Assignment 1 and 2

Copyright Information (bibliographic) Document Type: Book Chapter Title of book: Operations and Supply Chain Management (15 th Edition) Author of book: F. Robert Jacobs, Richard B. Chase Chapter Title: Chapter 4 Projects Author of Chapter: F. Robert Jacobs, Richard B. Chase Year: 2018 Publisher: McGraw-Hill Education Place of Publishing: United States of America The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted materials. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or reproduction is not to be used for any purpose other than private study, scholarship, or research. If a user makes a request for, or later uses, a photocopy or reproduction for purposes in excess of fair use that user may be liable for copyright infringement. learning Objectives LO 4-1 Explain what projects are and how projects are organized. LO 4-2 Analyze projects using network-planning models. LO 4-3 Evaluate projects using earned value management. LO 4-4 Exemplify how network-planning models and earned value management are implemented in commercial software packages. 1; fefx"~~ll ~ ns-smmR~ 11mmE! BE BWll!m Ill l!ESS i~,mll~ll ~ WEBI!~ lr A Chinese construction company recentlybUilt a 15-storyhotel in justs ix days. To show thi.s.was n.ota flljke,it then builta3()-story h?tel in OQIY 15 days! The company believes it can construct buildings th.at pre 150 stories tall using .the same .high-speed technique§.

Using these techniques, construction takes less than one:third the time it would take on a normal schedule.

The company uses manyworkers during the short c:onstruction period, and detailed schedules coordinate the many teams working simultaneously and a.round the clock on the building. Materials are prefabricated ahead of time in a factory. Premade modul.es are. carried to the con:

struction site on large trucks where they are placed in the steel structure with cranes. Special inspection and review processes are. used to. eliminate these delays in the construction process.

CHINESE WORKERS MANUFACTURE STEEL FRAMES TO .BE USED IN BUILDING THE 1s;sTORY NEW ARK HOTEL; WHICH WAS BUILT IN SIX DAYS. 73 74 Section 1 Strategy, Products, and Capacity WHAT IS PROJECT MANAGEMENT?

Explain what projects "are and how projects are organized. Although most of the material in this chapter focuses on the technical aspects of project manage­ ment (structuring project networks and calculating the critical path), the management aspects are certainly equally important. Success in project management is very much an activity that requires careful control of critical resources. We spend much of the time in this book focused on the management of nonhuman resources such as machines and material; for projects, however, the key resource is often our employees' time. Human resources are frequently the most expen­ sive, and those people involved in the projects critical to the success of the firm are often the most valuable managers, consultants, and engineers.

At the highest levels in an organization, management often involves juggling a portfolio of projects. There are many different types of projects, ranging from the development of totally new products, to revisions of old products, to new marketing plans, as well as a vast array of projects for better serving customers and reducing costs.

Most companies deal with projects individually-pushing each through the pipeline as quickly and cost-effectively as possible. Many of these same companies are very good at applying the techniques described in this chapter in a manner where myriad tasks are exe­ cuted flawlessly, but the projects just do not deliver the expected results. Worse, what often happens is that the projects consuming the most resources have the least connection to the firm's strategy.

Projects can be categorized based on the type of change being planned. For example, a development project might be looking at ways to change the product in response to market feedback, or it might be looking at ways to change the process in order to improve efficiency or quality. The four major types of change are product change, process change, research and devel­ opment, and alliance and partnership. Projects can also be categorized based on the amount of change that is planned. In the case of a project that will make changes to the product itself, it might involve just some minor tweaks to the product-as often happens from year to year with automobiles-or it could be a complete redesign of the product that might happen once or twice a decade, as in the case of a new automobile model. The three categories based on the amount of change are derivative (incremental changes such as new packaging or no-frills versions), platform (fundamental improvements to existing products), and breakthrough (major changes that create entirely new markets). Exhibit 4.1 relates these two dimensions of projects with some examples.

In this chapter, we only scratch the surface in our introduction to the topic of project management. Professional project managers are individuals skilled at not only the technical aspects of calculating such things as early start and early finish time but, just as important, Types of Development Projects More Amount of Change Less Breakthrough Projects Platform Projects Derivative Projects Product Change New core product Addition to product family Product enhancement '­0

Your success at leading a project will spread quickly through the individuals in the team. As organizations flatten (through reengineering, downsizing, outsourcing), more will depend on projects and project leaders to get work done, work that previously was handled within departments. A may be defined as a series of related jobs usually directed toward some major output and requiring a significant period of time to perform. can be defined as planning, directing, and controlling resources (people, equipment, material) to meet the technical, cost, and time constraints of the project.

Although projects are often thought to be one-time occurrences, the fact is that many projects can be repeated or transferred to other settings or products. The result will be another project output. A contractor building houses or a firm producing low-volume products such as supercomputers, locomotives, or jet airliners can effectively consider these as projects. Organizing the Project Team Before the project starts, senior management must decide which of three organizational structures will be used to tie the project to the parent firm: pure project, functional project, or matrix project. We next discuss the strengths and weaknesses of the three main forms. Pure Project Tom Peters predicts that most of the world's work will be "brainwork," done in semipermanent networks of small project-oriented teams, each one an autonomous, entrepreneurial center of opportunity, where the necessity for speed and flexibility dooms the hierarchical management structures we and our ancestors grew up with. Thus, out of the three basic project organizational structures, Peters favors the (nicknamed skunkworks), where a self-contained team works full time on the project. ADVANTAGES • The project manager has full authority over the project.

• Team members report to one boss. They do not have to worry about dividing loyalty with a functional-area manager.

Lines of communication are shortened. Decisions are made quickly.

• Team pride, motivation, and commitment are high. DISADVANTAGES • Duplication of resources. Equipment and people are not shared across projects.

Organizational goals and policies are ignored, as team members are often both physically and psychologically removed from headquarters.

• The organization falls behind in its knowledge of new technology due to weakened func­ tional divisions.

• Because team members have no functional area home, they worry about life-after-project, and project termination is delayed. Fu nctiona I Project At the other end of the project organization spectrum is the housing the project within a functional division. ADVANTAGES A team member can work on several projects.

• Technical expertise is maintained within the functional area even if individuals leave the project or organization. A series of related jobs usually directed toward some major output and requiring a significant period of time to perform.

management Planning, directing, and controlling resources (people, equipment, material) to meet the technical, cost, and time constraints of a project. Pure A structure for organizing a project where a self­ contained team works full time on the project.

In this structure, team members are assigned from the functional units of the organization. The team members remain a part of their functional units and typically are not dedicated to the project. 76 Section 1 Strategy, Products, and Capacity President Matrix project A structure that blends the functional and pure project structures. Each project uses people from different functional areas. A dedicated project manager decides what tasks need to be performed and when, but the functional managers control which people to use. Project Project Project Project Project Project Project Project Project A B C D E F G H I The functional area is a home after the project is completed. Functional specialists can advance vertically.

A critical mass of specialized functional-area experts creates synergistic solutions to a project's technical problems.

DISADVANTAGES Aspects of the project that are not directly related to the functional area get shortchanged.

Motivation of team members is often weak.

Needs of the client are secondary and are responded to slowly.

Matrix Project The classic specialized organizational form, the attempts to blend properties of functional and pure project structures. Each project utilizes people from different functional areas. The project manager (PM) decides what tasks will be performed and when, but the func­ tional managers control which people and technologies are used. If the matrix form is chosen, different projects (rows of the matrix) borrow resources from functional areas (columns). Senior management must then decide whether a weak, balanced, or strong form of a matrix is to be used. This establishes whether project managers have little, equal, or more authority than the functional managers with whom they negotiate for resources. Manager Project A Manager Project B Manager Project C President ADVANTAGES Communication between functional divisions is enhanced.

A project manager is held responsible for successful completion of the project.

Duplication of resources is minimized.

Team members have a functional "home" after project completion, so they are less wor­ ried about life-after-project than if they were a pure project organization.

Policies of the parent organization are followed. This increases support for the project.

77 Projects Chapter4 DISADVANTAGES There are two bosses. Often the functional manager will be listened to before the project manager. After all, who can promote you or give you a raise?

It is doomed to failure unless the PM has strong negotiating skills.

Suboptimization is a danger, because PMs hoard resources for their own project, thus harming other projects.

Note that regardless of which of the three major organizational forms is used, the project manager is the primary contact point with the customer. Communication and flexibility are greatly enhanced because one person is responsible for successful completion of the project. rganizing Project Tasks A project starts out as a statement of work (SOW). The SOW may be a written description of the objectives to be achieved, with a brief statement of the work to be done and a proposed schedule specifying the start and completion dates. It also could contain performance measures in terms of budget and completion steps (milestones) and the written reports to be supplied.

A task is a further subdivision of a project. It is usually not longer than several months in duration and is performed by one group or organization. A subtask may be used if needed to further subdivide the project into more meaningful pieces.

