1. For Activity B, PV = $100

2. For Activity C, EV = $200

3. For Activity D, AC = $300

4. Activity A has not started yet.

5. For all of the activities EV (Total) = $930

Activity PV EV AC SV CV

A ($100) 0

B 50 60

C 60 60

D 100 80

E 120 (20)

Total

▶ Logic problem #4: another Mysterious network Diagram

Duration (weeks): 1, 2, 3, 4, 5, 6, 7

Slack time (weeks): 0, 0, 0, 1, 1, 3, 7

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Using the clues provided below, determine the duration of each activity as well as the early start, early finish, latest start, and latest finish times for each activity.

Clues

1. Activity E is the longest-duration activity and is on the critical path, which is the unlucky number 13; also, there is only one critical path.

2. The early finish time (EF) for Activity F is eleven weeks.

3. The latest start time (LS) for Activity D is nine weeks.

4. If Activity A slips by one week, it will be on a critical path.

Activity Duration Early Start Early Finish Latest Start Latest Finish

▶ Logic problem #5: another Mysterious network Diagram

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Duration (weeks): 1, 2, 3, 4, 5, 6, 7 Slack time (weeks): 0, 0, 0, 3, 6, 8, 8

Using the clues provided below, determine the duration of each activity as well as the early start, early finish, latest start, and latest finish times for each activity.

Clues

1. There exists only one critical path and it is the largest possible number given the possible durations shown.

2. Activity E has the smallest amount of slack that is greater than zero.

3. The early finish time (EF) for Activity A is four weeks and this does not equal the latest finish time (LF). (Note: There is no negative slack in the network.)

4. The slack in Activity C is eight weeks.

5. The duration of Activity F is greater than the duration of Activity C by at least two weeks.

Activity Duration Early Start Early Finish Latest Start Latest Finish

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▶ answers

◾ Logic problem #1

Position #1: Paul; CPIF Position #2: Alice; CPFF Position #3: Richard; FFP Position #4: Frank; CPPC Position #5: Jane; T & M Position #6: Tim; FPIC

◾ Logic problem #2

Activity Duration ES EF LS LF

A 3 0 3 4 7

B 7 0 7 0 7

C 5 0 5 2 7

D 2 7 9 11 13

E 6 7 13 7 13

F 1 5 6 12 13

G 4 13 17 13 17

◾ Logic problem #3

Activity PV EV AC

A 100 0 0

B 100 150 90

C 140 200 140

D 280 380 300

E 80 200 220

700 930 750

◾ Logic problem #4

Activity Duration ES EF LS LF

A 4 0 4 1 5

B 2 0 2 3 5

C 5 0 5 0 5

D 3 2 5 9 12

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Activity Duration ES EF LS LF

E 7 5 12 5 12

F 6 5 11 6 12

G 1 12 13 12 13

The critical path is thirteen weeks. Activity F has an early finish time of eleven weeks, but Activity F cannot be on the critical path because there is only one critical path, and Activity E is on the critical path. Therefore, Activity G must have a duration of one week. We now know ES, EF, LS, and LF for Activity E. Because Activity F has an EF of eleven weeks, the durations of Activities C and F must be eleven weeks, and therefore five and six weeks. Activity C must be five weeks to align with the ES of five in Activity E. If Activity C were six weeks in duration, the length of the critical path could not be thirteen weeks. Using clue 3, and knowing that LF of Activity D must be twelve weeks, the duration of Activity D must be three weeks. Using clue 4, which tells us that Activity A has only one week of slack, and knowing that the LF for activity A is five weeks, the duration of Activity A must be four weeks.

▶ Logic problem #5

Activity Duration ES EF LS LF

A 3 0 3 4 7

B 7 0 7 0 7

C 5 0 5 2 7

D 2 7 9 11 13

E 6 7 13 7 13

F 1 5 6 12 13

G 4 13 17 13 17

From the clues, Activities A, C, and E have slack. Activity F must also have slack since Activity C is on a path with it. Therefore, the critical path must be B-D-G. Since Activity C has eight weeks of slack, Activity F must also have eight weeks of slack, which means, by elimination, that Activity A has six weeks of slack and the duration for Activity A must be four weeks. From clue 1, the critical path, which must have three and only three activities in it, must be the numbers five, six, and seven, and must be equal to eighteen weeks. From clue 5, the duration for Activity F must be three weeks and Activity C must be one week. Therefore, Activity E must be two weeks in duration. Now we can calculate ES, EF, LS, and LF for Activities C and F. Since the length of the critical path is eighteen weeks, we now know that the duration of Activity G must be six weeks. After calculating ES, EF, LS, and LF for Activity E, we know that the duration of Activity B must be seven weeks.

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▶ Challenging Questions and scenarios

exam tip

The PMP® exam and the CAPM® exam will include several questions regarded as “challenging” and scenario-based. These are questions where a situation is provided and the basic question asks, “What should the proj- ect manager do next?” or “What will most likely happen next?” or “What tool would be most appropriate to use?” Consider the following examples. They will assist you in your exam preparation and help to further enhance your existing project management skills.

