Cost and Performance Tracking Schedule

Projected Completed Time Projected Actual Overruns

Tracking date line

Weeks after start of project

Milestones 1. Purchasing order release 2. Invoices received 3. Material received Time Project 1 Project 2 Project 3 1 2 3 Short lead procurement 20 18 16 14 12 10 8 6 4 2 0 20 40 60 40 20 0 20 50 e x h i b i t 2 . 4

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30 section 1 STRATEGY

for the U.S. Navy’s Polaris missile project. This was a massive project involving over 3,000 contractors. Because most of the activities had never been done before, PERT was developed to handle uncertain time estimates. As years passed, features that distinguished CPM from PERT have diminished, so in our treatment here we just use the term CPM. In a sense, the CPM techniques illustrated here owe their development to the widely used predecessor, the Gantt chart. Although the Gantt chart is able to relate activities to time in a usable fashion for small projects, the interrelationship of activities, when displayed in this form, becomes extremely difficult to visualize and to work with for projects that include more than 25 activities. Also, the Gantt chart provides no direct procedure for determining the critical path, which is of great practical value to identify.

Thecritical pathof activities in a project is the sequence of activities that form the longest chain in terms of their time to complete. If any one of the activities in the critical path is delayed, then the entire project is delayed. Determining scheduling information about each activity in the project is the major goal of CPM techniques. The techniques calculate when an activity must start and end, together with whether the activity is part of the critical path.

C r i t i c a l P a t h M e t h o d ( C P M )

Here is a procedure for scheduling a project. In this case, a single time estimate is used because we are assuming that the activity times are known. A very simple project will be scheduled to demonstrate the basic approach.

Consider that you have a group assignment that requires a decision on whether you should invest in a company. Your instructor has suggested that you perform the analysis in the following four steps:

A Select a company.

B Obtain the company’s annual report and perform a ratio analysis. C Collect technical stock price data and construct charts.

D Individually review the data and make a team decision on whether to buy the stock.

Your group of four people decides that the project can be divided into four activities as suggested by the instructor. You decide that all the team members should be involved in se- lecting the company and that it should take one week to complete this activity. You will

Critical path

NEWZEALAND’STEAPITIWIND

FARMPROJECT CONSTRUCTED THE LARGEST WIND FARM IN THE SOUTHERN HEMISPHERE, WITHIN ONE YEAR FROM COMMISSION TO COMPLETION, ON-TIME AND WITHIN BUDGET. EMPLOYING EFFECTIVE PROJECT MANAGEMENT AND USING THE CORRECT TOOLS AND TECHNIQUES, THEMERIDIAN

ENERGY COMPANY PROVIDED A VIABLE OPTION FOR RENEWABLE ENERGY INNEWZEALAND, AND ACTS AS BENCHMARK FOR LATER WIND FARM PROJECTS.

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meet at the end of the week to decide what company the group will consider. During this meeting you will divide your group: two people will be responsible for the annual report and ratio analysis, and the other two will collect the technical data and construct the charts. Your group expects it to take two weeks to get the annual report and perform the ratio analysis, and a week to collect the stock price data and generate the charts. You agree that the two groups can work independently. Finally, you agree to meet as a team to make the purchase decision. Before you meet, you want to allow one week for each team member to review all the data.

This is a simple project, but it will serve to demonstrate the approach. The following are the appropriate steps.

1. Identify each activity to be done in the project and estimate how long it will

take to complete each activity. This is simple, given the information from your

instructor. We identify the activities as follows: A(1), B(2), C(1), D(1). The number is the expected duration of the activity.

2. Determine the required sequence of activities and construct a network re-

flecting the precedence relationships. An easy way to do this is to first identify

the immediate predecessorsassociated with an activity. The immediate prede- cessors are the activities that need to be completed immediately before an activ- ity. Activity A needs to be completed before activities B and C can start. B and C need to be completed before D can start. The following table reflects what we know so far:

IMMEDIATE

ACTIVITY DESIGNATION PREDECESSORS TIME(WEEKS)

Select company A None 1

Obtain annual report B A 2

and perform ratio analysis

Collect stock price data C A 1

and perform technical analysis

Review data and make D B and C 1

a decision

Here is a diagram that depicts these precedence relationships:

PROJECTMANAGEMENT chapter 2 31

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32 section 1 STRATEGY

3. Determine the critical path. Consider each sequence of activities that runs from the beginning to the end of the project. For our simple project there are two paths: A–B–D and A–C–D. The critical path is the path where the sum of the ac- tivity times is the longest. A–B–D has a duration of four weeks and A–C–D, a du- ration of three weeks. The critical path, therefore, is A–B–D. If any activity along the critical path is delayed, then the entire project will be delayed.

4. Determine the early start/finish and late start/finish schedule. To schedule the project, find when each activity needs to start and when it needs to finish. For some activities in a project there may be some leeway in when an activity can start and finish. This is called theslack timein an activity. For each activity in the project, we calculate four points in time: the early start, early finish, late start, and late finish times. The early start and early finish are the earliest times that the activity can start and be finished. Similarly, the late start and late finish are the latest times the activities can start and finish. The difference between the late start time and early start time is the slack time. To help keep all of this straight, we place these numbers in special places around the nodes that represent each activity in our network diagram, as shown here.