A work package is a group of activities combined to be assignable to a single organiza­ tional unit. It still falls into the format of all project management; the package provides a description of what is to be done, when it is to be started and completed, the budget, mea­ sures of performance, and specific events to be reached at points in time. These specific events are called Typical milestones might be the completion of the design, the production of a prototype, the completed testing of the prototype, and the approval of a pilot run.

The defines the hierarchy of project tasks, subtasks, and work packages. Completion of one or more work packages results in the completion of a subtask; completion of one or more subtasks results in the completion of a task; and, finally, the completion of all tasks is required to complete the project. A representation of this structure is shown in Exhibit 4.2.

Exhibit 4.3 shows the WBS for an optical scanner project. The WBS is important in organiz­ ing a project because it breaks the project down into manageable pieces. The number of levels An Example of a Work Breakdown Structure Level Program 2 1-----------,- - - - - - - - - - ­ 3 Subtask 1.1.l Subtask 1.1.2 Project milestone A specific event in a project. Work breakdown structure (WBS) The hierarchy of project tasks, subtasks, and work packages. >---------~ - - - - - - ­ 4 Work package 1.1.1.l Work package 1.1. 1.2 78 Section 1 Strategy, Products, and Capacity Work Breakdown Structure, Large Optical Scanner Design Level Pieces of work within a project that consume time.

The completion of all the activities of a project marks the end of the project. 1 2 3 4 x x x x x x x x x x x x x x x x x x x x x x x v 1 Optical simulator design I.I Optical design I.I.I Telescope design/fab 1.1.2 Telescope/simulator optical interface 1.1.3 Simulator zoom system design 1.1.4 Ancillary simulator optical component specification 1.2 System performance analysis 1.2.I Overall system firmware and software control 1.2.1.1 Logic flow diagram generation and analysis 1.2.1.2 Basic control algorithm design 1.2.2 Far beam analyzer 1.2.3 System inter-and intra-alignment method design 1.2.4 Data recording and reduction requirements 1.3 System integration 1.4 Cost analysis 1.4.1 Cost/system schedule analysis 1.4.2 Cost/system performance analysis 1.5 Management 1.5. I System design/engineering management 1.5.2 Program management 1.6 Long lead item procurement 1.6.1 Large optics 1.6.2 Target components 1.6.3 Detectors will vary depending on the project. How much detail or how many levels to use depends on the following:

The level at which a single individual or organization can be assigned responsibility and accountability for accomplishing the work package.

The level at which budget and cost data will be collected during the project.

There is not a single correct WBS for any project, and two different project teams might develop different WBSs for the same project. Some experts have referred to project manage­ ment as an art rather than a science, because there are so many different ways that a project can be approached. Finding the correct way to organize a project depends on experience with the particular task.

are defined within the context of the work breakdown structure and are pieces of work that consume time. Activities do not necessarily require the expenditure of effort by people, although they often do. For example, waiting for paint to dry may be an activity in a project. Activities are identified as part of the WBS. From our sample project in Exhibit 4.3, activities would include telescope design and fabrication (l.1.1), telescope/simulator optical interface (l.1.2), and data recording (l.2.4). Activities need to be defined in such a way that when they are all completed, the project is done. NETWORK-PLANNING MODELS The two best-known network-planning models were developed in the 1950s. The Critical Path Method (CPM) was developed for scheduling maintenance shutdowns at chemical processing Analyze projects using plants owned by DuPont. Since maintenance projects are often performed in this industry, rea­ network-planning models. sonably accurate time estimates for activities are available. CPM is based on the assumptions that project activity times can be estimated accurately and that they do not vary. The Program Evaluation and Review Technique (PERT) was developed for the U.S. Navy's Polaris mis­ sile project. This was a massive project involving over 3,000 contractors. Because most of the 79 Projects Chapter4 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 treat­ ment here we just use the term CPM.

In a sense, the CPM techniques illustrated here owe their development to their 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 about 25 activities.

The of activities in a project is the sequence of activities that form the longest Critical chain in terms of their time to complete. If any one of the activities in the critical path is The sequence(s) of delayed, then the entire project is delayed. It is possible and it often happens that there are activities in a project that form the longest chain multiple paths of the same length through the network so there are multiple critical paths. in terms of their time Determining scheduling information about each activity in the project is the major goal of to complete. This path CPM techniques. The techniques calculate when an activity must start and end, together with contains zero slack time. It whether the activity is part of the critical path. is possible for there to be multiple critical paths in a project. Techniques used Critical Path Method (CPM) to find the critical path are Here is a procedure for scheduling a project. In this case, a single time estimate is used because called CPM, or critical path we are assuming that the activity times are known. A very simple project will be scheduled to method, techniques. demonstrate the basic approach.

Consider that you have a group assignment that requires a decision on whether you should Activities that need to be invest in a company. Your instructor has suggested that you perform the analysis in the follow­ completed immediately ing four steps: before another activity. 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 select­ ing the company and that it should take one week to complete this activity. You will meet at the end of the week to decide what company the group will consider. During this meeting, you will divide up 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 per­ form 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 NEW ZEALAND'S TE APITI WIND FARM PROJECT CONSTRUCTED allow one week for each team member to review all the data. THE LARGEST WIND FARM IN THE SOUTHERN HEMISPHERE, WITHIN This is a simple project, but it will serve to demonstrate the ONE YEAR FROM COMMISSION TO COMPLETION, ON-TIME AND WITHIN BUDGET. EMPLOYING EFFECTIVE PROJECT MANAGEMENT approach. The following are the appropriate steps. AND USING THE CORRECT TOOLS AND TECHNIQUES, MERIDIAN 1. Identify each activity to be done in the project and ENERGY COMPANY PROVIDED A VIABLE OPTION FOR RENEWABLE ENERGY IN NEW ZEALAND AND THE PROJECT ACTS AS A estimate how long it will take to complete each BENCHMARK FOR LATER WIND FARM PROJECTS. activity. This is simple, given the information from © Wernher Krutein/Corbis your instructor. We identify the activities as follows:

A(l), B(2), C(l), D(l). The number is the expected duration of the activity.

2. Determine the required sequence of activities and construct a network reflecting the precedence relationships. An easy way to do this is to first identify the ""'"''"',." associated with an activity. The immediate predecessors 80 Section 1 Strategy, Products, and Capacity are the activities that need to be completed immediately before an activity. 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: Activity Designation Immediate Predecessors Time (Weeks) Select company A None Obtain annual report and perform ratio analysis B A 2 Collect stock price data and perform technical analysis c A Review data and make a decision D Band C Here is a diagram that depicts these precedence relationships: Report and Ratio Analysis Make Decision B vTechnical Analysis 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 activity times is the lon­ gest. A-B-D has a duration of four weeks and A-C-D has a duration 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. Slack time This is called the in an activity. For each activity in the project, we calculate The time that an activity Early start Early Late start Late finish finish four points in time: the early start, early finish, late start, can be delayed without and late finish times. The early start and early finish are the delaying the entire project; earliest times that the activity can start and be finished. the difference between the Similarly, the late start and late finish are the latest times late and early start times of an activity. the activities can start and finish without delaying the proj­ ect. 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, calculat­ ing the early start and early finish numbers. Start counting with the current 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 81 l 3 Projects Chapter4 finish for C is 2. Now consider activity 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 o rev~ v2 3 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 it can be done is at time 4; and if we do not want to delay the completion of the project, the late finish 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. 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!) 34 8.·· D(l) 1 3 Q/3·.·· .4 v2 3 EXAMPLE 4.1: Critical Path Method Many firms that have tried to enter the notebook computer market have failed. Suppose your firm believes 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 x 9112 inches x 1 inch with a fold­ ing keyboard. It should weigh no more than 15 ounces and have an LCD display, a solid state drive, and a wireless bluetooth connection. This should appeal to traveling business­ people, but it could have a much wider market, including students. It should be priced in the $17 5 to $200 range. 82 Section I Strategy, Products, and Capacity 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 determine if the prototype computer can be completed within the 35-week target. 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, methods 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, equipment, 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 4.4. When constructing a network, take care to ensure that the activities are in the proper order and that the logic of their relationships is main­ tained. For example, it would be illogical to have a situation where Event A precedes Event B, B precedes C, and C precedes A. CPM Network for Computer Design Project CPM Immediate Time Predecessors Design A 21 Build prototype B A 5 Evaluate equipment c A 7 Test prototype D B 2 Write equipment report E C,D 5 Write methods report F C,D 8 Write final report G E,F 2 3. Determine the critical path. The critical path is the longest sequence of con­ nected activities through the network and is defined as the path with zero slack time. This network has four different 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 indic(lte that this would be a fairly difficult project to manage. Calculating the early start and late start schedules gives additional insight into how difficult this project might be to com­ plete on time. 83 Projects Chapter4 CPM Network for Computer Design Project with Slack Calculations 0 ::~~038 ~ 0 28~.· .3 3~3 36 38 31 36 i-----~- Slack Calculations and Critical Path Determinations LS-Es Slack On Critical Path A 0-0 0 B 21-21 0 c 21-21 0 D 26-26 0 E 31-28 3 F 28-28 0 36-36 Ea r I y St a rt a n d L a t e St a rt S c h e d u I e s An is 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.