The following questions are designed to improve your ability to assess a situation from a project manager’s perspective and determine the most appropriate response or action.

Example #1: You hire a contractor to perform several activities on your project. After a period of time, the contractor informs you that they are running late. What should the project manager do next? Your choices are:

a. Call a meeting with the contractor.

b. Call a meeting with the executives in the contractor’s company.

c. Look at the penalty clauses in the contract.

d. Implement the risk management plan.

On the surface, it appears that you could argue any of the answers as being the correct answer. That’s because we have a tendency to make assumptions and read things into the wording of the question, things that aren’t there. The correct answer is to call a meeting with the contractor. After all, you cannot make a decision with- out gathering the facts first, and having a meeting with the contractor allows you to gather the facts.

Example #2: Let’s use the same scenario as in Example #1, but in this case the contractor informs you that they have no chance of catching up on the schedule. In this case, you might be able to justify any of the four answers, but some additional infor- mation may need to be provided to differentiate between the answers. If no additional information is provided, then implementing the risk management plan may be correct.

For each of the following questions, pick the correct answer assuming the question asks, “What should the project manager do next?”

1. One of your contractors is running late and presents to you a plan to get back on schedule. The plan calls for running 10 tests rather than the 15 tests that are called

PMP and CAPM are registered marks of the Project Management Institute, Inc.

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out in the contractual requirements plan. The contractor believes this will save you money as well.

a. Agree to it quickly to maintain the schedule and reduce costs.

b. Ask your sponsor to make the decision.

c. Tell the contractor that you cannot violate requirements.

d. Ask the contractor to put it in writing, and present the recommendation to the change control board.

2. Your project is behind schedule. You just learned that another project in the com- pany is further behind schedule than your project and senior management has instructed the functional managers to remove some of the resources from your project to see if they can be of assistance on the other project.

a. Begin looking at contingency plans and alternatives.

b. Meet with the executives and plead your case.

c. Meet with the functional managers and plead your case.

d. Ask your customer to plead your case with the executives.

3. Paula is an important member of your project team. She informs you that the com- pany approved her application for tuition reimbursement to attend the MBA pro- gram at a local university. Most of the courses are in the evenings, but there may be one or two courses that meet in the mornings twice a week. You must sign off on this request because it could impact your project.

a. Refuse to let Paula attend the program until the project is completed.

b. Let Paula attend the program but replace her as a member of the project team as quickly as possible.

c. Discuss with Paula the options for attending class and still maintaining her performance on the project team.

d. Let the project sponsor make the final decision.

4. You hire a contractor to work on your project. In order for the contractor to per- form correctly, your team must exchange some company proprietary information with the contractor. To make sure this flows smoothly you should:

a. Personally brief the team on the techniques for disclosing proprietary information.

b. Ask the sponsor to debrief the team on the company’s policy for disclosing proprietary information.

c. Ask a representative from the legal group, or whoever is the company expert in proprietary information, to make the presentation.

d. Ask the team to read the confidentiality agreement that was part of the contract.

5. You have asked the team to voluntarily work a significant amount of overtime to maintain the project’s schedule. You discover that one of the members of the team, while working overtime, inadvertently used the wrong lot of raw materials

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during a production run and all of the units produced had to be thrown away. The loss was $75,000 and the production run had to be redone. Management has convened a meeting with you and the team to discuss what went wrong and who should be blamed.

a. At the beginning of the meeting, you should take personal responsibility for what happened without disclosing the name of the person who made the mistake.

b. At the beginning of the meeting, you should take personal responsibility for what happened and identify the person who made the mistake.

c. Say nothing. Let the executives run the meeting and see what develops.

d. Ask the team member who made the mistake to immediately step forward and explain what happened.

6. You are working on a firm-fixed-price contract. At the end of the first month, you provide the client with project performance reports that were generated from your enterprise project management methodology. The format of each report is standardized and used on all contracts. The client informs you that they want the reports modified to better fit their needs. There is a significant cost for modifying the reports, and you are unsure about whether the client would be willing to pay for the modifications.

a. Submit a change request to the client asking for payment for the modification. If the client refuses to pay, then refuse to make the modifications.

b. Make the modifications and then submit a change request to the client for payment.

c. Refuse to make the changes since you already have a signed contract.

d. Ask your sponsor for advice in this matter. There may be other factors, such as enterprise environmental factors, that you may not know about.

7. During an interface meeting with the client, one of your highly competent team members acts in an arrogant and disruptive manner to the point where the cus- tomer becomes upset. After the interface meeting is over, the customer requests that this person be removed from the project team so that the customer will no lon- ger have to interface with this person.

a. Grant the customer’s request and remove the person from the team.

b. Counsel the person and see if there is a way that he can change his behavior.

c. Explain the situation to the sponsor and ask for advice.

d. Talk to the functional manager first to see if a replacement exists in case this person must be removed.

