Project Management Chapter 8 6p4x4h

Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Chapter Overview 1) Overview – This chapter continues the discussion of project implementation by covering various scheduling techniques. 2) Background – Per the text, “A schedule is the conversion of a project action plan into an operating timetable.” Because projects are unique, a schedule is especially important because there is often no on-going process that simply has to be repeated on a daily basis. The basic process is to identify all the tasks and the sequential relationships among them, that is, which tasks must precede or succeed others. There are a number of benefits to the creation and use of these networks including: a) It is a consistent framework for planning, scheduling and controlling the project. b) It can be used to determine a beginning and ending date for every project task. c) It identifies the activities that if delayed will delay the project. 3) Network Techniques: PERT () and M (PDM) – PERT and M are the most commonly used approaches to project scheduling. Both were introduced in the 1950’s. PERT has been primarily associated with R&D projects, while M with construction projects. Today PERT is not used much since project management software generates M style networks. The primary difference between them is that PERT uses probabilistic techniques to determine task durations, while M relies on a single duration estimate for each task. Both techniques identify the critical path (tasks that cannot be delayed without delaying the project) and associated float or slack in the schedule. In 2005 the Project Management Institute (PMI) deemed it necessary to change the names of these techniques. According to PMI, PERT is called /PERT (Arrow Diagram Method) and M is PDM/M (Precedence Diagramming Method). a) Terminology – The following are the key associated with the development and use of networks: i) Activity – A specific task or set of tasks that have a beginning and end and consume resources. ii) Event – The result of completing one or more activities. Events don’t use resources. iii) Network – The arrangement of all activities and events in their logical sequence represented by arcs and nodes. iv) Path – The series of activities between any two events. v) Critical – Activities, events or paths which, if delayed, will delay the project. To construct the network the predecessors and successors of each activity must be identified. Activities that start the network will have no predecessor. Activities that end the network have no successor. Regardless of the technique used, it is

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition good practice to link the activities with no other predecessor to a START milestone. Those without any successor should be linked to an END milestone. PDM/M networks identify the activities as nodes in the network: the so-called Activity on Node (AON) network. The arrows in between the nodes depict the predecessor/successor relationships among the activities. The /PERT method, on the other hand, uses Activity on Arrow (AOA) networks. Here the nodes represent events and the arrows represent the actual activities. b) Constructing the Network, AON Version – The text illustrates the development of a simple AON network. All the major project management software packages will generate this type of network. c) Constructing the Network, AOA Version – The AOA network has some development rules that make it somewhat more difficult to construct than the AON network. The primary rule is that any given activity must have its source in one and only one node. As a result, some network relationships can only be depicted with the use of a “dummy” activity. This is an activity that has no duration and consumes no resources. Its sole purpose is to indicate a precedence relationship. The text uses various figures to illustrate the use of dummy activities. d) Gantt (Bars) Charts and Microsoft® Project (MSP) – The most familiar tool for depicting project schedules is the Gantt chart, invented by Henry L. Gantt in 1917. The activities are depicted as horizontal bars with their length proportional to their duration. This method results in an easy to read graphical depiction of the project schedule. Gantt charts can be difficult to maintain if there are large changes in the project schedule. Tools like Microsoft® Project (MSP) will automatically draw the Gantt chart as a by-product of the network entered by the . The disadvantage of the Gantt chart is that it typically does not depict the network relationships. e) Solving the Network – The text illustrates the development of another AON network based on the project detailed in Table 8-1. f) Calculating Activity Times – The sample project in the text has three duration estimates for each activity: optimistic (a), most likely (m) and pessimistic (b). Optimistic and pessimistic are defined as the durations that represent 99 percent certainty. In other words the actual duration of an activity will be less than the optimistic or greater than the pessimistic only one percent of the time. Then the expected time (TE) is found with the formula: TE = (a + 4m + b)/6 where: a = optimistic time estimate b = pessimistic time estimate

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition m = most likely time estimate, the mode This formula is based on the beta statistical distribution. In spite of a flurry of discussion in the 1980’s the assumptions used to derive this formula have stood the test of time. Along with TE, the variance of the durations can be calculated as:



2



  b a / 6

2

and the standard deviation as:

 2 g) Critical Path and Time – Using the example network, the text describes the concept of the critical path. For simple projects, the critical path can be found by determining the longest path through the network. h) Slack (aka, Float) – In the previous section, the earliest possible dates for each activity were determined. By starting the analysis at the end of the network and working through it backwards, the latest possible dates for each activity can be determined. The difference between the early dates and the late dates is float or slack. Activities on the critical path have zero float. i) Precedence Diagramming – The Precedence Diagram Method allows for additional relationships to be established between activities. They are: i) Finish to Start – The successor activity cannot begin until the predecessor finishes. This is the most common relationship depicted in networks. ii) Start to Start – The successor activity cannot begin until the predecessor begins. iii) Finish to Finish – The successor activity cannot finish until the predecessor activity finishes. iv) Start to Finish – The successor activity cannot finish until the predecessor activity starts. This relationship is rarely used. In addition to these relationships, PDM allows for leads and lags which is the introduction of a specific time period between the linked activities. For example, in a Start to Start relationship with five days of lag, the successor activity cannot begin until five days after the predecessor starts. The critical path and slack calculation resulting from these relationships can be complicated and counter intuitive. j) Once again, Microsoft® Project – The text illustrates the use of MSP for calculating the most likely project duration using the PERT method.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition k) Exhibits Available from Software, a Bit More MSP – The text illustrates the types of outputs available from MSP. l) Uncertainty of Project Completion Time – The chance of completing a project within a given time period can be calculated. The project activities are assumed to be statistically independent and the variance of a set of activities is equal to the sum of the variances of the individual activities comprising the set. Then the chance of meeting a particular project duration can be calculated as:

Z  D   /



2



where: D = the desired project completion time µ = the critical time of the project, the sum of the TEs for activities on the critical path = the variance of the critical path, the sum of the variances of activities on the  critical path 2



Z = the number of standard deviation of a normal distribution (the standard normal deviate) The weakest element of this technique is that it is difficult to for the possibility that other paths through the network may become critical due to variation in their duration. Simulation techniques using tools like Crystal Ball® or Risk +® can be used to better model this situation. m) Toward Realistic Time Estimates – The traditional PERT method uses optimistic and pessimistic duration estimates at the 99% confidence level. The calculations can be adjusted for lower confidence levels that estimators may be more comfortable in predicting such as 90 or 95%. 4) Risk Analysis Using Simulation With Crystal Ball® – Tools like Crystal Ball® can be used to model the project and determine the likelihood of completion within a certain time. Since Crystal Ball® works with Microsoft® Excel, the project network must be modeled in the spreadsheet. This involves creating cells that calculate the early and late dates for each activity. Then a distribution (commonly triangular) with the appropriate parameters can be assigned to each duration. Finally, Crystal Ball® runs its simulation and the results are displayed. a) Traditional Statistics or Simulation? – With the advent of inexpensive and easy to use tools, simulation is the recommended way to model uncertainty in project durations. Both methods require the development of three durations for each activity. The simulation method, however, does a much better job of handling the possibility that the critical path will shift due to variation in durations of the