A lists 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 4.5. 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. CPM with Three Activity Time Estimates Ifa single estimate of the time required to complete an activity is not reliable, the best procedure is to use three time estimates. These three times not only allow us to estimate the activity time but also let us obtain a probability estimate for completion time for the entire network. Briefly, the procedure is as follows: The estimated activity time is calculated using a weighted average of a minimum, maximum, and most likely time estimate. The expected completion time of the network is computed using the procedure described previously. Using estimates of variability for the activities on the criti­ cal path, the probability of completing the project by particular times can be estimated. (Note that the probability calculations are a distinguishing feature of the classic PERT approach.) EXAMPLE 4.2: Three Time Estimates We use the same information as in Example 4.1 with the exception that activities have three time estimates.

SOLUTION 1. Identify each activity to be done in the project.

2. Determine the sequence of activities and construct a network reflecting the prece­ dence relationships. start schedule A project schedule that lists all activities by their early start times. start schedule A project schedule that lists all activities by their late start times. This schedule may create savings by postponing purchases of material and other costs associated with the project. 84 Section 1 Strategy, Products, and Capacity 3. The three estimates for an activity time are a = Optimistic time: The minimum reasonable period of time in which the activity can be completed. (There is only a small probability, typically assumed to be 1 percent, that the activity can be completed in less time.) m = Most likely time: The best guess of the time required. Since m would be the time thought most likely to appear, it is also the mode of the beta distribution dis­ cussed in step 4.

b = Pessimistic time: The maximum reasonable period of time the activity would take to be completed. (There is only a small probability, typically assumed to be 1 per­ cent, that it would take longer.) Typically, this information is gathered from those people who are to perform the activity.

4. Calculate the expected time (ET) for each activity. The formula for this calculation is ET= a +4m +b [4. l] 6 This is based on the beta statistical distribution and weights the most likely time (m) four times more than either the optimistic time (a) or the pessimistic time (b). The beta distribution is extremely flexible. It can take on the variety of forms that typi­ cally arise; it has finite end points (which limit the possible activity times to the area between a and b); and, in the simplified version, it permits straightforward computa­ tion of the activity mean and standard deviation. 5. Determine the critical path. Using the expected times, a critical path is calculated in the same way as the single time case. 6. Calculate the variances (a2) of the activity times. Specifically, this is the variance, a2, associated with each ET and is computed as follows: "-(b-a) 2

7. Determine the probability of completing the project on a given date, based on the application of the standard normal distribution. A valuable feature of using three time estimates is that it enables the analyst to assess the effect of uncertainty on project completion time. (If you are not familiar with this type of analysis, see the box titled Probability Analysis.) The mechanics of deriving this probability are as follows: a. Sum the variance values associated with each activity on the critical path. b. Substitute this figure, along with the project due date and the project expected completion time, into the Z transformation formula. This formula is D-T Z= E [4.1] ~ where D = Desired completion date for the project Expected completion time for the project Sum of the variances along the critical path c. Calculate the value of Z, which is the number of standard deviations (of a standard normal distribution) that the project due date is from the expected completion time. d. Using the value of Z, find the probability of meeting the project due date (using a table of normal probabilities such as Appendix G). The expected completion time is the starting time plus the sum of the activity times on the critical path.

Following the steps just outlined, we developed Exhibit 4.6 showing expected times and variances. The project network was created the same way we did previously. The only differ­ ence is that the activity times are weighted averages. We determine the critical path as before, 85 Projects Chapter4 using these values as if they were single numbers. The difference between the single time estimate and the three times (optimistic, most likely, and pessimistic) is in computing prob­ abilities of completion. Exhibit 4.7 shows the network and critical path.

Because there are two critical paths in the network, we must decide which variances to use in arriving at the probability of meeting the project due date. A conservative approach dictates using the critical path with the largest total variance to focus management's attention on the activities most likely to exhibit broad variations. On this basis, the variances associ­ ated with activities A, C, F, and G would be used to find the probability of completion. Thus 2:;a~P =9 + 2. 7778 + 0 .1111 + 0 = 11. 8889. Suppose management asks for the probabil­ ity of completing the project in 35 weeks. D, then, is 35. The expected completion time was found to be 38. Substituting into the Z equation and solving, we obtain D-T Z= E 35 -38 = - 0. 87 ,/f,a2cp ~11.8889 Looking at Appendix G, we see that a Z value of -0.87 yields a probability of 0.1922, which means that the project manager has only about a 19 percent chance of completing the project in 35 weeks. Note that this probability is really the probability of completing the criti­ cal path A-C-F-G. Because there is another critical path and other paths that might become critical, the probability of completing the project in 35 weeks is actually less than 0.19.

Activity Expected Times and Variances Expected Times (ET) Activity Variance (o-2 ) Activity Time Estimates a+4m +b (bsaY Activity Designation a m b 6 Design A 10 22 28 21 9 Build prototype B 4 4 10 5 Evaluate equipment c 4 6 14 7 2.7778 Test prototype D 2 3 2 0.1111 Write report E 5 9 5 1.7778 Write methods report F 7 8 9 8 0.1111 Write final report G 2 2 2 2 0 Computer Design Project with Three Time Estimates a2= I a2=0.1111 86 Section 1 Strategy, Products, and Capacity Time-Cost Models and Project Crashing In practice, project managers are as much concerned with the cost to complete a project as with Time-cost models Extension of the critical path models that considers the trade-off between the time required to complete an activity and the cost.

This is often referred to as "crashing" the project. the time to complete the project. For this reason, have been devised. These models-extensions of the basic critical path method-attempt to develop a minimum-cost schedule for an entire project and to control expenditures during the project. Minimum-Cost Scheduling (Time-Cost Trade-Off) The basic assumption in minimum-cost scheduling, also known as "crashing," is that there is a relationship between activity completion time and the cost of a project. Crashing refers to the compression or shortening of the time to complete the project. On one hand, it costs money to expedite an activity; on the other, it costs money to sustain (or lengthen) the project. The costs associated with expediting activities are termed activity direct costs and add to the project direct cost. Some may be worker-related, such as requiring overtime work, hiring more workers, and transferring workers from other jobs; others are resource-related, such as buying or leasing additional or more efficient equipment and drawing on additional support facilities.

The costs associated with sustaining the project are termed project indirect costs: overhead, facilities, and resource opportunity costs, and, under certain contractual situations, penalty costs or lost incentive payments. Because activity direct costs and project indirect costs are oppos­ ing costs dependent on time, the scheduling problem is essentially one of finding the project duration that minimizes their sum or, in other words, finding the optimum point in a time-cost trade-off. areas of the cumulative. stand~rd normal distribution for different values of Z. Z measures the number of standard deviations either to the right or to the left of zero in. the dis-. tribution. The values correspond to the cumulative probabil­ ity associated with each value of Z. For example, the first value in the table, -4.00, has a G(z) equal to .00003. This means that the probability associated with a Z value of -4.0 is only .003 percent. Similarly, a Z value of 1.50 has a G(z) equal to .93319 or 93.319 percent. The Z values are calcu­ lated using Equation (4.3) given in Step 7b of the "Three Time Estimates" example solution. These cumulative prob­ abilities also can be obtained by using the NORMSDIST (Z) function built into Microsoft Excel.

Negative values of Z 0 Positive values of Z The three-time-estimate approach introduces the ability to consider the probability that a project will be completed within a particular amount of time. The assumption needed to make this probability estimate is that the activity dura~ tion times are independent random variables. If this is true, the central limit theorem can be used to find the mean and the variance of the sequence of activities that form the criti­ cal path. The central limit theorem says that the sum of a group of independent, identically distributed random vari­ ables approaches a normal distribution as the number of random variables increases. In the case of project manage­ ment problems, the random variables are the actual times for the activities in the project. (Recall that the time for each activity is assumed to be independent of other activities and to followia beta statistical distribution.) For this, the expected time to complete the critical path activities is the sum of the activity times.

Likewise, because of the assumption of activity time independence, the sum of the variances of the activities along the critical path is the variance of the expected time to complete the path. Recall that the standard deviation is equal to the square root of the variance.