8. After an interface meeting with the client from a foreign country, you and your wife along with the client and his wife are dining at an elegant restaurant celebrat- ing how successfully the project is progressing thus far. During dinner, the client’s wife presents your wife with a gift of jewelry. The gift is composed of precious stones native to the client’s country. You company has a policy that all gifts under $1000 need not be reported. You believe that this gift is less than $1000 in value, but you are unsure.

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a. Refuse to accept the gift since it may violate company policy.

b. Accept the gift but do not report the gift since it was given to your wife rather than you.

c. Accept the gift and report it to your company even though you do not believe its value is over the $1000 limit.

d. Explain the gift acceptance policy to you client and tell him that you cannot accept the gift until after discussions with your legal department.

9. Your external client has assigned an onsite representative to monitor the perfor- mance of the contract. All reports are provided to the onsite representative who reviews the reports for accuracy and then forwards the reports to his parent com- pany. After reviewing one of the reports, the onsite representative asks you to make changes to one of the reports by including some false statements. The false state- ments will make the onsite representative look good in the eyes of his boss.

a. Make the changes as long as no damage is done to the project but do not leave an audit trail of what happened.

b. Make the changes and prepare an audit trail in case questions arise in the future.

c. Refuse to make the changes.

d. Discuss this with your sponsor and possibly corporate legal before responding to the onsite representative.

10. During project staffing activities, one of the functional managers informs you that she will not have available all of the resources she would need for your project when you need the resources because of resource requirements for other projects. When the project was initially approved, she estimated that she would use eight people, and they would be available at the right time. Now, because some of the other projects are delayed, she has only five people available.

a. Send her a memo demanding the eight people she promised you.

b. Ask for a meeting with her to discuss options and contingency plans.

c. Ask your sponsor to step in and get you the resources you need.

d. Delay the start date of the project until you have firm commitments from all functional managers.

▶ answers to Challenging Questions

1. The correct answer is d. Any and all changes to the scope baseline should be in writing and approved by the change control board.

2. The correct answer is a. This is reality in project management. Before asking for help from above, you must assess the risks to your project and see what options or contingency plans are available.

3. The correct answer is c. Project managers must show a concern for people and help them satisfy their personal needs and ambitions. You must first discuss this with Paula to make sure that she can still perform her job as expected.

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4. The correct answer is c. Project managers are not always professionally trained in the legalities of protecting proprietary information. Whoever the expert is in the company should brief the team on the protocols.

5. The correct answer is a. You created the problem by asking people to work exten- sive overtime. Extensive overtime is an invitation for mistakes. Project managers should try to protect the people on their team when mistakes are made. Answer a is what the project manager should do first to diffuse the situation. Of course, senior management may wish to dig deeper.

6. The correct answer is d. Your sponsor may view this as goodwill and desire to absorb the cost internally. Your sponsor may ask you to submit a change request to the client. But the first step would be to approach the sponsor for advice to make sure you understand all of the ramifications.

7. The correct answer is d, but answer b runs a close second. Project managers may not have the authority to remove someone from the project team without support from the functional manager. In any event, there must be a replacement.

8. The correct answer is c. It can never be wrong to report the gift to your company and let them tell you how to proceed.

9. The correct answer is d. This is a situation where your sponsor and corporate legal should be involved before you take any action. You need allies and there may be a company policy already established on how to handle these types of situations.

10. The correct answer is b. The first step should be to discuss this with the functional manager that controls the resources.

▶ Matching (Memory Jogger) exercises

Memory jogger and matching the terms exercises provide you with an opportunity to “flex” your brain and help you to recall the connection between terminology, acronyms, and processes. You may have noticed that the “language” of project management is unique, and it is helpful to become very familiar with the lexicon used by most project managers.

The following items are three matching terms or memory jogger exercises. In each exercise, select a letter from the right hand column that best matches the left hand col- umn. Although it may appear that more than one answer is correct, select one and only one answer. At the end of the exercise, make sure that each of the letters A–U appears once and only once. You may wish to review the PMBOK® Guides’ dictionary of terms for precise definitions.

PMBOK is a registered mark of the Project Management Institute, Inc.

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◾ Matching (Memory Jogger) exam a

1. Progress, status and forecast A. Request for quotation

2. Reduce functionality B. A risk reduction process

3. Assumptions C. Information gathering process

4. RFQ D. Time a task can slip

5. Code of accounts E. Person/organization providing project funding

6. Mitigation F. Project management information system

7. Workaround G. Factors considered to be true

8. PMO H. Accelerate task start time

9. Delphi technique I. Soft logic

10. Float J. Performance reports

11. Virtual team K. Total quality management

12. CV L. Project or program management office

13. Discretionary dependency M. Grouping of charge numbers

14. RAM N. Acquirer of goods or services

15. Lead O. Responsibility assignment matrix

16. CCB P. Detailed project description

17. Scope statement Q. Schedule compression technique

18. TQM R. Change control board

19. Buyer S. Remotely located team members

20. PMIS T. Response mechanism to an unfavorable risk

21. Sponsor U. Cost variance

◾ Matching (Memory Jogger) exam B

1. Project charter A. Cost performance index

2. Mandatory dependency B. Required delay or elapsed time

3. EAC C. Total quality management

4. Acceptance criteria D. Schedule variance

5. Bottom up and parametric E. Restriction

6. Scope baseline F. Schedule compression technique

7. Constraint G. Characterization of the product/scope

8. COQ H. Cost estimating techniques

9. Contract I. Initiates the project

(Continued)