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition activities. This issue can be analyzed with traditional statistics, but it takes considerable manual effort on the part of the analyst. 5) Using These Tools – The text gives an example of the use of the tools on a specific project. Teaching Tips The authors correctly applaud the advent of the many -friendly and powerful project management tools available for PC’s. They have performed a great service by integrating the use of tools like Microsoft® Project into the subject matter. My experience in teaching these tools, however, reminds me of the story about IBM’s new programming language. The story goes that IBM, in their marketing campaign for their new language, said that the language was so easy to use that it would virtually eliminate the position of programmer. Anybody would be able to use this language to easily create computer programs. The punch line is that the new language was FORTRAN, a 1960’s era product long ago supplanted by other “ friendly” products. Even today, with all the marvelous tools we have available, the position of programmer has not disappeared. The point of all this is that in the classroom students will have a wide range of skills and abilities that may or may not be applicable to Microsoft® Project and similar tools. My experience is that it is unreasonable to expect students to pick up MSP and use it successfully based solely on the printed examples in the text. Unfortunately, even students who claim to be experienced in the use of the tool often know how to draw a Gantt chart and little else. This is due to three reasons: 

MSP on the surface may look like a fancy spreadsheet, but “under the hood” it’s is a very complex tool. Many of its processes are dependent on complex algorithms, controlled by a seemingly endless series of settings with mysterious titles.



The training provided by most organizations ranges between non-existent and abominable. If there is training, it’s usually istered by someone who has never managed a project and doesn’t understand much more than the students he or she is teaching. One of my very computer literate colleagues will probably become homicidal if he is forced to go to yet another training session that concentrates on issues vital to the PM like changing the color of the fonts. In my twenty years of both managing projects and teaching project management, I have encountered one person who is both an accomplished of MSP on actual projects and a capable instructor.



MSP training, if it exists, is usually done out of context. It is taught as a standalone computer tool, without any of the concepts of project management to put its use in the proper perspective.

The opportunity then, for any project management instructor, is to provide both the concept and meaningful tools training in one package. Ideally, lectures on concept

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition should be alternated with lab sessions using the tool. If this is not possible then, at a minimum, the instructor must set aside class time to demonstrate the key elements of MSP needed to complete the homework problems. Then, a week later, be prepared for the questions and frustrations that will erupt from the class. A good reference case for this chapter follows: Ivey cases: 9A97D001 Note on Introduction to Project Management. An introduction to projects with a simple AON problem. 9A97D002 Gadget Toy Company. A simple AON problem that also introduces Microsoft Project (MSP). 9A95D015 H.M.S. Pinafore. A moderately longer AOA problem. 9A98D020 Procter & Gamble Canada: Dayquil Sampling Operations. A realistic problem based on an actual summer intern’s experience involving a quick decision on a new product line that requires a number of tasks to be executed. Univ. of Virginia Darden case: UVA-OM-0803 Tastee Snax Cookie Company. A straightforward but more involved network problem.

Material Review Questions Question 1: 1) Activity: Activities have a start and finish and consume resources. 2) Event: Events do not consume resources. Typically, events designate the start or the completion of an activity or of a path. 3) Path: A path traces the predecessor-successor relationships that exist among a set of interconnected activities and events. The boundaries of a path use a starting event and a completion event to designate the path’s endpoints. 4) Dummy Activity: Dummy activities are tasks of zero duration that have no resources assigned to them. They are used to maintain predecessor/successor relationships in AOA networks. Question 2: Activities along the critical path cannot be delayed without delaying the completion of the project.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Question 3: 1)

Gantt Chart: The Gantt chart compares planned and actual progress for the detailed tasks in a project.

2)

Master Schedule: The Gantt chart format (bars to represent progress over time) may be used to display data regarding the master project schedule, but the master schedule is oriented towards overall management of the project and will only focus on the major project tasks. For example, the Gantt view in MS-Project can be filtered to only show summary tasks at a particular level of the WBS hierarchy.

Question 4: Total slack vs. free slack: Total slack is the difference between the calculated earliest finish time of the very last activity and the project’s required completion time. Free slack is the time an activity can be delayed without affecting the start time of any successor activity. So, the total slack deals with the relationship between the current activity and the total project completion time, while free slack relates to the next activity. Question 5: The authors of the text have suggested that PERT/M are very similar. Therefore, the PERT and M have been used interchangeably throughout most of the textbook when explaining basic educational concepts about project schedules. The following guidelines are suggested regarding when to use each type of scheduling technique discussed in this chapter. 1)

PDM/M should be used when the control of costs associated with expediting work is an important concern. PDM networks should be used when the project requires the use of leads and lags between activities. PDM is easier to draw than , is used in most project software applications, and tends to be preferred when M is used.

2)

/PERT should be used when the activity times are estimated using probability distributions in order to evaluate the range of uncertainty around the expected project duration. networks should be used when it is desirable to show completion events as part of the scheduling network, though nothing prevents the use of Start and Finish events in a PDM/M network.

3)

The Gantt chart is a useful tool for displaying the schedule regardless of what method is used to derive it. The Gantt chart can be used directly to develop small project schedules.

4)

A less-known approach: GERT should be used when the project plan is complex enough to require loop backs and/or the use of multiple probability distributions associated with branching options in the relationships between activities.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition

Question 6: AON (activity on node) places the activities or tasks on a rectangle (node), whereas the AOA places the activities on arrows connecting nodes. Typically the AON provides more information per activity in the diagram itself because more information can be placed on the node itself (start time, finish time, etc) Question 7: Simulation requires the project schedule be modeled mathematically, which happens to be a by-product of any of the network scheduling techniques. Once the model is established, simulation involves inputting appropriately distributed random numbers into the independent variables and analyzing the resulting distribution of the dependent variables (those calculated by the model). To make the result meaningful, hundreds if not thousands of trials are run, to build a statistically significant output distribution. Once the output distribution is established, probabilities of various outcomes can be calculated. Question 8: Networks are drawn from left to right. Arrowheads indicate the direction of flow in the network. The flow designates the precedence relationships between activities in the network Question 9: The early start time and the early finish time are computed by performing the “forward ” calculation in a network. The late start time is computed by performing the “backward ” calculation in a network. 1)

Late start time: Given the precedence relationships in a network, this is the latest time that an activity can begin without extending the time required to complete the entire project.