To determine the actual probability of complet­ ing the critical path activities within a certain amount of time, we need to find where on our probability distribution the time falls. Appendix G shows the 87 Projects Chapter4 EXAMPLE 4.3: Time-Cost Trade-off Procedure The procedure for project crashing consists of the following five steps. It is explained by using the simple four-activity network shown in Exhibit 4.8. Assume that indirect costs are $10 per day for the first eight days of the project. If the project takes longer than eight days, indirect costs increase at the rate of $5 per day. 1. Prepare a CPM-type network diagram. For each activity, this diagram should list: a. Normal cost (NC): the lowest expected activity costs. (These are the lesser of the cost figures shown under each node in Exhibit 4.8.) b. Normal time (NT): the time associated with each normal cost. c. Crash time (CT): the shortest possible activity time. d. Crash cost (CC): the cost associated with each crash time. 2. Determine the cost per unit of time (assume days) to expedite each activity. The relationship between activity time and cost may be shown graphically by plotting CC and CT coordinates and connecting them to the NC and NT coordinates by a concave, convex, or straight line-or some other form, depending on the actual cost structure of activity performance, as in Exhibit 4.8. For activity A, we assume a linear relationship between time and cost. This assumption is common in practice and helps us derive the cost per day to expedite because this value may be found directly by taking the slope of the line using the formula Slope =(CC -NC) -:-(NT -CT). (When the assumption of linearity cannot be made, the cost of expediting must be determined graphically for each day the activity may be shortened.) The calculations needed to obtain the cost of expediting the remaining activities are shown in Exhibit 4.9A. 3. Compute the critical path. For the simple network we have been using, this sched­ ule would take 10 days. The critical path is A-B-D. Example of Time-Cost Trade-Off Procedure Step 1. Prepare CPM Diagram with Activity Costs Step 2. Determine Cost per Unit of Time $10 i--- 1 CC, CT Activity A ~ 5~2 8 Activity t­ ~@ cost h') 3, 1 6 .-..---i---°""'NC, NT ::::::

$6,$10 if $5, $9 I I 2 3 4 iNC.. i • r $6, $8 Time- cc Step 3. Compute the Critical Path o~:~ .10 A(2) . ~ CC Crash cost 2 6 CT Crash time ~ 7 0 2 ... 10 NC Normal cost NT Normal time 3 ~- 7 88 Section 1 Strategy, Products, and Capacity 4. Shorten the critical path at the least cost. The easiest way to proceed is to start with the normal schedule, find the critical path, and reduce the path time by one day using the lowest-cost activity. Then, recompute and find the new critical path and reduce it by one day also. Repeat this procedure until the time of completion is satisfactory, or until there can be no further reduction in the project completion time. Exhibit 4.9B shows the reduction of the network one day at a time.

Working through Exhibit 4.9B might initially seem difficult. In the first line, all activi­ ties are at their normal time, and costs are at their lowest value. The critical path is A-B­ D, cost for completing the project is $26, and the project completion time is 10 days.

The goal in line two is to reduce the project completion time by one day. We know it is necessary to reduce the time for one or more of the activities on the critical path. In the second column, we note that activity A can be reduced one day (from two days to on), activity B can be reduced three days (from five to two days), and activity D can be reduced two days (from three days to one). The next column tracks the cost to reduce each of the activities by a single day. For example, for activity A, it normally costs $6 to complete in two days. It could be completed in one day at a cost of $10, a $4 increase.

So we indicate the cost to expedite activity A by one day is $4. For activity B, it nor­ mally costs $9 to complete in five days. It could be completed in two days at a cost of $18. Our cost to reduce B by three days is $9, or $3 per day. For C, it normally costs $5 to complete in three days. It could be completed in one day at a cost of $9; a two­ day reduction would cost $4 ($2 per day). The least expensive alternative for a one-day A. Calculation of Cost per Day to Expedite Each Activity Activity CC-NC NT-CT CC-NC NT-CT Cost per Day To Expedite Maximum Number of Days Activity May Be Shortened A $10- $6 2-1 $10- $6 2-1 $4 B $18 ­$9 5-2 $18 ­$9 5-2 $3 3 c $8-$6 4-3 $8-$6 4=-3 $2 0 $9-$5 3 ­ 1 $9-$5 3=-1 $2 2 B. Reducing the Project Completion Time One Day at a Time Current Remaining Number of Cost per Day Least-Cost Total Cost of Project Critical Days Activity to Expedite Activity to All Activities Completion Path(s) May Be Shortened Each Activity Expedite in Network Time 10 ABO All times and costs are normal. $26 ABO A-1, B-3, 0-2 A-4, B-3, 0-2 0 28 9 ABO A-1, B-3, 0-1 A-4,B-3,0-2 0 30 8 ABO A-1, B-3 A-4,B-3 B 33 7 ABOACO A-1, B-2, C-1 A-4, B-3, C-2 A* 37 6 ABOACO B-2,C-1 B-3, C-2 B&C' 42 5 ABOACO B-1 B-3 B' 45 5 *To reduce the critical path by one day, reduce either A alone or B and C together at the same time (either B or C by itself just modifies the critical path without shortening it).

'Band C must be crashed together to reduce the path by one day.

+Crashing activity B does not reduce the length of the project, so this additional cost would not be incurred.

89 Projects Chapter4 Plot of Costs and Minimum-Cost Schedule 60 50 Project total costs 40 Cost ($) 30 Project direct costs 20 Project indirect costs 10~~~~--~~~~~~---~~~~---~· 0 5 6 7 8 9 JO Minimum cost schedule (days) reduction in time is to expedite activity D at a cost of $2. Total cost for the network goes up to $28 and the project completion time is reduced to nine days.

Our next iteration starts in line three, where the goal is to reduce the project com­ pletion time to eight days. The nine-day critical path is A-B-D. We could shorten activity A by one day, B by three days, and D by one day (note D has already been reduced from three to two days). Cost to reduce each activity by one day is the same as in line two. Again, the least expensive activity to reduce is D. Reducing activity D from two days to one results in the total cost for all activities in the network going up to $30 and the project completion time being reduced to eight days.

Line four is similar to line three, but now only A and B are on the critical path and can be reduced. B is reduced, which takes our cost up $3 to $33 and reduces the proj­ ect completion time to seven days. In line five (actually our fourth iteration in solving the problem), activities A, B, C, and D are all critical. D cannot be reduced, so our only options are activities A, B, and C. Note that B and C are in parallel, so it does not help to reduce B without reducing C. Our options are to reduce A alone at a cost of $4 or B and C together at a cost of $5 ($3 for B and $2 for C), so we reduce A in this iteration.

In line six, we take the B and C option that was considered in line five. Finally, in line seven, our only option is to reduce activity B. Since Band Care in parallel and we cannot reduce C, there is no value in reducing B alone. We can reduce the project completion time no further. 5. Plot project direct, indirect, and total-cost curves and find the minimum-cost schedule. Exhibit 4.10 shows the indirect cost plotted as a constant $10 per day for up to eight days and increasing $5 per day thereafter (as stated in the problem). The direct costs are plotted from Exhibit 4.9B, and the total project cost is shown as the total of the two costs.

Summing the values for direct and indirect costs for each day yields the project total cost curve. As you can see, this curve is at its minimum with an eight-day schedule, which costs $40 ($30 direct + $10 indirect). MANAGING PROJECTS After seeing the arithmetic used when projects are being planned, we now look at how projects are actually managed while they are being completed. Charts and various types of standard forms are useful because their visual presentations are easily understood. Computer programs Evaluate projects using are available to quickly generate the charts, and we discuss these later in the chapter. earned value management. c::J Projected c::J Completed Time Projected --Actual 90 Section 1 Strategy, Products, and Capacity Exhibit 4.11 is a sample sometimes referred to as a bar chart, showing both the amount of time involved and the sequence in which activities can be performed. The chart is named after Henry L. Gantt, who won a presidential citation for his application of this type of chart to shipbuilding during World War I. In the example in Exhibit 4.1 lA, "long lead Sample of Graphic Project Reports A. Gantt Chart for Single Activities B. Total Program Cost Breakdown Activity Contract - - ­ negotiated Contract -0 signed Long lead -~I~ procurement Manufacturing -D Dollars($) schedules Bill of - - - ­ -----D materials Short lead - ­ -------D procurement Material · - - - - - - - - - - - ­ C=:J specifications Manufacturing -- - - - - - - - - - - - LJ Time plans Start-up ------------------0 2 4 6 8 10 12 14 16 18 20 Weeks after start of project D. Cost and Performance Tracking Schedule C. Divisional Breakdown of Costs and Labor Hours Percentage of labor hours Percentage of cost Manufacturing Finance t Engineering Total program Overhead costs$ Personnel 0 20 40 Time--""'.!»- I Tracking date line 1 ..Purchasing order t~lease 2. Invoices received 3. Material received 0 60 40 20 E. Bar/Milestone Chart Short lead procurement 10 Weeks after start of 11 9 91 Projects Chapter4 procurement" and "manufacturing schedules" are independent activities and can occur simul­ taneously. All other activities must be done in the sequence from top to bottom. Exhibit 4.1 lB graphs the amounts of money spent on labor, material, and overhead. Its value is its clarity in identifying sources and amounts of cost.