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10. Lag J. Enterprise environmental factors

11. Crashing K. Precedence networks

12. SV L. Ordered frequency of occurrence

13. Politics, culture and infrastructure M. Estimated cost at completion

14. FS, FF, SS, and SF N. Cost of quality

15. CPI O. Hard logic

16. Pareto chart P. Mutually binding agreement

17. Dependencies Q. A system of practices

18. TQM R. Relationships

19. Methodology S. Scope statement, WBS and WBS dictionary

20. Deliverable T. Conditions of acceptance

21. Product scope U. End result

◾ Matching (Memory Jogger) exam C

1. Activity duration A. Ability to do something without having authority

2. Authority B. Number of work periods

3. RACI C. People with vested interest in the project

4. Baseline D. Expected monetary value

5. Analogy or budgetary E. A provision to mitigate risk

6. SPI F. A reusable document

7. Fast-tracking G. Type of responsibility chart

8. Critical path H. Smoothing out manpower peaks and valleys

9. Duration I. Cost variance

10. Forward pass J. Calendar dates of an activity

11. SWOT K. Legal right to do something

12. S-curve L. Estimation techniques for cost

13. Reserve M. Firm-Fixed-Price Contract

14. Template N. Cumulative cost versus time

15. CV O. Schedule compression technique

16. Power P. Estimation techniques for duration

17. Three-point or triangular distribution

Q. Early start and early finish

18. FFP R. An approved plan

19. Resource leveling S. Strengths, weaknesses, opportunities and threats

20. EMV T. Longest path in a network

21. Stakeholders U. Schedule performance index

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▶ Matching Memory Jogger answer key:

exam a

1. J

2. Q

3. G

4. A

5. M

6. B

7. T

8. L

9. C

10. D

11. S

12. U

13. I

14. O

15. H

16. R

17. P

18. K

19. N

20. F

21. E

exam B

1. I

2. O

3. M

4. T

5. H

6. S

7. E

8. N

9. P

10. B

11. F

12. D

13. J

14. K

15. A

16. L

17. R

18. C

19. Q

20. U

21. G

exam C

1. J

2. K

3. G

4. R

5. L

6. U

7. O

8. T

9. B

10. Q

11. S

12. N

13. E

14. F

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15. I

16. A

17. P

18. B

19. H

20. D

21. C

▶ Crashing the schedule exercises

◾ Crashing the Schedule (part 1)

1. Your client has asked you to look at the additional cost for compressing the sched- ule by a given number of weeks. The information you need is shown below in Exhibits 1 and 2. First, complete the network diagram by determining the earliest and latest start and finish times, as well as the critical path:

table 1 Network Start and Finish Information

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

2. In Table 2, complete the column for determining the crashing cost per week.

table 2 Possible Compression Times for Table 1

Activity

Normal

Time, Weeks

Maximum

Compression

Time, Weeks

Normal

Cost, $

Maximum

Crashing

Cost, $

Crashing

Cost per

Week, $

A 7 6 $20,000 $23,000

B 12 10 $30,000 $32,000

C 12 8 $30,000 $36,000

D 18 16 $50,000 $56,000

E 11 6 $40,000 $50,000

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3. Using the data in Table 2, what is the total normal cost for the project?

4. If the client wants the project completed in 29 weeks rather than 30 weeks, how much additional cost will be expended and which activities are crashed and by how many weeks?

5. If the client wants the project completed in 28 weeks rather than 30 weeks, how much additional cost will be expended and which activities are crashed and by how many weeks?

6. If the client wants the project completed in 27 weeks rather than 30 weeks, how much additional cost will be expended and which activities are crashed and by how many weeks?

7. If the client wants the project completed in 26 weeks rather than 30 weeks, how much additional cost will be expended and which activities are crashed and by how many weeks?

8. If the client wants the project completed in 25 weeks rather than 30 weeks, how much additional cost will be expended and which activities are crashed and by how many weeks?

▶ Crashing the Schedule (part 2)

1. Part 2 is a continuation of Part 1. Use the same data from Part 1. Let’s assume that the client wants the project done in the shortest possible time. Crash all the activi- ties to their maximum compression time and identify the critical path.

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

2. Which activities had to be crashed the maximum amount to get to a 22-week schedule and which activities did not have to be crashed the maximum amount?

3. Determine the early start and finish times, as well as the critical path elements, for the cheapest maximum crash.

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

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4. Determine the cheapest total cost for the project for a maximum compression.