2)

Early start time: Given the precedence relationships in a network, this is the earliest time that an activity can begin. In order to begin, all predecessor constraints must have been satisfied.

3)

Early finish time: Given the precedence relationships in a network and the activities duration, this is the earliest time that an activity can be completed if all predecessor constraints are satisfied.

Question 10: The critical path is determined by performing the “forward ” and backward calculations. Float is calculated by subtracting the early dates from the late dates, specifically the early start from the late start, or the early finish from the late finish. If an activity has zero float, then it is on the critical path because any delay would extend the project’s completion date.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Question 11: The reason slack is important is for two reasons: 1) Slack tells us that we can be a bit more forgiving about delays on paths with slack whereas our primary attention should be directed to the critical path. 2) If we need additional resources for some reason (such as a delay on the critical path), the first place to look is at the resources on paths with slack in case they might be available for use. Class Discussion Questions Question 12: The network diagram could serve as a rough process flowchart showing the steps in a manufacturing cycle. The direct and indirect costs for each step could be identified and scheduled for each iteration of the total manufacturing cycle. However, the basic networks would not be sophisticated enough to capture costs associated with variables such as production yields, rework loop backs, and branching logic commonly associated with control points to assure quality. Question 13: 1)

Benefits:

2)

a)

Illustrates task interdependencies

b)

Establishes the sequence of activities (precedence)

c)

Highlights critical and near-critical paths and their tasks

d)

Highlights activities that contain float

Disadvantages: a)

Emphasizes time at the expense of other dimensions of project success

b)

Large networks are difficult to print in a convenient format and they may require significant wall space to view the entire network

c)

As the network technique becomes more complex, its effectiveness as a control tool is reduced

Question 14: This is a great question to kick off a lively class discussion. There are no black and white answers to this question but here are a couple thoughts: 

It’s easy to become obsessed by the use of even more sophisticated tools and lose sight of the big picture. Project management tools are only useful if they help projects achieve their cost, schedule and scope goals. Just because a tool is more sophisticated doesn’t mean that it will yield a better result for the business.



Organizations have to clearly articulate the goals of a project, put together some kind of a plan, and then meticulously monitor its execution. Many organizations

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition gloss over the monitoring part because they believe it smacks of micromanagement. In spite of what Dilbert thinks, managers must have a mechanism for knowing where their project is every day. This allows corrective action to be taken before the problem grows beyond recovery. This attention to detail is boring and repetitive, but it’s far more fundamental to the success of the project than the sophistication of the simulation tools used to model the plan. Question 15: Both methods are of significant value because they force the PM to consider the relationships among the project activities. Then using these relationships, both methods produce a schedule for those activities. In addition, both methods can be used for analysis of variances and problems when the schedule is executed. Question 16: There are many ways to deal with uncertainty. The most common in the scheduling process are: 

Adding buffer or padding to the duration of each activity



Adding buffer to the overall project schedule



Developing schedules based on a range of activity durations



Calculating probabilities of completion using statistical or simulation techniques



Taking specific actions to reduce the uncertainty in duration for some or all the activities

Question 17: The “free slack” as it is called, is the slack along a path in the project and is the minimum of all the slacks on that path. Thus, if the path of interest is A-B-C and the slacks on A and B are each 3 while the slack on C is 2, the free slack on the path is 2. Question 18: Activity times are generally estimated in a manner similar to budgets. For example, they can be individually estimated by the participants, or calculated based on rate data from an earlier project. Question 19: Yes and no. Critical path activities deserve closer scrutiny because if they run late the project is sure to be late. In a situation where scant resources have to be allocated to help late activities recover, for example, the critical path activities would get the resources before the non-critical path activities. This, however, does not absolve the PM from monitoring the non-critical path items. Items off the critical path may feed the critical path, so if they are late they could delay

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition the project indirectly. Also if non-critical path activities get late enough then the critical path may shift to them, again delaying the entire project. Question 20: I’m not aware of any network relationship that can’t be built through some combination of the PDM relationships with leads and lags. As the text points out though, the relationships can become quite complicated, leading to anomalies in the critical path. Questions for Project Management in Practice Replacing the Atigun Section of the TransAlaska Pipeline Question 21: The pipeline does have sections that go below ground, allowing animals to end up on top. The bear in this picture hasn’t found a way to get on top yet. Question 22: Petroleum engineers built a by system that allows diverting the oil flow temporarily for repairs without interrupting it. Question 23: The environment for this project was very hostile. In addition to limited sunlight (3 hours per day), temperatures were as low as -60 degrees during winter. Unless robots could be used, shifts were likely to be limited to the time one could withstand the temperatures and still avoid frostbite. Hosting the Annual Project Management Institute Symposium Question 24: One unique aspect of this project is its length. The Gantt chart shows that planning for the symposium began more than four years before the event and continued for a year after. This means that several symposia are in the continuously in the planning process throughout the United States. Question 25: The symposium took place in September 1992 and the ing project completed in April of 1993. Question 26: The activities after completion of the symposium are tasks associated with project closeout work. This would include tasks related to contract closeout and istrative closeout, to include creation of a project archive and a summary report of lessons learned. For this project, closeout lasted approximately 6 months. This question points out the importance of establishing a common understanding of when any project is actually done. The answer may not be obvious, and it can come back to bite the PM when he or she least expects it.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Problems NOTE: Many of the AON graphics in this solutions set depict the start day of the successor activity to be the same day as the completion of the predecessor. This is consistent with the presentation in the text. It is not consistent with the result that would be obtained using Microsoft® Project, where the start day of the successor is always the next working day after the completion of the predecessor. Problem 1:

Problem 2:

Problem 3: 1)

The arrows cannot form a loop such as the one shown between nodes 2, 3, and 5.

2)

The dummy arrow between nodes 6 and 7 is not required because 6 precedes 5 and 5 precedes 7.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition 3)

Nodes 8 and 9 do not have successors, so it appears that this network has two final termination nodes. That is not a conventional diagramming technique. An arrow from 8 should point to 9.

Problem 4: a)

The critical path is B-E-G.

b)

23 work periods.

Problem 5: Initial PDM Diagram

Adjusted PDM Diagram

Problem 6: PDM Diagram 6a

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PDM Diagram 6b Problem 7: Figure 7a is format.

Figure 7b is PDM format. A

C

F G

Start

D

B

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H

End

E

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Problem 8: Please see note about network depiction preceding Problem 1 a)

The critical path activities are A, C, E, and G.

b)

The project’s duration is 22 days.

c)

Yes, activity B can be delayed one day without delaying the completion of the project.

Problem 9: Task

a

m

b

Expected

Variance

Std Dev.