Exhibit 4.1 lC shows the percentage of the project's labor hours that come from the various areas of manufacturing, finance, and so on. These labor hours are related to the proportion of the project's total labor cost. For example, manufacturing is responsible for 50 percent of the project's labor hours, but this 50 percent has been allocated just 40 percent of the total labor dollars charged.

The top half of Exhibit 4.1 lD shows the degree of completion of these projects. The dot­ ted vertical line signifies today. Project 1, therefore, is already late because it still has work to be done. Project 2 is not being worked on temporarily, so there is a space before the projected work. Project 3 continues to be worked on without interruption. The bottom of Exhibit 4.1 lD compares actual total costs and projected costs. As we see, two cost overruns occurred, and the current cumulative costs are over the projected cumulative costs.

Exhibit 4.1 lE is a milestone chart. The three milestones mark specific points in the project where checks can be made to see if the project is on time and where it should be. The best place to locate milestones is at the completion of a major activity. In this exhibit, the major activities completed were "purchase order release," "invoices received," and "material received." Other standard reports can be used for a more detailed presentation comparing cost to prog­ ress (such as cost schedule status report-CSSR) or reports providing the basis for partial pay­ ment (such as the earned value report, which we discuss next). Earned Value Management (EVM) is a technique for measuring project progress in an objec­ tive manner. EVM has the ability to combine measurements of scope, schedule, and cost in a project. When properly applied, EVM provides a method for evaluating the relative success of a project at a point in time. The measures can be applied to projects focused on either revenue generation or cost, depending on the type of project.

Essential features of any EVM implementation include: 1. A project plan that identifies the activities to be accomplished. 2. A valuation of each activity work. In the case of a project that generates revenue, this is called the Planned Value (PV) of the activity. In the case where a project is evaluated based on cost, this is called the Budgeted Cost of Work Scheduled (BCWS) for the activity. 3. Predefined earning or costing rules (also called metrics) to quantify the accom­ plishment of work, called Earned Value (EV) or Budgeted Cost of Work Performed (BCWP).

The terminology used in the features is general since the valuations could be based on either a value measure (revenue or profit) or a cost measure. EVM implementations for large or com­ plex projects include many more features, such as indicators and forecasts of cost performance ( overbudget or underbudget) and schedule performance (behind schedule or ahead of schedule).

However, the most basic requirement of an EVM system is that it quantifies progress using PV (or BCWS) and EV (or BCWP). Project Tracking without EV M It is helpful to see an example of project tracking that does not include earned value pe1formance management. Consider a project that has been planned in detail, including a time-phased spend plan for all elements of work. This is a case where the project is evaluated based on cost. Exhibit 4.12A shows the cumulative cost budget for this project as a function of time (the blue line, labeled BCWS). It also shows the cumulative actual cost of the project (red line) through week 8. To those unfamiliar with EVM, it might appear that this project was over budget through week 4 and then under budget from week 6 through week 8. However, what is missing from this chart is any understanding of how much Gantt chart Shows in a graphic manner the amount of time involved and the sequence in which activities can be performed. Often referred to as a bar chart. Technique that combines measures of scope, schedule, and cost for evaluating project progress. IDEAS Comparing the work that has been completed in a project to the work that should have been completed according to the project plan is the key idea behind EVM analysis. 92 Section 1 Strategy, Products, and Capacity work has been accomplished during the project. If the project was actually completed at week 8, then the project would actually be well under budget and well ahead of schedule. If, on the other hand, the project is only 10 percent complete at week 8, the project is significantly over budget and behind schedule. A method is needed to measure technical performance objectively and quantitatively, and that is what EVM accomplishes. Project Tracking with EVM Consider the same project, except this time the project plan includes predefined methods of quantifying the accomplishment of work. At the end of each week, the project manager identifies every detailed element of work that has been completed, and sums the Budgeted Cost of Work Performed for each of these completed elements by estimating the percent complete of the activity and multiplying by the activity budgeted cost.

Budgeted Cost of Work Performed (BCWP) may be accumulated monthly, weekly, or as progress is made.

Exhibit 4.12B shows the BCWS curve (in orange) along with the BCWP curve from Chart C. The chart indicates that technical performance (i.e., progress) started more rapidly than planned, but slowed significantly and fell behind schedule at week 7 and 8. This chart illustrates the schedule performance aspect of EVM. It is complementary to critical path schedule man­ agement (described in the next section).

Exhibit 4.12C shows the same BCWP curve (blue) with the actual cost data from Chart A (in green). It can be seen that the project was actually under budget, relative to the amount of work accomplished, since the start of the project. This is a much better conclusion than might be derived from Chart A. Earned Value Management Charts Chart A $200,000 2 Chart C 3 4 5 6 7 8 Time (weeks) 9 IO $150,000 $100,000 Project AC Tracking without Earned Value Is Inconclusive II 12 --- Budgeted Cost of Work Scheduled (BCWS) -o- Actual Cost (AC) ......... Budgeted Cost of Work Performed (BCWP) I ..._Actual Cost (AC) I 1 $200,000 - $150,000 - $100,000 - Cost ~}Variance($) $50,000 _ ~ Under Budget $0 I I < I < I I I I I I 2 3 4 5 6 7 8 9 IO 11 12 Time (weeks) ChartB $200,000 $150,000 $100,000 $50,000 $0'-=--'--~-~-'--~-~-'--~-~_,__~~ 2 3 4 5 6 7 8 9 IO II 12 Time (weeks) ChartD -o- Budgeted Cost of Work Scheduled (BCWS) -o- Budgeted Cost of Work Performed (BCWP) -o- Actual Cost (AC) $200.000 I~------------~ BCWS 2 3 4 5 6 7 8 9 IO 11 12 Time (weeks) -o- Budgeted Cost of Work Scheduled (BCWS) - Budgeted Cost of Work Pe1formed (BCWP) BCWS Behind Schedule , } Schedule ____ ' Variance($) Variance (Time) 93 Projects Chapter4 Exhibit 4.12D shows all three curves together-which is a typical EVM line chart. The best way to read these three-line charts is to identify the BCWS curve first, then compare it to BCWP (for schedule performance) and AC (for cost performance). It can be seen from this illustration that a true understanding of cost performance and schedule performance relies first on measuring technical performance objectively. This is the foundational principle of EVM. EXAMPLE 4.4: Earned Value Management x Activity A Activity B (Actual) 80% Activity C (Actual) 70%-80% (Expected) $40K Activity D 15% The figure illustrates how to determine the Budgeted Cost of Work Scheduled by summing the dollar values (in $1,000s) of the work scheduled for accomplishment at the end of period X. The Budgeted Cost of Work Performed is determined by summing the earned value for the work actually accomplished, shown in red shading. SOLUTION From the diagram, the budgeted cost of all the project work is the following: Activity A= $1SK, B = $10K, C = $20K, D = $40K. This is the cost of each activity when they are 100% completed.

The project is currently at day X, and so from the diagram, 100% of activity A should be com­ pleted, and it is; 100% of activity B should be completed, but only SO% is; SO% of activity C should be completed, but only 70% is; and 15% of activity D should be completed, but it has not started.

Step 1: Calculate the Budgeted Cost of Work Scheduled (BCWS) given the current state of the project. This is the value or cost of the project that is expected, given the project is at time X: Activity A 100% of $1SK = $1SK Activity B 100% of$ lOK = $1 OK Activity C SO% of $20K = $16K Activity D 15% of $40K = $6K BCWS = $1SK + $10K + $16K + $6K =$SOK Step 2: Calculate the Budgeted Cost of Work Performed (BCWP) given the current state of the project. This is the actual value or cost of the project to date, given the project is at time X: Activity A 100% of $1SK = $1SK Activity B SO% of $10K =$SK Activity C 70% of $20K = $14K Activity D 0% of $40K = $0 BCWP = $1SK +$SK+ $14K +$OK= $40K 94 Section 1 Strategy, Products, and Capacity Step 3: Obtain the Actual Cost (AC) of the work performed. This would need to be obtained from accounting records for the project. Assume that the AC for this project to date is $45K.

AC = $45K (Data from Acct. System) Step 4: Calculate key performance measures for the project:

Schedule Variance: This is the difference between the Budgeted Cost of Work Performed (BCWP) and the Budgeted Cost of Work Scheduled (BCWS) for the project:

Schedule Variance = BCWP -BCWS Schedule Variance= $40K- $SOK= -$10K Greater than 0 is generally good because it implies the project is ahead of schedule.

Schedule Performance Index: This is the ratio of the BCWP versus the BCWS for the project:

Schedule Performance Index = BCWP/BCWS Schedule Performance Index = $40K/$50K = 0.8 Greater than 1 is generally good because it implies the project is ahead of schedule.

Cost Variance: This is the difference between BCWP and the Actual Cost (AC):

Cost Variance = BCWP -AC Cost Variance = $40K $45K = -$5K Greater than 0 is generally good because it implies under budget.