Activity

Normal Time,

Weeks

Compression

Time, Weeks

Normal

Cost, $

Additional Cost

for Crashing, $

Total Activity

Cost, $

A 7 6 $20,000 $1,500

B 12 12 $30,000 0

C 12 8 $30,000 $6,000

D 18 16 $50,000 $6,000

E 11 8 $40,000 $6,000

$170,000 $189,500

5. If an activity is crashed for two weeks and the crashing cost per week is $2,000, does that mean that each week incurs an expense of $2,000?

▶ analyzing the Schedule

1. In the network below, determine the early start and finish times, as well as the critical path activities.

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

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2. What is the impact on the end date if Activity B slips by two weeks?

3. What is the impact on the end date if Activity F slips by three weeks?

4. What is the most any activity can slip without extending the end date of the project?

▶ analyzing yet another Schedule

1. In the network below, determine the early start and finish times, as well as the criti- cal path activities.

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

2. What is the impact on the end date if Activity B slips by two weeks?

3. By how much can Activity F slip before it is also on the critical path?

4. By how much can Activity C slip before a new critical path is created?

5. What is the most any activity can slip before the end date of the project may be extended?

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▶ answers

◾ Crashing the Schedule (part 1)

1. Network Start and Finish Information

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

A 0 7 0 7 Yes

B 0 12 7 19 No

C 7 19 7 19 Yes

D 7 25 12 30 No

E 19 30 19 30 Yes

2. Table 2: Possible Compression Times for Table 1

Activity

Normal

Time, Weeks

Maximum

Compression

Time, Weeks

Normal

Cost, $

Maximum

Crashing

Cost, $

Crashing

Cost per

Week, $

A 7 6 $20,000 $23,000 $3,000

B 12 10 $30,000 $32,000 $1,000

C 12 8 $30,000 $36,000 $1,500

D 18 16 $50,000 $56,000 $3,000

E 11 6 $40,000 $50,000 $2,000

3. $170,000

4. Activity C is the lowest crashing cost per week activity on the critical path. Compress it by one week at an additional cost of $1,500. Activity B has a lower crashing cost per week than Activity C, but it is not on the critical path.

5. You must crash Activity C by two weeks for an additional cost of $3,000.

6. You must crash Activity C by three weeks at an additional cost of $4,500.

7. You must crash Activity C by four weeks at an additional cost of $6,000.

8. Activity C can be crashed for only four weeks. Therefore, you must crash Activity E by one week at an additional cost of $8,000. Activity E is crashed because it is cheaper than Activity A.

◾ Crashing the Schedule (part 2)

1. The critical path is now 22 weeks rather than 30 weeks, and there is a new critical path.

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

A 0 6 0 6 Yes

B 0 10 6 16 No

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Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

C 6 14 8 16 No

D 6 22 6 22 Yes

E 14 20 16 22 No

2. Activities A and D are on the new critical path and therefore had to be crashed to the maximum. Activities B, C, and E are not on the critical path and have some slack.

For the activities that are not on the critical path, namely Activities B, C, and E, they may not need to be crashed. To determine whether or not they need to be crashed, at least from a financial point of view, you must be willing to allow multiple critical paths to exist. Therefore, by working backward, determine the cheapest way to allow the paths B-E and A-C-E to be 22 weeks in length. It is possible that an activity may not need to be crashed at all, thus saving money. There are algorithms for these calculations, but more often than not they are trial-and-error solutions.

Out of the remaining activities, B, C, and E, Activity E is the most expensive to crash. Therefore you must look at ways to minimize the cost of crashing. Since Activity E has two weeks of slack according to the answer to Question 1 Activity E can be crashed from 11 weeks to 8 weeks only, thus saving $4000. If we do this, then Activity B does not have to be crashed at all.

There are other types of problems where eliminating slack in Activities B and C may be the cheapest way to do a maximum compression. But this is not the case for this problem.

3. We now have two critical paths and Activity B did not need to be crashed at all.

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

A 0 6 0 6 Yes

B 0 12 2 14 No

C 6 14 6 14 Yes

D 6 22 6 22 Yes

E 14 22 14 22 Yes

4. The project’s cost of $170,000 has now increased $19,500 to $189,500 for the cheapest possible maximum crash.

Activity

Normal

Time, Weeks

Compression

Time, Weeks Normal Cost, $

Additional

Cost for

Crashing, $

Total Activity

Cost, $

A 7 6 $20,000 $1,500 $21,500

B 12 12 $30,000 0 $30,000

C 12 8 $30,000 $6,000 $36,000

D 18 16 $50,000 $6,000 $56,000

E 11 8 $40,000 $6,000 $46,000

$170,000 $189,500

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5. We generally assume linearity, but it is entirely possible that crashing the first week will be $1,000 and crashing the second week will be $3,000 because the compression of the second week is more difficult than the compression of the first week. However, most people just use linearity in making the calculations.