A

6.5

7.5

14.5

8.5

1.78

1.33

B

8.5

10.5

12.5

10.5

0.44

0.67

C

2.5

3.5

4.5

3.5

0.11

0.33

D

6.5

7.5

8.5

7.5

0.11

0.33

E

5.5

5.5

9.5

6.2

0.44

0.67

F

5.5

7.5

9.5

7.5

0.44

0.67

G

4.5

6.5

8.5

6.5

0.44

0.67

H

2.5

3.5

3.5

3.3

0.03

0.17

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Sum of Expected Variances Desired Project Critical Duration Duration Path

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Z

Probability

21

24.7

2.78

-2.2

a) 1.4%

22

24.7

2.78

-1.6

b) 5.5%

25

24.7

2.78

0.2

c) 57.9%


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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Problem 10:

a) The critical path is AC CB BE EF. b) The only event with slack is “D” at 3 days. c) If “D” were the final event in the network, then the critical path would be AC CB BD. d) The following spreadsheet excerpt illustrates the calculation of the probability of completion in 14 days: Task

a

m

b

Expected

Variance

Std Dev.

AB

3

6

9

6.0

1.00

1.00

AC

1

4

7

4.0

1.00

1.00

CB

0

3

6

3.0

1.00

1.00

CD

3

3

3

3.0

0.00

0.00

CE

2

2

8

3.0

1.00

1.00

BD

0

0

6

1.0

1.00

1.00

BE

2

5

8

5.0

1.00

1.00

DF

4

4

10

5.0

1.00

1.00

DE

1

1

1

1.0

0.00

0.00

EF

1

4

7

4.0

1.00

1.00

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Sum of Expected Variances Desired Project Critical Duration Duration Path 14

16.0

4.00

Z

Probability

-1

15.9%

e) If CD slips to six days the critical path is unchanged but slack on D is reduced. If CD slips to seven days then there are two critical paths: AC CB BE EF and AC CD DF. If CD slips to eight days then the critical path shifts to AC CD DF and the project duration extends to 17 days.

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Problem 11:

B 1

10

G

17

3

28

8

28

I

36 41

10 9

2

4 A

0 0

3

C

7 7

2

F

18 18

11

H

37 37

6

J

43 43

1 4

5 6

3 D

3 3

3 8

E

13 13

Figure 8.11 shows duration on the arrow in matching the “(i,j)” notation used to define the problem’s source data. b) The critical path is A, D, C, E, F, G, H, J. c) The completion time is 43 days.

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Figure 8.12a shows the PDM network for the data from Table A of Problem 8-12 assuming that the data were applied as shown in Figure 8.12b. Please see note about network depiction preceding Problem 1 1)

The critical path is 2,3,4,5,7,8,9.

2)

The slack for activity 1 is 11.7 days. The slack for activity 6 is 4 days.

2) The following table shows the calculation of the expected completion time: Activity

a

m

b

Expected

1

8

10

13

10.2

2

5

6

8

6.2

3

13

15

21

15.7

4

10

12

14

12.0

5

11

20

30

20.2

6

4

5

8

5.3

7

2

3

4

3.0

8

4

6

10

6.3

9

2

3

4

3.0

Expected Project Duration 66.4

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Problem 13: Figure 8.13 shows the network for problem 13. 1)

The critical path is A, B, E, I, L, M, N, P.

2)

The completion time is 75 months.

Problem 14:

Figure 8.14a shows the original network diagram for problem 14. Please see note about network depiction preceding Problem 1

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition 1) The critical path activities are A, D, G, and J. Activities B and E should be closely monitored as a near critical path.

Figure 8.14b shows the impact of the project’s performance to date. 2) The project will be completed in 12.5 days instead of the 13 days originally expected. The near critical path (B, E, G, J) is now critical. Activities A, D, F, and H are now near critical activities. Problem 15:

Figure 8.15a shows the network.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Using critical path analysis results in the following table:

Activity

a

m

b

Expected

Variance

Std Dev.

1,2

5

11

11

10.0

1.00

1.00

1,3

10

10

10

10.0

0.00

0.00

1,4

2

5

8

5.0

1.00

1.00

2,6

1

7

13

7.0

4.00

2.00

3,6

4

4

10

5.0

1.00

1.00

3,7

4

7

10

7.0

1.00

1.00

3,5

2

2

2

2.0

0.00

0.00

4,5

0

6

6

5.0

1.00

1.00

5,7

2

8

14

8.0

4.00

2.00

6,7

1

4

7

4.0

1.00

1.00

Z

Probability

Sum of Expected Variances Desired Project Critical Duration Duration Path 17

21.0

6.00

-1.63299

5.1%

18

21.0

6.00

-1.22474

11.0%

22

21.0

6.00

0.408248

65.8%

24

21.0

6.00

1.224745

89.0%

24.13

21.0

6.00

1.277817

89.9%

The probability of completion at 17 weeks is quite poor, only 5.1%. Management can be sure that the project will complete 90% of the time in slightly over 24 weeks. This analysis suggests that 11% of the time the project will achieve the bonus and 34.2% (100 – 65.8) of the time the project will incur the penalty. Since the project is expected to generate no profit or loss independent of the bonuses and penalties the expected value calculation yields: 11% X $10,000 + 34.2% X $(-5000) = $(-604)

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Strictly based on the expected return management should “no bid” the project. Because the loss is so small, however, the firm may wish to apply other criteria to decide whether to pursue the project. Problem 16: Using critical path analysis with the data provided gives the following table: Activity Expected Std Dev.

Variance

a

2.0

2.00

4.00

b

3.0

1.00

1.00

c

4.0

0.00

0.00

d

2.0

3.00

9.00

e

1.0

1.00

1.00

f

6.0

2.00

4.00

g

4.0

2.00

4.00

h

2.0

0.00

0.00

Expected Sum of Desired Project Variances Duration Duration Critical Path

Z

Probability

12

13.0

9.00

-0.33

36.9%

13

13.0

9.00

0.00

50.0%

16

13.0

9.00

1.00

84.1%

17.3

13.0

9.00

1.43

92.5%

For this problem the variance has to be calculated from the standard deviation, and the durations provided are assumed to be the expected durations. As can be seen there is about an 84% chance of completing the project within the drop dead time. If a little more than a week is added to the duration, the chance of completing the project on time rises to 92.5%.

Rev: Aug, 2008


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Figure 8.17 shows the network for problem 17. Please see note about network depiction preceding Problem 1 a)

There are two critical paths: C, G and C, F, I.

b)

The earliest complete date is 16 days.

c)

E = 6d slack, F = 0d slack, and H = 1d slack.

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Problem 18:

C, F, H is the critical path as indicated in the network. The slack times are as indicated for all activities.