Cost Performance Index: This is the ratio of the BCWP versus the AC for the project to date:

Cost Performance Index= BCWP/AC Cost Performance Index = $40K/$45K = 0.89 < 1 means the cost of completing the work is higher than planned, which is bad.

= 1 means the cost of completing the work is right on plan, which is good.

> 1 means the cost of completing the work is lower than planned, which is usually good.

That CPI means the project is spending about $1.13 for every $1.00 of budgeted work accom­ plished. This is not very good because the project is overbudget and tasks are not being com­ pleted on time or on budget. A Schedule Performance Index and a Cost Performance Index greater than 1 are desirable. PROJECT MANAGEMENT INFORMATION SYSTEMS Exemplify how network­ planning models and earned value management are implemented in commercial software packages. Interest in the techniques and concepts of project management has exploded in the past 10 years. This has resulted in a parallel increase in project management software offerings.

Now there are over 100 companies offering project management software. For the most up-to­ date information about software available, check out the website of the Project Management Institute (www.pmi.org). Two of the leading companies are Microsoft, with Microsoft Proj­ ect, and Primavera, with Primavera Project Planner.

The Microsoft Project program comes with an excellent online tutorial, which is one reason for its overwhelming popularity with project managers tracking midsized projects. This pack­ age is compatible with the Microsoft Office Suite, which opens all the communications and Internet integration capability that Microsoft offers. The program includes features for schedul­ ing, allocating, and leveling resources, as well as controlling costs and producing presentation­ quality graphics and reports. Projects Chapter4 95 MonS/7/12 MonS/7/12 s 4days Tue 5/8/12 Frl5/ll/12 c 3days Tue 5/8/12 Thu 5/10/12 1 D 7days Tue5/8/12 WedS/16/12 1 6days MonS/14/12 MonS/21/12 2 2days ThuS/17/12 FrlS/18/12 3,4 G 7 WedS/30/12 5,6 For managing very large projects or programs having several projects, Primavera Project Planner is often the choice. Primavera was the first major vendor of this type of software and has possibly the most sophisticated capability.

In addition to scheduling tasks, a major capability of all these software packages is assign­ ing resources to competing tasks and projects. For example, the systems can schedule back labor and equipment for a project. Mid-to high-level project management information systems (PMIS) software can also resolve overallocations through a "leveling" feature. Several rules of thumb can be used. You can specify that low-priority tasks should be delayed until higher­ priority ones are complete, or that the project should end before or after the original deadline.

The real action starts after the project gets under way. Actual progress will differ from your original, or baseline, planned progress. Software can hold several different baseline plans, so you can compare monthly snapshots.

A tracking Gantt chart superimposes the cmTent schedule onto a baseline plan so deviations are easily noticed. If you prefer, a spreadsheet view of the same information could be output.

Deviations between planned start/finish and newly scheduled start/finish also appear, and a "slipping filter" can be applied to highlight or output only those tasks that are scheduled to fin­ ish at a later date than the planned baseline. Management by exception also can be applied to find deviations between budgeted costs and actual costs. Concept Connections s~ " ~I!© 4-tl EXBlain wliat grojeets are ana How 9rojeets are organizea. · & ~ x • Projects can be categorized into four major types: prod­ on many different projects at the same time; and matrix uct change, process change, research and development, project, which blends the pure project and functional and alliance and partnerships.

project structures.

• Even though some projects are often thought to be one­ • The activities of the projects are organized according to time occurrences, they are sometimes repeated.

the work breakdown structure, which groups them into • The project team can be organized in different ways.

subtasks and work packages. Completion of a work The most common are pure project, where the team package results in the completion of a subtask, and works full time on the project; functional project, where completion of all of the subtasks is required to com­ team members stay in their functional group and work plete the project. 96 Section 1 Strategy, Products, and Capacity Key Terms Project A series of related jobs usually directed toward sgme major output and requiring a significant period of time to perform.

Project management Planning, directing, and control­ ling resources (people, equipment, material) to meet the technical, cost, and time constraints of a project. Pure project A structure for organizing a project where a self-contained team works full time on the project. Functional project In this structure, team members are assigned from the functional units of the organization.

The team members remain a part of their functional units and typically are not dedicated to the project. Matrix project A structure that blends the functional and pure project structures. Each project uses people from different functional areas. A dedicated project manager decides what tasks need to be performed and when, but the functional managers control which people to use. Project milestone A specific event in a project. Work breakdown structure (WBS) The hierarchy of project tasks, subtasks, and work packages.

Activities Pieces of work within a project that consume time. The completion of all the activities of a project marks the end of the project. t.0 4-2 Analyze projects using network-planning models. Summary • The critical path method (CPM) is the most widely used approach to scheduling projects. There are a num­ ber of variations on the basic approach.

• The goal is to find the earliest time that the entire proj­ ect can be completed.

• The techniques also identify what activities are critical, meaning that there cannot be delays with- Key Terms Critical path The sequence(s) of activities in a project that form the longest chain in terms of their time to com­ plete. This path contains zero slack time. It is possible for there to be multiple critical paths in a project. Tech­ niques used to find the critical path are called CPM, or critical path method, techniques.

Immediate predecessor Activities that need to be com­ pleted immediately before another activity.

Slack time The time that an activity can be delayed with­ out delaying the entire project; the difference between the late and early start times of an activity.

Early start schedule A project schedule that lists all activities by their early start times.

Late start schedule A project schedule that lists all activ­ ities by their late start times. This schedule may create out delaying the earliest time that the project can be completed.

• The three techniques studied in the chapter are the fol­ lowing: CPM with a single activity time, CPM with three activity time estimates, and time-cost models with project crashing.

savings by postponing purchases of material and other costs associated with the project. Time-cost models Extension of the critical path models that considers the trade-off between the time required to complete an activity and the cost. This is often referred to as "crashing" the project. ET= a+4m+b 6 [4.1] er= (b6ay [4.2] Z=-D_-_T_ [4.3] ~ ll© 4-B Evaluate grojects using e,,arned value management. Summary • A key aspect to managing a project is understanding the work completed together with what is left to be the current status of its activities.

done.

• Simple graphical techniques are often augmented • Earned value management (EVM) is a technique com­ with standard reports that give a detailed analysis of monly used for measuring project progress. 97 Projects Chapter4 Terms Gantt chart Shows in a graphic manner the amount of Earned value management (EVM) Technique that com­ time involved and the sequence in which activities can bines measures of scope, schedule, and cost for evaluat­ be performed. Often referred to as a bar chart. ing project progress. :m 1:1-1:1 ExemBli~ tiow networl<-Blanning models ana earneCI v-alue management are imBle­ entei:I in commercial software Bacl

• Two of the most common packages are Microsoft Proj­ ect and Primavera Project Planner. Solved Problems L04-2 SOLVED PROBLEM 1 A project has been defined to contain the following list of activities, along with their required times for completion: Activity Time (days) Immediate Predecessors A 8 4 A c 3 A D 7 A E 6 8 F 2 C,D G 7 E, F H 9 D 4 G,H a. Draw the critical path diagram. b. Show the early start, early finish, late start, and late finish times. c. Show the critical path. d. What would happen if activity F was revised to take four days instead of two? Solution The answers to a, b, and c are shown in the following diagram. 18 22 GJ) 18 22 2 9 A-B-E-G-1 Critical path: 9 18 98 0 Critical path -ADCFG, Section 1 Strategy, Products, and Capacity Path Length (days) A-B-E-G-1 22 (critical path) A-C-F-G-1 17 A-D-F-G-1 21 A-D-H-1 21 d. New critical path: A-D-F-G-1. Time of completion is 23 days. L04-3 SOLVED PROBLEM 2 A project has been defined to contain the following activities, along with their time estimates for completion: Time Estimates (weeks) Activity a m b Immediate Predecessor A 4 7 B 2 6 7 A c 3 4 6 D D 6 12 14 A E 3 6 12 D F 6 8 16 B,C G 5 6 E,F a. Calculate the expected time and the variance for each activity. b. Draw the critical path diagram. c. Show the early start, early finish times, and late start, late finish times. d. Show the critical path. e. What is the probability that the project can be completed in 34 weeks? Solution a. Activity Expected Time a+4m+b 6 Activity Variance (b~ay A B c D E F G b. 4.00 5.50 4.17 11.33 6.50 9.00 4.50 0.6944 0.2500 1.7778 2.2500 2.7778 0.6944 33 33 33 weeks 99 Projects Chapter4 c. Shown on diagram. d. Shown on diagram.