◾ analyzing the Schedule

1. In the network below, determine the early start and finish times, as well as the critical path activities.

Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

A 0 9 0 9 Yes

B 9 12 13 16 No

C 9 15 9 15 Yes

D 12 20 16 24 No

E 15 27 15 27 Yes

F 15 21 18 24 No

G 21 24 24 27 No

H 15 21 21 27 No

2. Activity B has four weeks of slack. There is no impact on the end date.

3. If Activity F slips by three weeks, then both Activities F and G are now critical path activities and there are two critical paths in the network.

4. Activity H has the most, six weeks of slack. If Activity H were to slip by more than six weeks, then the new critical path would be A-C-H.

◾ analyzing yet another Schedule

1. Activity Early Start Early Finish Latest Start Latest Finish On the Critical Path

A 0 5 0 5 Yes

B 0 4 5 9 No

C 0 3 4 7 No

D 5 13 5 13 Yes

E 5 9 9 13 No

F 3 9 7 13 No

G 13 20 13 20 Yes

H 13 20 13 20 Yes

I 9 12 19 22 No

J 20 29 20 29 Yes

K 20 27 22 29 No

There are two critical paths: A-D-G-J and A-D-H-J.

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2. There is no impact on the end date of the project.

3. Activity F can slip by four weeks.

4. Activity C must slip by more than four weeks.

5. Activity I has 10 weeks of slack. A slippage of more than 10 weeks will extend the end date of the project.

▶ earned Value problems

remember

Earned value analysis provides the project manager and the key stakehold- ers to assess the condition or “health” of a project by determining the level of variance from the scheduled work and budgeted cost of project activi- ties. The three main elements for determining the condition of the project are: planned value (work that was scheduled to be accomplished), earned value (the planned budget for the work that was accomplished), and actual cost (the amount paid for the work that was accomplished). Typically earned value analysis is reported in dollars or other currency but other methods of measurement can be used. Review Chapter 15 in the workbook or in Project Management: A Systems Approach to Planning, Scheduling, and Closing (12th edition) for detailed information about earned value management.

The following problems will provide you with practice in the use of earned value analysis.

A small contractor wins a contract to lay tiles on the floors of all 40 offices in a small office complex. All 40 offices are the same dimensions. The contractor expects to work five days per week and to complete one office per day. The duration of the proj- ect is expected to be eight weeks. Labor is estimated at $1,000 per day. The raw mate- rial costs were paid by the client and are not part of the contract.

The customer has asked for an earned value report to be prepared at the end of the sixth week of the project. At the end of the sixth week of the project 24 offices had been completed at a cost of $27,000. This included a freak accident where the tiles for two of the offices had to be removed and replaced. Answer the following questions using the formulas for the end of week 6 report.

1. SV($) = EV – PV

2. CV($) = EV – AC

3. EAC = (AC / EV) × BAC = BAC / CPI

4. VAC = BAC – EAC

5. ETC = EAC – AC

6. SV(%) = SV($) / PV

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7. CV(%) = CV($) / EV

8. CPI = EV / AC

9. SPI = EV / PV

10. EV = % COMPLETE × BAC, or % COMPLETE = EV / BAC

11. % MONEY SPENT = AC / BAC

12. NEW TIME = ORIGINAL TIME / SPI

◾ earned Value Questions

1. What is PV?

2. What is EV?

3. What is AC?

4. What is BAC?

5. What is SV($)?

6. What is CV($)?

7. What is EAC?

8. What is ETC?

9. What is VAC?

10. What is the % complete?

11. What is the % money spent?

12. What is CPI?

13. What is SPI?

14. If the critical path is the duration of the project, eight weeks, then what is the new time to complete the project?

15. What are the values for SV(%) and CV(%), and how are they actually used during status reporting?

16. There are often multiple formulas that can be used to express some of the earned value elements. Formula 3 was used to calculate the estimated cost at completion (EAC). In that formula, (AC/EV) is the rate at which you are burning or spending money. But what if the freak accident that occurred was a one-time occurrence? It may be better to use another formula for EAC. Use the formula below for EAC and compare your results to your answer to Question 7.

EAC = [Actual to date] + [all remaining work and work in progress to be completed as planned.]

17. Most earned value calculations are based upon labor hours and labor dollars rather, and do not consider the cost of materials. If materials are considered, there are separate earned value calculations for materials, such as procurement of raw materials, and then the earned value calculations for materials and labor are added together to get a complete picture of the project’s health. What is the main issue with using earned value for procurement?

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◾ earned Value answers

1. PV was estimated at 30 offices completed at the end of the sixth week for a labor cost of $30,000.

2. EV is based upon only 24 offices being completed for a cost $24,000.

3. AC is $27,000.

4. BAC is 40 offices at $1000 each for a cost of $40,000.

5. SV from Formula 1 = $24,000 – $30,000 = <$6000>.

6. CV from Formula 2 = $24,000 – $27,000 = <$3000>.

7. EAC from Formula 3 = ($27,000/$24,000) × $40,000 = $45,000

8. ETC from Formula 5 = $45,000 – $27,000 = $18,000 to finish the work.

9. VAC from Formula 4 = $40,000 – $45,000 = <$5000>.

10. % complete from Formula 10 = ($24,000 / $40,000) × 100% = 60%. This is not good because you had planned to be 75% complete by this time.