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Problem 19: Figure 8.19 shows the network diagram for problem 19. Legend for Solution 3

0

10

10

C 0

0

5

14

Early Start

Slack

Early Finish

H

Activity Late Late Duration Start Finish

3 3

7

10

15

4

19

5

3

7

10

0

16

Critical Path

A 0

3

3

D Start

8 0

6

5

10

10

6

0

19

I

16

End

5 5

B 6

2

16

E

2

7

4

3

19

5

2

13

19

9

F

11

16

19

11

G 11

8

19

Please see note about network depiction preceding Problem 1

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Problem 20:

Figure 8.20 shows the network diagram for problem 20. Please see note about network depiction preceding Problem 1 a)

The critical path is A, D, E, G, I, J.

b)

The slack on process confirmation (F) is 20 days.

c)

The slack on test pension plan (C) is 61 days.

d)

The slack on debt restriction compliance (H) is 20 days.

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Problem 21: 2 0

0

2

5

5

D

2

A 0

0

7

9

H

2

3

5

2

6

7

5

2

0

12

13

4

16

13

1

I 5

8

13

E 0 Start

9

4

8

5

13

B 9

4

15

J 13

3

4

9

End

14

2

16

13

0

16

16 16

F 7 0

4

3

13 L

3 3

C 4

6

6

7

13

G

7 9

4

3

16

Legend for Solution 13

Early Start

Slack

Early Finish

Activity

Critical Path

Late Late Duration Start Finish

Figure 8.21 shows the network diagram for problem 21. Please see note about network depiction preceding Problem 1 a)

The ES and LS for each activity are shown in Figure 8.21.

b)

The website’s early completion time is 16 weeks.

c)

The slack on each activity is shown in Figure 8.21

d)

The critical activities are A, D, I, L plus J.

e)

The critical path is A, D, I, L.

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Problem 22:

Figure 8.22 shows the network diagram for problem 22. Please see note about network depiction preceding Problem 1 b)

The critical path is B, F, H.

c)

Week 9.

d) If activity E requires one extra week, the time will be absorbed in free float and will not affect any other activity. If activity E requires two extra weeks, then a second critical path will be created for activities B, E, G. If activity E requires three weeks, negative float will be created and the project cannot complete in nine weeks. The new completion time will rise to 10 weeks.

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Problem 23:

Figure 8.23 shows the network diagram solution for problem 23. The critical path is A, B, F, H, I as indicated above. Please see note about network depiction preceding Problem 1 Problem 24:

Figure 8.24a shows the network diagram for problem 24a.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition b)

The critical path is B, E, G, H.

Figure 8.24c shows the network diagram solution to problem 24c. Please see note about network depiction preceding Problem 1 d) Given a float value of 6 weeks, activity F seems to be the best candidate to supply resources needed to crash the project. Since the float is almost 50% of the activity’s duration, using its resources to work other activities is unlikely to convert activity F into a near-critical activity. Since activity D is both critical and concurrent to activity F, the resources should be transferred there.

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Problem 25: Following the discussion in the text, the calculations of TE and  need to be modified. For a confidence level of 95%, the calculation for variance would be:



2



b a  / 3.29 '

'

2

Using these values, the following table can be calculated: 95% Confidence Level Task

a

m

b

Expected

Variance

Std Dev.

AB

3

6

9

6.0

3.33

1.82

AC

1

4

7

4.0

3.33

1.82

CB

0

3

6

3.0

3.33

1.82

CD

3

3

3

3.0

0.00

0.00

CE

2

2

8

3.0

3.33

1.82

BD

0

0

6

1.0

3.33

1.82

BE

2

5

8

5.0

3.33

1.82

DF

4

4

10

5.0

3.33

1.82

DE

1

1

1

1.0

0.00

0.00

EF

1

4

7

4.0

3.33

1.82

Z

Probability

-0.54833

29.2%


16.0

13.30

Note that the expected durations for the critical path remain unchanged, however, the variances are quite a bit larger indicating that there is a larger chance that any given duration will fall outside of the optimistic/pessimistic limit. Similarly for the 90% confidence level, the following equations would be used:



Rev: Aug, 2008

2



b a  / 2.56 '

'


2

Page 33 of 57

Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition and the following table can be calculated: 90% Confidence Level Task

a

m

b

Expected

Variance

Std Dev.

AB

3

6

9

6.0

5.49

2.34

AC

1

4

7

4.0

5.49

2.34

CB

0

3

6

3.0

5.49

2.34

CD

3

3

3

3.0

0.00

0.00

CE

2

2

8

3.0

5.49

2.34

BD

0

0

6

1.0

5.49

2.34

BE

2

5

8

5.0

5.49

2.34

DF

4

4

10

5.0

5.49

2.34

DE

1

1

1

1.0

0.00

0.00

EF

1

4

7

4.0

5.49

2.34

Sum of Variances Critical Path

Z

Probability

21.97

-0.42667

33.5%

Expected Desired Project Duration Duration 14

Rev: Aug, 2008

16.0


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Problem 26:

Figure 8.26a shows the network, critical path and slack times. The critical path in the above diagram is 1-4, 4-5, 5-6, 6-7, 7-10, 10-11 with a duration of 59 days. Tabulating the calculations for expected durations and probability looks like this: Task

a

m

b

1-2

6

8

10

8

0.44

0.67

1-3

5

6

7

6

0.11

0.33

1-4

6

6

6

6

0.00

0.00

2-6

0

0

0

0

0.00

0.00

2-7

10

11

12

11

0.11

0.33

3-6

12

14

16

14

0.44

0.67

4-5

5

8

11

8

1.00

1.00

4-9

7

9

11

9

0.44

0.67

5-6

8

10

12

10

0.44

0.67

5-9

0

0

0

0

0.00

0.00

6-7

14

15

16

15

0.11

0.33

6-8

10

12

14

12

0.44

0.67

7-10

9

12

15

12

1.00

1.00

Rev: Aug, 2008


Expected Variance

Std Dev.

Page 35 of 57

Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Task

a

m

b

Expected Variance

8-10

0

4

14

5

5.44

2.33

9-11

5

5

5

5

0.00

0.00

10-11

7

8

9

8

0.11

0.33

Z

Probability

1.65

95.0%

Desired Expected Project Sum of Variances Duration Duration Critical Path 61.69

59.0

2.67

Std Dev.

The next longest path is 1-3, 3-6, 6-7, 7-10, 10-11 at 55 days. It will only be a concern if under some circumstances; its duration exceeds the actual critical path of 59 days. Using the same technique for calculating the probability of exceeding a particular duration gives the following table for this path: Probability for path 1-3-6-7-10-11 Desired Duration 59

Expected Path Sum of Path Duration Variances 55.0

1.78

Z

Probability

3.00

99.9%

Clearly the chance of exceeding 59 days is quite small. The same technique can be applied to the next longest path 1-4, 4-5, 5-6, 6-8, 8-10, 10-11 which while relatively short has high variance: Probability for path 1-4-5-6-8-10-11 Desired Duration 59

Expected Path Sum of Path Duration Variances 49.0

7.44

Z

Probability

3.67

100.0%

Again it is clear that it is unlikely that this path will cause problems with the overall project duration.