Path Length (weeks) A-B-F-G 23 A-D-C-F-G 33 (critical path) A-D-E-G 26.33 e. Z = D - TE= 34 33 =_l_ = .3922 ~ vi+ 1.7778 + .25 +2.7778 + .6944 2.5495 Look up that value in Appendix E and we see that there is about a 65 percent chance of com­ pleting the project by that date. LO 4-2 SOLVED PROBLEM 3 Here are the precedence requirements, normal and crash activity times, and normal and crash costs for a construction project: Required Time (weeks) Cost Preceding Activity Activities Normal Crash Normal Crash A 4 2 $10,000 $11,000 B A 3 2 6,000 9,000 c A 2 1 4,000 6,000 D B 5 3 14,000 18,000 E B,C 1 1 9,000 9,000 F c 3 2 7,000 8,000 G E, F 4 2 13,000 25,000 H D,E 4 1 11,000 18,000 H,G 6 5 20,000 29,000 a. What are the critical path and the estimated completion time? b. To shorten the project by three weeks, which tasks would be shortened and what would the final total project cost be? Solution The construction project network is shown as follows: --- 100 Section 1 Strategy, Products, and Capacity a. Path Length A-B-D-H-1 22 (critical path) A-B-E-H-1 18 A-B-E-G-1 18 A-C-E-H-1 17 A-C-E-G-1 17 A-C-F-G-1 19 Normal completion time is 22 weeks. b. Activity Crash Cost Normal Cost Normal Time Crash Time Cost per Week Weeks A $11,000 $10,000 4 2 $ 500 2 B 9,000 6,000 3 2 3,000 c 6,000 4,000 2 1 2,000 D 18,000 14,000 5 3 2,000 2 E 9,000 9,000 0 F 8,000 7,000 3 2 1,000 1 G 25,000 13,000 4 2 6,000 2 H 18,000 11,000 4 2,333 3 29,000 20,000 6 5 9,000 (1) 1st week: CP =A-B-D-H-I. A is least expensive at $500. Critical path stays the same.

(2) 2nd week: A is still the least expensive at $500. Critical path stays the same.

(3) 3rd week: Because A is no longer available, the choices are B (at $3,000), D (at $2,000), H (at $2,333), or I (at $9,000). Therefore, choose D at $2,000.

The total project cost if shortened by three weeks is A $11,000 B 6,000 c 4,000 D 16,000 E 9,000 F 7,000 G 13,000 H 11,000 20,000 $97,000 L04-3 SOLVED PROBLEM 4 You have been asked to calculate the Cost Performance Index for a project using earned value management techniques. It is currently day 20 of the project and the following summarizes the current status of the project: Expected Actual Expected Activity Expected Completion Expected% Actual% Cost to Activity Cost Duration Start Date Date Complete Complete Date Startup $100,000 10 days 0 10 100% 100% $105,000 Construction 325,000 14 days 8 22 12/14 =85.714% 90% 280,000 Finishing 50,000 12 days 18 30 2/12 = 16.667% 25% 2,500 Projects Chapter4 101 Calculate the Schedule Variance, Schedule Performance Index, and Cost Performance Index for the project.

Solution Step 1: Calculate Budgeted Cost of the Work Scheduled (BCWS) to date:

Startup is 100 percent complete and we are beyond the expected completion date, so budgeted cost is $100,000 for this activity.

Would expect Construction to be 85.714 percent complete and cost $278,571 to date.

Would expect Finishing to be 16.667 percent complete at a cost of $8,333 to date.

Budgeted Cost of Work Scheduled = $100,000 + $278,571 + $8,333 = $386,904 Step 2: Calculate the Budgeted Cost of the Work Performed (BCWP) to date:

Startup is 100 percent complete, so budgeted cost is $100,000.

Construction is actually only 90 percent complete, so budgeted cost for this much of the activ­ ity is (325,000 x .9) = $292,500.

Finishing is now 25 percent complete, so budgeted cost is ($50,000 x .25) = $12,500.

Budgeted Cost of Work Performed = $100,000 +$292,500 + $12,500 = $405,000 Step 3: Actual Cost (AC) of the project to date is $105,000 +$280,000 + $2,500 = $387,500.

Step 4: Calculate performance measures:

Schedule Variance = $405,000 -$386,904 = $18,096 Schedule Performance Index = $405,000/$386,904 = 1.05 Cost Performance Index = $405,000/$387,500 = 1.05 The project looks good because it is both ahead of schedule and below the budgeted cost. Discussion Questions L04-1 I. What was the most complex project you have been involved in? Give examples of the fol­ lowing as they pertain to the project: the work breakdown structure, tasks, subtasks, and work package. Were you on the critical path? Did it have a good project manager? L04-2 2. What are some reasons project scheduling is not done well? 3. Which characteristics must a project have for critical path scheduling to be applicable?

What types of projects have been subjected to critical path analysis? 4. What are the underlying assumptions of minimum-cost scheduling? Are they equally realistic? 5. "Project control should always focus on the critical path." Comment. L04-3 6. Why would subcontractors for a government project want their activities on the critical path? Under what conditions would they try to avoid being on the critical path? 7. Discuss the graphic presentations in Exhibit 4.11. Are there any other graphic outputs you would like to see if you were project manager? 8. Why is it important to use earned value management ( EVM) in the overall management of projects? Compare this to the use of baseline and current schedules only. 9. Consider the EVM charts in Exhibit 4.12. Are there any other measures you might want to use in the management of a project? What are some controllable variables that may affect the costs being tracked? L04-4 10. What do you think might be some barriers to the successful, effective use of the project management software packages discussed in the chapter? 102 Section 1 Strategy, Products, and Capacity Objective Questions L04-1 1. What are the three types of projects based on the amount of change involved? 2. What are the four major categories of projects based on the type of change involved? 3. Match the following characteristics with their relevant project team organizational structures:

__ The project is housed within a functional division of the firm. A. Pure project __ A project manager leads personnel from different B. Functional project functional areas. __ Personnel work on a dedicated project team. C. Matrix project __ A team member reports to two bosses. __ Team pride, motivation, and commitment are high. __ Team members can work on several projects. __ Duplication of resources is minimized. 4. What is the term for a group of project activities that are assigned to a single organiza­ tional unit? L04-2 5. The following activities are part of a project to be scheduled using CPM: Activity Immediate Predecessor Time (weeks) A 6 B A 3 c A 7 D c 2 E B,D 4 F D 3 G E, F 7 a. Draw the network. b. What is the critical path? c. How many weeks will it take to complete the project? d. How much slack does activity B have? 6. Schedule the following activities using CPM:

Activity Immediate Predecessor Time (weeks) A 1 B A 4 c A 3 D B 2 E C,D 5 F D 2 G F 2 H E,G 3 a. Draw the network. b. What is the critical path? c. How many weeks will it take to complete the project? d. Which activities have slack, and how much? 7. The R&D department is planning to bid on a large project for the development of a new communication system for commercial planes. The accompanying table shows the activi­ ties, times, and sequences required (answers in Appendix D). 103 Projects Chapter4 Activity Immediate Predecessor Time (weeks) A 3 B A 2 c A 4 D A 4 E B 6 F C,D 6 G D,F 2 H D 3 E,G,H 3 a. Draw the network diagram. b. What is the critical path? c. Suppose you want to shorten the completion time as much as possible, and you have the option of shortening any or all of B, C, D, and Geach one week. Which would you shorten? d. What is the new critical path and earliest completion time? 8. The following represents a project that should be scheduled using CPM: Times (days) Activity Immediate Predecessors a m b A 3 5 B 2 3 c A 1 2 3 D A 2 3 4 E B 3 4 11 F C,D 3 4 5 G D, E 4 6 H F, G 2 4 5 a. Draw the network. b. What is the critical path? c. What is the expected project completion time? d. What is the probability of completing this project within 16 days? 9. There is an 82 percent chance the following project can be completed in X weeks or less.

What is X? 0 Activity Most Optimistic Most Likely Most Pessimistic A 2 5 11 B 3 3 3 c 3 5 D 6 8 10 E 4 7 10 104 Section I Strategy, Products, and Capacity 10. The following table represents a plan for a project: Times (days) Job No. Predecessor Job(s) a m b 1 2 3 4 2 2 3 3 4 5 12 4 3 4 11 5 2 3 5 6 3 2 3 7 4 8 9 8 5,6 2 4 6 9 8 2 4 12 10 7 3 4 5 ~lL __ ··----~iQ~----·-· ._? --~-·-··-·z· a. Construct the appropriate network diagram. b. Indicate the critical path. c. What is the expected completion time for the project? d. You can accomplish any one of the following at an additional cost of $1,500: (1) Reduce job 5 by two days.

(2) Reduce job 3 by two days.

(3) Reduce job 7 by two days.