To calculate numbers, start from the beginning of the network and work to the end, calculating the early start and early finish numbers. Start counting with the cur- rent period, designated as period 0. Activity A has an early start of 0 and an early finish of 1. Activity B’s early start is A’s early finish or 1. Similarly, C’s early start is 1. The early finish for B is 3, and the early finish for C is 2. Now consider activ- ity D. D cannot start until both B and C are done. Because B cannot be done until 3, D cannot start until that time. The early start for D, therefore, is 3, and the early finish is 4. Our diagram now looks like this.

0 1 1 3 1 2 3 4 A(1) B(2) C(1) D(1)

To calculate the late finish and late start times, start from the end of the network and work toward the front. Consider activity D. The earliest that it can be done is at time 4; and if we do not want to delay the completion of the project, the late fin- ish needs to be set to 4. With a duration of 1, the latest that D can start is 3. Now consider activity C. C must be done by time 3 so that D can start, so C’s late finish time is 3 and its late start time is 2. Notice the difference between the early and late start and finish times: This activity has one week of slack time. Activity B must be done by time 3 so that D can start, so its late finish time is 3 and late start time is 1. There is no slack in B. Finally, activity A must be done so that B and C can start.

Activity (duration)

Early

start finishEarly

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PROJECTMANAGEMENT chapter 2 33

Because B must start earlier than C, and A must get done in time for B to start, the late finish time for A is 1. Finally, the late start time for A is 0. Notice there is no slack in activities A, B, and D. The final network looks like this. (Hopefully the stock your investment team has chosen is a winner!)

0 1 0 1 1 3 1 3 1 2 2 3 3 4 3 4 B(2) A(1) C(1) D(1) Excel: Project Management

Example 2.1: Critical Path Method

Many firms that have tried to enter the notebook computer market have failed. Suppose your firm believes that there is a big demand in this market because existing products have not been designed correctly. They are too heavy, too large, or too small to have standard-size keyboards. Your intended computer will be small enough to carry inside a jacket pocket if need be. The ideal size will be no larger than 5 inches × 91_{⁄2inches × 1 inch with a folding keyboard. It should weigh no more than}

15 ounces and have an LCD display, a micro disk drive, and a wireless connection. This should ap- peal to traveling businesspeople, but it could have a much wider market, including students. It should be priced in the $175–$200 range.

The project, then, is to design, develop, and produce a prototype of this small computer. In the rapidly changing computer industry, it is crucial to hit the market with a product of this sort in less than a year. Therefore, the project team has been allowed approximately eight months (35 weeks) to produce the prototype.

SOLUTION

The first charge of the project team is to develop a project network chart and estimate the likelihood of completing the prototype computer within the 35 weeks. Let’s follow the steps in the development of the network.

1. Activity identification. The project team decides that the following activities are the major components of the project: design of the computer, prototype construction, prototype testing, meth- ods specification (summarized in a report), evaluation studies of automatic assembly equipment, an assembly equipment study report, and a final report summarizing all aspects of the design, equip- ment, and methods.

2. Activity sequencing and network construction. On the basis of discussion with staff, the project manager develops the precedence table and sequence network shown in Exhibit 2.5. When constructing a network, take care to ensure that the activities are in the proper order and that the logic of their relationships is maintained. For example, it would be illogical to have a situation where Event A precedes Event B, B precedes C, and C precedes A.

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34 section 1 STRATEGY

3. Determine the critical path. The critical path is the longest sequence of connected activi- ties through the network and is defined as the path with zero slack time. This network has four dif- ferent paths: A–C–F–G, A–C–E–G, A–B–D–F–G, and A–B–D–E–G. The lengths of these paths are 38, 35, 38, and 35 weeks. Note that this project has two different critical paths; this might indicate that this would be a fairly difficult project to manage. Calculating the early start and late start sched- ules gives additional insight into how difficult this project might be to complete on time.

•

E a r l y S t a r t a n d L a t e S t a r t S c h e d u l e s Anearly start scheduleis one that lists all of the activities by their early start times. For activities not on the critical path, there is slack time between the completion of each activity and the start of the next activity. The early start schedule completes the project and all its activities as soon as possible.

Alate start schedulelists the activities to start as late as possible without delaying the completion date of the project. One motivation for using a late start schedule is that savings are realized by postponing purchases of materials, the use of labor, and other costs until necessary. These calculations are shown in Exhibit 2.6. From this we see that the only activity that has slack is activity E. This certainly would be a fairly difficult project to complete on time.

T i m e – C o s t M o d e l s

In practice, project managers are as much concerned with the cost to complete a project as with the time to complete the project. For this reason,time–cost modelshave been devised. These models—extensions of the basic critical path method—attempt to develop a mini- mum-cost schedule for an entire project and to control expenditures during the project.

Early start schedule

Late start schedule

Time–cost models A(21) C(7) B(5) D(2) E(5) G(2) F(8) Design Build prototype Evaluate equipment Test prototype Write equipment report Write methods report Write final report

A B C D E F G – A A B C, D C, D E, F 21 5 7 2 5 8 2 ACTIVITY DESIGNATION IMMEDIATE PREDECESSORS T IME (WEEKS) CPM ACTIVITY DESIGNATIONS AND TIME ESTIMATES