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Problem 27:

Figure 8.27a shows the PDM network for problem 27. The critical path in the above figure is 1, 4, 6, 8, 12, 15 with a duration of 52 days. Please see note about network depiction preceding Problem 1 b)

See Figure 8.27a for the critical path and its early completion time.

c)

See the following table for the probabilities: Task

a

m

b

1

2

4

6

4

0.44

0.67

2

5

5

5

5

0.00

0.00

3

3

5

7

5

0.44

0.67

4

7

10

13

10

1.00

1.00

5

11

12

13

12

0.11

0.33

6

5

6

7

6

0.11

0.33

7

9

10

11

10

0.11

0.33

8

5

7

9

7

0.44

0.67

9

7

9

11

9

0.44

0.67

10

3

3

3

3

0.00

0.00

Rev: Aug, 2008

Expected Variance Std Dev.


Page 37 of 57

Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Task

a

m

b

Expected Variance Std Dev.

11

15

17

19

17

0.44

0.67

12

6

8

10

8

0.44

0.67

13

7

8

15

9

1.78

1.33

14

12

14

16

14

0.44

0.67

15

16

17

18

17

0.11

0.33

Z

Probability

Desired Expected Sum of Variances Duration Project Duration Critical Path 53.35

52.0

2.56

0.84

80.1%

51.6

52.0

2.56

-0.25

40.1%

d) Since the play is ing an Independence Day event, a one day delay would be severe.

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Figure 28a shows the PDM network diagram for problem 28. The duration in the figure above is 1, 3, 6 with a duration of 41 days. The following table tabulates the variances and probability for this project: Task

a

m

b

Expected

Variance

Std Dev.

1

6

10

14

10

1.78

1.33

2

0

1

2

1

0.11

0.33

3

16

20

30

21

5.44

2.33

4

3

5

7

5

0.44

0.67

5

2

3

4

3

0.11

0.33

6

7

10

13

10

1.00

1.00

7

1

2

3

2

0.11

0.33

8

0

2

4

2

0.44

0.67

9

2

2

2

2

0.00

0.00

10

2

3

4

3

0.11

0.33

11

0

1

2

1

0.11

0.33

12

1

2

3

2

0.11

0.33

Z

Probability

1.05

85.2%


Rev: Aug, 2008

41.0

8.22


Page 39 of 57


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Problem 29: To simulate the network in Crystal Ball®, a spreadsheet must be prepared that calculates the duration of each possible path through the network: 1 4.0

2 5.0

1-5-10-13-15 46.0

3 5.0

4 10.0

1-4-9-13-15 50.0

6 6.0

Activities 7 8 10.0 7.0

1-4-6-8-12-15 52.0

Paths 2-6-8-12-15 29.0

5 12.0

9 9.0

10 3.0

2-3-8-12-15 44.0

11 17.0

12 8.0

2-3-7-11 37.0

13 10.0

14 14.0

2-3-7-14 34.0

15 17.0 Project Completion 52.0

The path durations are calculated by summing the expected duration of each participating activity. The Project Completion is calculated as the maximum duration of any of the possible paths. Once the spreadsheet is setup, Crystal Ball® can be used for the simulation. Each of the Expected durations is set to a triangular distribution with minimum and maximum equal to the optimistic and pessimistic durations respectively using the Define Assumption function. The setup for activity 1 looks like this:

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Then a forecast cell is setup for the Project Completion to view how it changes due to the simulation. The resulting histogram looks like this:

The statistics that correspond to this graph look like this:

By adjusting the sliders on the histogram, the 80% and 40% confidence levels can be checked. They look like this:

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These graphs show that a 54-day duration can be achieved with an 80% confidence level and a 52-day duration with a 40% confidence level. These are slightly worse than the results calculated with the variance method. The reason is that the simulation properly takes into the possibility that the critical path shifts for some possible combinations of activity durations.

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Problem 30: The setup for problem 30 is similar to that for problem 29. First the spreadsheet in Excel is prepared with the calculations for the paths: 1 10

2 1

1-2-4-5 19

3 22

4 5

Activities 5 6 3 10

Paths 1-2-4-7-8-11-12 1-2-4-7-9-10-12 23 25

7 2

8 2

1-3-9-10-12 39

9 2

10 3

1-3-6 42

11 1

Project Completion 42

Then, similar to problem 29, triangle distributions are established to calculate the durations for all activities except 9 (no variation in the estimate). The resulting forecast for the duration of the project and corresponding statistics are:

Rev: Aug, 2008


12 2

Page 44 of 57


Note that the probability of completing the project in 44 days has dropped to about 70%. Problem 31: ID 1

Task Name Start

2 3

Dec '05 Jan '06 Finish 4 11 18 25 1 8 Sun 12/11/05 12/11

Duration 0 days

Start Sun 12/11/05

a

2 wks

Mon 12/12/05

Fri 12/23/05

b

2 wks

Mon 12/12/05

Fri 12/23/05

4

c

4 wks

Mon 12/26/05

Fri 1/20/06

5

d

3 wks

Mon 1/23/06

Fri 2/10/06

6

e

1 wk

Mon 1/23/06

Fri 1/27/06

7

f

2 wks

Mon 2/13/06

Fri 2/24/06

8

g

3 wks

Mon 2/27/06

Fri 3/17/06

9

h

1 wk

Mon 3/20/06

Fri 3/24/06

10

End

0 days

Fri 3/24/06

Fri 3/24/06

Feb '06 Mar '06 Apr '06 15 22 29 5 12 19 26 5 12 19 26 2 9

3/24

The figure shows the default Gantt chart view of the problem, with a project start day of Sunday December 11, 2005. Note that MSP moves the beginning of the first task to the first workday of Monday the 12th. This display shows the default calendar of 5 day 40 hr. weeks with no holidays. A “Start” and “End” milestone have been inserted to insure that all activities have at least one predecessor and successor.