11. % money spent from Formula 11 = ($27,000 / $40,000) × 100% = 67.5%. You have spent 67.5% of the money and completed 60% of the work.

12. CPI from Formula 8 = $24,000 / $27,000 = 0.88

13. SPI from Formula 9 = $24,000 / $30,000 = 0.80

14. Using Formula 12, New time = 8 weeks / 0.80 = 10 weeks. You will finish 2 weeks late.

15. Using Formulas 6 and 7, SV(%) = <20%> and CV(%) = <12.5%>. This indicates that you are behind schedule by 20% and over budget by 12.5%. CV(%) is used fre- quently for status reporting, especially if your company’s project management meth- odology requires that an exception report be prepared if you are above or below a certain financial envelop, but SV(%) has limitations. Although a negative SV(%) indicates that you are behind schedule, it may be the result of activities that are not on the critical path and the original end date may still be workable. If you prepared a schedule where activities that were not on the critical path were assumed to start as early as possible, you could be using up slack without altering the critical path.

16. Assuming you have 16 offices left to complete, EAC = $27,000 + $16,000, or $43,000. This is $2000 less than your answer to Question 7 and probably closer to the true EAC.

17. The main issue is in the determinate of EV for raw materials. EV can be calculated when the materials are ordered, when they are received, when they are placed in inven- tory, when they are used, or when they are paid for. The number of choices for calcu- lating EV makes it a little complicated for standard earned value calculations

▶ estimating the Budget at Completion Questions

A company is undertaking a project internal to their organization. Only one functional department will be involved and the functional manager has estimated that 10,000 hours will be required to complete the work. The project is scheduled to begin in two weeks.

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The functional manager states that he has six people already selected to be assigned to your project, and their average hourly pay rate is $44.80. The functional pay grade system for the department is shown below. The overhead rate for this department is 125%.

Pay Grade

Number of

Employees

Low End of

Pay Grade

High End of

Pay Grade

Average Pay

Grade Salary

6 4 $31.40 $41.50 $36.20

7 7 $36.55 $48.75 $45.40

8 5 $44.90 $52.70 $49.10

9 6 $50.65 $62.33 $58.25

1. What is the fully burdened cost for completing the 10,000 hours of work?

2. Senior management has approved the budget for your project according to your answer to Question 1. Unfortunately, the start date of the project had been delayed by three months and the functional manager does not know whom he will be able to assign. How will you now price out the 10,000 hours?

3. Assume the functional manager tells you that he will assign two Grade 6 workers, two Grade 7 workers, and two Grade 8 workers but is unsure exactly who they will be. How will you price out the 10,000 hours now?

4. Assume that the functional manager tells you that he will assign Grade 8 and Grade 9 workers only, but is not sure about how many from each of the pay grades. How will you price out the 10,000 hours now?

5. If you compare your answers to the above four questions, what are your conclusions?

▶ estimating the Budget at Completion answers

1. The fully burdened cost will be $1,120,000.

2. Using weighted averages, the weighted average salary would be:

4 36 20 7 45 40 5 49 10 6 58 25

22 48 07

($ . ) ($ . ) ($ . ) ($ . ) $ .

+ + + =

The fully loaded cost of 10,000 hours at this rate = $1,201,818

3. Using weighted averages, the weighted average salary would be:

2 36 20 2 45 40 2 49 10 45 57

($ . ) ($ . ) ($ . ) $ .

+ + = 6

The fully loaded cost of 10,000 hours at this rate = $1,089,166

4. Using weighted averages again, the weighted average salary would be:

5 49 10 6 58 25 54 09

($ . ) ($ . ) $ .

+ = 11

The fully loaded cost of 10,000 hours at this rate = $1,352,273

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5. The most accurate budgetary estimates are made from the actual salary of the workers to be assigned. If weighted averaging of salaries is used, then the project manager must be prepared to tell senior management that the budget they approved at the initiation stage of the project may have to be adjusted.

▶ decision trees

remember

To be an effective project manager, you must know how to solve prob- lems and make decisions. Several factors influence decision making, such as the number of alternatives, the favorable or unfavorable result of each alternative, the probabilities assigned to each alternative, the risk associ- ated with each alternative, and enterprise environmental factors that may not be able to be quantified but identify possible opportunities and threats. Most executives prefer a discussion regarding your decision explained to them in financial terms. Fortunately, there are tools that can be used such as expected monetary value (EMV) and decision tree analysis.

Calculating the EMV for each possible decision path is a way to quantify each deci- sion in monetary terms. EMV and decision trees can be used throughout the project’s life cycle but they are most frequently used as part of project risk management. As an example, you conduct a SWOT analysis to determine whether an idea is worth pursuing. Unfortunately, there may be a lack of sufficient data to reach a decision. Decision tree analysis is a means by which you can quantify the data that exists, arrive at a decision, and convince management that your decision is worth considering.