Rev: Aug, 2008


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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition The default “Tracking Gantt” view can be used to display the critical path: Duration 0 days

Dec '05 Jan '06 Start 4 11 18 25 1 8 Sun 12/11/05 12/11

ID 1

Task Name Start

2

a

2 wks

Mon 12/12/05

0%

3

b

2 wks

Mon 12/12/05

0%

4

c

4 wks

Mon 12/26/05

5

d

3 wks

Mon 1/23/06

6

e

1 wk

Mon 1/23/06

7

f

2 wks

Mon 2/13/06

8

g

3 wks

Mon 2/27/06

9

h

1 wk

Mon 3/20/06

10

End

0 days

Fri 3/24/06

Feb '06 Mar '06 Apr '06 15 22 29 5 12 19 26 5 12 19 26 2 9

0% 0% 0% 0% 0% 0% 3/24

The project duration (in workdays) can be displayed in the “Project” >> “Project Information” >> “Project Statistics” window, which looks like this:

Problem 32: The “Pert Entry Form” in Microsoft® Project is used to enter the three durations. After they are in the “Calculate Pert” button is clicked to populate the Duration field with the expected durations. Note that MSP uses the non-standard terminology “Expected” in lieu of “Most Likely.”

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Using the calculated durations, the Gantt chart looks like this: ID 1

Task Name Start

Duration 0 days

Start Sun 12/11/05

2 3

Finish Predecessors Sun 12/11/05

a

7.5 days

Mon 12/12/05

Wed 12/21/05 1

b

8 days

Mon 12/12/05

Wed 12/21/05 1

4

c

6 days

Wed 12/21/05

Thu 12/29/05 2

5

d

14.5 days

Thu 12/22/05

6

e

7 days

Wed 1/11/06

Fri 1/20/06 4,5

7

f

11.5 days

Fri 1/20/06

Mon 2/6/06 3,6

8

g

8 days

Tue 2/7/06

Thu 2/16/06 7

9

End

0 days

Thu 2/16/06

Thu 2/16/06 8

Dec '05 Jan '06 4 11 18 25 1 8 12/11

Feb '06 15 22 29 5 12 19 26

Wed 1/11/06 2,3

2/16

The figure shows the default Gantt chart view of the problem, with a project start day of Sunday December 11, 2005. Note that MSP moves the beginning of the first task to the first workday of Monday the 12th. This display shows the default calendar of 5 day 40 hr. weeks with no holidays. A “Start” and “End” milestone have been inserted to insure that all activities have at least one predecessor and successor. The tracking Gantt view can be used to display the critical path: Dec '05 Jan '06 Duration 4 11 18 25 1 8 0 days 12/11

ID 1

Task Name Start

2

a

7.5 days

0%

3

b

8 days

0%

4

c

6 days

5

d

14.5 days

6

e

7 days

7

f

11.5 days

8

g

8 days

9

End

0 days

Rev: Aug, 2008

Feb '06 15 22 29 5 12 19 26

0%


0% 0% 0% 0% 2/16

Page 47 of 57

Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition The network diagram can be displayed directly from MSP using the “Network Diagram” view. A portion of it with the default format settings looks like this: a

Start

Start: 12/12/05 ID: 2

Milestone Date: Sun 12/11/05

Finish: 12/21/05 Dur: 7.5 days

ID: 1

Res:

b Start: 12/12/05 ID: 3 Finish: 12/21/05 Dur: 8 days Res:

The slack values are automatically calculated by MSP. They can be revealed in a number of different views: Nov '05 Dec '05 Total Slack 27 4 11 0 days

ID 1

Task Name Start

Start Sun 12/11/05

Finish Sun 12/11/05

Late Start Mon 12/12/05

Late Finish Mon 12/12/05

Free Slack 0 days

2

a

Mon 12/12/05

Wed 12/21/05

Mon 12/12/05

Wed 12/21/05

0 days

0.5 days

3

b

Mon 12/12/05

Wed 12/21/05

Mon 12/12/05

Wed 12/21/05

0 days

0 days

4

c

Wed 12/21/05

Thu 12/29/05

Tue 1/3/06

Wed 1/11/06

9 days

9 days

5

d

Thu 12/22/05

Wed 1/11/06

Thu 12/22/05

Wed 1/11/06

0 days

0 days

6

e

Wed 1/11/06

Fri 1/20/06

Wed 1/11/06

Fri 1/20/06

0 days

0 days

7

f

Fri 1/20/06

Mon 2/6/06

Fri 1/20/06

Mon 2/6/06

0 days

0 days

8

g

Tue 2/7/06

Thu 2/16/06

Tue 2/7/06

Thu 2/16/06

0 days

0 days

9

End

Thu 2/16/06

Thu 2/16/06

Thu 2/16/06

Thu 2/16/06

0 days

0 days

18 25

Jan '06 1 8

Feb '06 Mar '06 Apr '06 15 22 29 5 12 19 26 5 12 19 26 2 9

9 days

This view shows the View “Detail Gantt” combined with the “Schedule” Table. Note that the Gantt chart also displays the slack as a green line.

Rev: Aug, 2008


Page 48 of 57

16 23


Incidents for Discussion Yankee Chair Company This incident is a good opportunity to engage the students in a discussion of what’s important in the planning and scheduling process. The spirit of the case is to not do dumb things like apply scheduling techniques that aren’t understood by the s. Gort’s approach won’t work, because he doesn’t understand the scheduling process that he intends to apply. The sophistication of the technique is not the issue. If he doesn’t use PERT he can still come up with a useable schedule with any one of several techniques. The issue is that as the PM he needs to understand why the schedule comes out the way it does. He needs to be able to explain the schedule to others. He needs to be able to understand the implications of uncertain data, and he needs to be able to understand the impact of a reschedule. If he is using a scheduling technique that he doesn’t understand, then he won’t be able to perform any of these important management tasks. Cincinnati Software This incident, like the previous one, is an excellent opportunity to engage the students in a discussion of what’s really important in the project management process. I have seen discussions similar to this incident take place many times in business situations. The flavor of the discussion is, “what’s the latest technology and how much can we apply to this project?” The real question should be, “ which technology is appropriate for the goal we are trying to achieve?” In business we fall prey to the fallacy that the sophistication of the technology will make up for our lack of planning and discipline. As the text has discussed the keys to a good planning and scheduling process are: 

Solid understanding of senior management’s and the customer’s goals in pursuing the project



A complete listing of all the activities and products the project must accomplish



A schedule that provides a start and complete date for each identified task



A budget for each task



A clear understanding of the outcome of each task



A system for monitoring the progress of each task



A process for identifying and managing change to the project scope

Note that the schedule is only one element, and as the text has explained, there are several ways to get there. I will take a project that has every one of these in place, but creates the schedule on a white board over a project that uses other methods, but has no clear idea of what the customer’s expectations are.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition That being said the options look like this: 

I would reject the Gantt chart as being too simplistic for the large plan and schedule that will have to be maintained for a project as complicated as an ERP system.



I would work with the PERT and M camps to reach a compromise and use the best of both worlds. That would be a M based network using PERT for estimating durations.

CASE: The Sharon Construction Corporation Question 1: The first element necessary to analyze this situation is a project schedule for the base plan. The Gantt chart from Microsoft® Project for the plan without any alterations looks like this:

Figure 1: Base Schedule The following assumptions were used in preparing this schedule: 1) The start date was chosen as February 15, 1999 so that the project penalty date would be Tuesday February 15, 2000. 2) A five day, forty-hour work calendar was used with no holidays. 3) The durations were designated in weeks, and predecessors established per the Appendix.

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition As can be seen, the project would end on 1/14/00 well before the penalty would kick in. This date will be used as the baseline for all subsequent analysis. The next step is to understand the impact of a strike on the schedule. For the first scenario eight weeks of non-working time was added to the calendar between 11/29/99 and 1/21/00. The new schedule looks like this:

Figure 2: 8-Week Strike Note that the project completion is delayed until 3/10/00. This causes the following additional costs to be incurred: Overhead costs: 8 weeks at $500/week = $4000 Penalty costs: 4 weeks at $15,000/week = $60,000

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Next the 12-week strike will be analyzed:

Figure 3: 12 Week Strike Note that now the completion date is delayed until 4/7/00. This causes the following additional costs to be incurred: Overhead costs: 12 weeks at $500/week = $6000 Penalty costs: 8 weeks at $15,000/week = $120,000 Next, the expected value of each possible outcome is calculated. To determine expected value, the payoff is multiplied times the chance of occurrence. The following chart was prepared following the format presented in Spreadsheet Modeling and Decision Analysis by Cliff T. Ragsdale:

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Figure 4: Project Expected Value Without Mitigations The numbers below the horizontal line and to the left represent the cost or payout of that individual scenario. Item 1 is the overall payout for the project if no penalties are incurred. Similarly Item 2 is the cost of an 8-week strike as previously discussed. Item 3 shows the total of all the options on that branch. In this case it is the payout for the project, less the penalty costs for an 8-week strike. Note that if there is a strike, no additional costs are incurred for weather problems in December since the strike prevents work during that month. On the branch with no strike, an additional heating cost of $2000 would be incurred for an unusually cold December to mitigate the temperature impact on pouring the seats. The expected value is calculated by working from right to left starting with the total payout for the branch and is displayed just to the left and below the node point. For example Item 5 is calculated as the sum of: 0.33 X 236,000 + 0.67 X 236,000 = 236,000. Similarly Item 6 is calculated as: 0.7 X 236,000 + 0.3 X 174,000 = 217,400 Finally the expected value of the project with no mitigating activities against strikes and weather is $258,370. This is in fact the expected value of the fifth proposal, doing nothing. The next step is to evaluate the expected value of the other four proposals. Proposal one improves the project completion time to 12/3/99 with no strike, 1/28/00 if there is an 8week strike and to 2/25/99 for a 12 week strike. This reduces the additional costs to

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition $1000 for the 8-week (two weeks of overhead and zero weeks of penalty) and $33,000 for the 12-week (six weeks of overhead and two weeks of penalty). Note that once again a strike and cold weather problems in December are mutually exclusive. Also, because of the earlier completion with no strike, no concrete pouring activity will take place in December and in fact the overhead costs are reduced because the project completes six weeks before the baseline date. This allows a cost savings for the no strike branches of 6 X $500 or $3000 The updated expected value chart looks like this:

Figure 5: Project Expected Value with Expedited Gallery Pour Note that the total maximum value of the project has been reduced to $280,000 because proposal one requires an additional $20,000 expense for all possible scenarios. The expected value of the project, however, rises to $276,200 with this proposal. For proposal two, examination of Figures 2 and 3 shows that filling the field is not on the critical path. Hence this amount of money would be wasted. Specifically, it lowers the expected value of proposal one by $10,000 to $266,200. Similarly proposal three also reduces the duration of a task off the critical path. As in proposal two, this expense simply lowers the expected value of proposal one by $9,000 to $267,200. The fourth proposal is a little more challenging to evaluate. If there were an 8 or 12week strike the same two activities would benefit from expediting; Pour Seats and Paint Seats. For the 8-week strike a smaller amount of expediting will be used to reduce the

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition extra cost incurred. Specifically, Pour Seats could be reduced to 2 weeks from 4 weeks for a cost of $6000 and Paint Seats could be reduced to 1 week from 3 weeks for a cost of $6000. The Gantt chart for the 8-week strike looks like this:

Figure 6: 8-Week Strike with Proposal Four Mitigations For the 12-week strike, the maximum possible expediting would be used, specifically Pour Seats would be reduced to 1.3 weeks for a cost of $8000 (2.66X$3000) and Paint Seats would be reduced to 1 week for a cost of $6000:

Figure 7: 12-Week Strike with Proposal 4 Mitigations The delay for the 8-week strike plus the expediting costs would cause costs of:

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition 4 wks X $500/week (overhead) + 0 wks penalty + $12,000 expediting costs = $14,000 For the 12-week strike the delay plus expediting would be: 7.3 wks X $500/week (overhead) + 3.3 wks X $15,000/week (penalty) + $14,000 = $67,666 If there is no strike, but a cold winter, than four weeks of heating costs will be incurred as in the base scenario. Placing these values in the appropriate place on the expected value chart gives the following:

Figure 8: Project Expected Value for Proposal 4 This analysis shows that proposal four has the best expected value and should be selected. Question 2: Other solution techniques drawn from decision analysis such as the minimax decision rule can be used. To employ this technique a table will be built of the possible payouts for proposals 1, 4 and 5 (the others can be safely eliminated as no better than one of these three):

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Chapter 8 - Instructor’s Resource Guide to Project Management: A Managerial Approach, seventh edition Using minimax the best (biggest) worst case is in proposal 1($247,000), so it would be selected. Another technique is the minimax regrets. Using this rule we compare each proposal to the best one in that column (state of nature) to determine how much would be lost if that proposal were selected instead of the best one. For example, in the “8-Week Strike” column the best outcome is $286,000 so the regret for choosing proposal 1 is $279,000$286,000 = $(-7,000). In other words it we choose proposal one and an 8-week strike occurred we would regret our choice because we would have been $7000 better if we had chosen proposal 4. The complete regrets table looks like this:

Using the minimax regrets criteria we compare the maximum regrets of each proposal and choose the smallest one. In this case, proposal 4 has the smallest maximum regret at $(-14,666) so it would be chosen. Question 3: There are a number of non-financial factors that could be considered in making the decision including: 

The impact on long term labor relations of “working around” a strike.



The political and marketing implications of not completing the job on time.



The organization’s ability to quickly change and then execute an updated project plan in response to events.



Sharon Construction’s track record in predicting the outcome of labor problems.



The company’s overall ability to execute any project, let alone one with problems

Question 4: As the president I would execute proposal 4, based on its highest expected value.

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