Decision tree analysis is a four-step process usually accomplished in the following order:

1. Prepare a decision tree outlining all decisions that are required.

2. Assign a probability of occurrence to the risk, impact or outcome of that decision.

3. Assign a monetary value to the risk, impact or outcome of that decision should it occur.

4. Calculate the EMV for each decision that must be made.

There are three standard symbols or nodes that are commonly used in decision tree diagrams:

1. Decision nodes commonly represented by a rectangle.

2. Chance nodes commonly represented by a circle.

3. Outcome nodes commonly represented by a triangle.

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◾ problem

For the past several years, your company has been purchasing a product from a sup- plier and selling it to your customers at a somewhat lower price than your customers could get by purchasing it directly from your supplier. Although you have made money doing this, your customers believe that the quality of the product can be improved. Your supplier has indicated that they have no plans to improve the quality of the prod- uct in the near term. Management in your company wants to know if the idea of pur- chasing some equipment and manufacturing it yourself to improve quality will increase profits over the next year. The purchase price of the necessary equipment is $500,000 and training your workers will required an added cost of $100,000. Your market- ing team says that the chances of a good market for the product next year is 60% and the chances of a poor market are 40%. If you manufacture the product yourself and improve the quality of the product, you estimate that a good market will generate $1,000,000 in gross revenue and a poor market will bring in $200,000. If you continue selling the product provided by your supplier, a good market will generate $300,000 in gross revenue and a poor market will bring in $50,000. The procurement costs associ- ated with working with your supplier are estimated at $30,000 yearly.

The decision tree for this problem is shown in the sample decision tree on page 528. The decision to be made is whether to manufacture it yourself or continue purchasing the product from your supplier. Decision trees are analyzed from right to left. First, we must calculate the EMV at chance nodes A and B:

EMV 680 000A = + =( %* $ , , ) ( %* $ , ) $ ,60 1 000 000 40 200 000

EMVB = + =( %* $ , ) ( %* $ , ) $ ,60 300 000 40 50 000 200 000

Looking at these two amounts, it appears that significantly more revenue is gener- ated by manufacturing it ourselves. But this is not necessarily the best choice because we must subtract our costs from the gross revenue in order to arrive at profits. We must continue working from right to left and calculate EMV for decision node C.

EMVMANUFACTURING = − =$ , $ , $ ,680 000 600 000 80 000

EVMPURCHASING = − =$ , $ , $ ,200 000 30 000 170 000

Therefore, in this example here, the best decision for next year appears to be the continuation of purchasing the components from our supplier and selling them to our customers.

Even though the example provided in Exhibit 1 is relatively simple, there are modi- fications that could be made to this problem:

■ Rather than using a good or poor market for the product, we could use optimistic, most likely, and pessimistic outcomes such as with a beta distribution, or we could use the triangular distribution. This adds some complexity to the problem.

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■ The probabilities of good and poor occurring when manufacturing the product could be different than the probabilities for purchasing the product. For example, with a higher-quality product, the probabilities of a good market might be 80% or 90%. In the above example, if the probabilities of a good/poor market for manufactur- ing are 80% and 20%, and the probabilities of a good/poor market using procure- ment remain the same at 60% and 40%, then the EMV for manufacturing would be $240,000 and would be the better choice.

■ The probabilities could be based upon the chances of a specific revenue stream occurring rather than the chances of the market being good or poor.

■ In the example in Exhibit 1, the best decision was purchasing the product from a supplier. But if we consider the profitability over several years with the cost of the equipment and training spread over several years, purchasing the equipment now may be the better choice.

■ Additional decision points can be included, such as whether to conduct a marketing survey on market demand should we decide to manufacture the product. There can be several decision points in one decision tree diagram.

■ Exhibit 1 did not consider the cost of raw material procurement as an addition expense when manufacturing a product.

■ The final decision is highly dependent upon the accuracies of the probabilities and impacts.

■ In many situations the EMV calculation can indicate negative numbers.

■ The more assumptions we make and the more scenarios that are added into the deci- sion tree, the more cautious we should be over the end result.

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528

SaMpLe DeCISIon tree

We can see the advantages and disadvantages of using decision trees. The advantages are:

■ Easy to create, understand, and interpret

■ Can be enhanced to include several different scenarios

■ Has significant value

■ Can be combines with other decision-making tools

The disadvantage are:

■ The decision tree identifies a possible decision that is based upon future rather than present outcomes.

■ The more complex the decision tree becomes, and the more assumptions that must be made, the greater the chance that the final result may be suspect.

■ Outcomes and EMV calculations are based upon an “average” result, which may be unrealistic.

■ Management may become more enamored with the possibility of one highly favorable outcome that overshadows the possibilities of unfavorable outcomes that can occur. The corollary is also true.

While decision trees have value for project managers, there are other tools that can be used. The information in a decision tree can be represented more compactly as an influence diagram, focusing attention on the issues and rela- tionships between events. However, this could add complexity to the decision- making process.