Ifyou will save $1,000 for each day that the earliest completion time is reduced, which action, if any, would you choose?

e. What is the probability that the project will take more than 30 days to complete? 11. A construction project is broken down into the following 10 activities: Activity Immediate Predecessor Time (weeks) 2 3 4 5 6 7 8 9 10 1 2, 3 3 4 5 6, 7 8,9 4 2 4 3 5 6 2 3 5 7 a. Draw the network diagram. b. Find the critical path. c. If activities I and 10 cannot be shortened, but activities 2 through 9 can be shortened to a minimum of one week each at a cost of $10,000 per week, which activities would you shorten to cut the project by four weeks? 12. Here is a CPM network with activity times in weeks (answers in Appendix D): ~w .... ~ ~~.;.· ~ C _________..-@ ...·· E(4) '"'~ Projects Chapter4 105 a. Determine the critical path. b. How many weeks will the project take to complete? c. Suppose F could be shortened by two weeks and B by one week. How would this affect the completion date? 13. Here is a network with the activity times shown in days: a. Find the critical path. b. The following table shows the normal times and the crash times, along with the asso­ ciated costs for each activity. Activity Normal Time Crash Time Normal Cost Crash Cost A 7 6 $7,000 $ 8,000 B 2 5,000 7,000 c 4 3 9,000 10,200 D 5 4 3,000 4,500 E 2 1 2,000 3,000 F 4 2 4,000 7,000 G 5 4 5,000 8,000 Ifthe project is to be shortened by four days, show which activities, in order of reduction, would be shortened and the resulting cost. 14. The home office billing department of a chain of department stores prepares monthly inventory reports for use by the stores' purchasing agents. Given the following informa­ tion, use the critical path method to determine: a. How long the total process will take. b. Which jobs can be delayed without delaying the early start of any subsequent activity. Job Immediate Time and Description Predecessors (hours) A Start 0 B Get computer printouts of customer purchases A 10 c Get stock records for the month A 20 D Reconcile purchase printouts and stock records B,C 30 E Total stock records by department B,C 20 F Determine reorder quantities for coming period E 40 G Prepare stock reports for purchasing agents D, F 20 H Finish G 0 106 Section 1 Strategy, Products, and Capacity 15. For the network shown:

a. Determine the critical path and the early completion time in weeks for the project. b. For the data shown, reduce the project completion time by three weeks. Assume a lin­ ear cost per week shortened, and show, step by step, how you arrived at your schedule. Activity Normal Time Normal Cost Crash Time Crash Cost A 5 $ 7,000 3 $13,000 B 10 12,000 7 18,000 c 8 5,000 7 7,000 D 6 4,000 5 5,000 E 7 3,000 6 6,000 F 4 6,000 3 7,000 G 4 7,000 3 ~00 16. The following CPM network has estimates of the normal time in weeks listed for the activities: a. Identify the critical path. b. What is the length of time to complete the project? c. Which activities have slack, and how much? d. Here is a table of normal and crash times and costs. Which activities would you shorten to cut two weeks from the schedule in a rational fashion? What would be the incremental cost?

Is the critical path changed? Activity Normal Time Crash Time Normal Cost Crash Cost A 7 6 $7,000 $8,000 B 3 2 5,000 7,000 c 4 3 9,000 10,200 D 5 4 3,000 4,500 E 2 2,000 3,000 F 4 2 4,000 7,000 G 5 4 5,000 8,000 17. Bragg's Bakery is building a new automated bakery in downtown Sandusky. Here are the activities that need to be completed to get the new bakery built and the equipment installed. 107 Projects Chapter4 Normal Crash Expediting Predecessor Time Time (weeks) Cost/Week A 9 6 $3,000 B A 8 5 3,500 c A 15 10 4,000 D B,C 5 3 2,000 E c 10 6 2,500 F D, E 2 5,000 a. Draw the project diagram. b. What is the normal project length? c. What is the project length if all activities are crashed to their minimum? d. Bragg's loses $3,500 in profit per week for every week the bakery is not completed.

How many weeks will the project take if we are willing to pay crashing cost as long as it is less than $3,500? 18. Assume the network and data that follow: Normal Normal Crash Crash Immediate Activity Time (weeks) Cost Time (weeks) Cost Predecessors A 2 $ 50 1 $70 B 4 80 2 160 A c 8 70 4 110 A D 6 60 5 80 A E 7 100 6 130 B F 4 40 3 100 D G 5 100 4 150 C, E,F a. Construct the network diagram. b. Indicate the critical path when normal activity times are used. c. Compute the minimum total direct cost for each project duration based on the cost associated with each activity. Consider durations of 13, 14, 15, 16, 17, and 18 weeks. d. If the indirect costs for each project duration are $400 (18 weeks), $350 (17 weeks), $300 (16 weeks), $250 (15 weeks), $200 (14 weeks), and $150 (13 weeks), what is the total project cost for each duration? Indicate the minimum total project cost duration. L04-3 19. Your project to obtain charitable donations is now 30 days into a planned 40-day proj­ ect. The project is divided into three activities. The first activity is designed to solicit individual donations. It is scheduled to run the first 25 days of the project and to bring in $25,000. Even though we are 30 days into the project, we still see that we have only 90 percent of this activity complete. The second activity relates to company donations and is scheduled to run for 30 days starting on day 5 and extending through day 35. We estimate that, even though we should have 83 percent (25/30) of this activity complete, it is actually only 50 percent complete. This part of the project was scheduled to bring in $150,000 in donations. The final activity is for matching funds. This activity is sched­ uled to run the last 10 days of the project and has not started. It is scheduled to bring in an additional $50,000. So far, $175,000 has actually been brought in on the project.

Calculate the Schedule Variance, Schedule Performance Index, and Cost (actually value in this case) Performance Index. How is the project going? (Hint: Note that this problem is different since revenue rather than cost is the relevant measure. Use care in how the measures are interpreted.) 20. A project to build a new bridge seems to be going very well because the project is well ahead of schedule and costs seem to be running very low. A major milestone has been reached where the first two activities have been totally completed and the third activ­ ity is 60 percent complete. The planners were expecting to be only 50 percent through 108 Section 1 Strategy, Products, and Capacity the third activity at this time. The first activity involves prepping the site for the bridge.

It was expected that this would cost $1,420,000 and it was done for only $1,300,000.

The second activity was the pouring of concrete for the bridge. This was expected to cost $10,500,000 but was actually done for $9,000,000. The third and final activity is the actual construction of the bridge superstructure. This was expected to cost a total of $8,500,000. To date, they have spent $5,000,000 on the superstructure.

Calculate the Schedule Variance, Schedule Performance Index, and Cost Performance Index for the project to date. How is the project going? L04-3 21. What feature in project management information systems can be used to resolve over­ allocation of project resources?

22. What was the first major project management information system that is now commonly used for managing very large projects?

23. What type of chart compares the current project schedule with the original baseline schedule so that deviations from the original plan can be easily noticed? Analytics Exercise: Product Design Project You work for Nokia in its global cell phone group. You have 3. been made project manager for the design of a new cell phone. Your supervisors have already scoped the project, 4. so you have a list showing the work breakdown structure, and this includes major project activities. You must plan the project schedule and calculate project duration. Your boss wants the schedule on his desk tomorrow morning! You have been given the information in Exhibit 4.13.

It includes all the activities required in the project and the duration of each activity. Also, dependencies between the activities have been identified. Remember that the pre­ ceding activity must be fully completed before work on the following activity can be started.

Your project is divided into five major subprojects.

Subproject "P" involves developing specifications for the new cell phone. Here, decisions related to such things as battery life, size of the phone, and features need to be made. These details are based on how a customer uses the cell phone. These user specifications are redefined in 5.

terms that have meaning to the subcontractors that will actually make the new cell phone in subproject "S" sup­ plier specifications. These involve engineering details for how the product will perform.

The individual components that make up the product are the focus of subproject "D." Subproject "I" brings all the components together, and a working prototype is built and tested.

Finally, in subproject "V," suppliers are selected and contracts are negotiated. I. Draw a project network that includes all the activities. 6. 2. Calculate the start and finish times for each activ­ ity and determine the minimum number of weeks for completing the project. Find the activities that are on the critical path for completing the project in the shortest time. Identify slack in the activities not on the project critical path.

Your boss would like you to study the impact of making two changes to how the project is orga­ nized. The first change involves using dedicated teams that would work strictly in parallel on the activities in each subproject. For example, in sub­ project P (product specifications) the team would work on Pl, P2, P3, and P4 all in parallel. In other words, there would be no precedence relationships within a subproject-all tasks within a subproject would be worked on at the same time and each would take the same amount of time as originally specified. With this new design, all the subprojects would be done sequentially with P done first, then S, D, I, and finally V. What would be the expected impact on how long it would take to complete the project if this change were made?

The second change your boss would like you to consider would be to select the suppliers during subproject P and have them work directly with the dedicated teams as described in step 4. This would involve adding an additional activity to subproject P called supplier selection and contract negotiation (P5) with a duration of 12 weeks. This new activ­ ity would be done in parallel with Pl, P2, P3, and P4. Subprojects S and V would be eliminated from the project. What would be the expected impact on how long it would take to complete the project if this additional change were made?

Evaluate the impact of making these changes using criteria other than just the time to complete the project. Do you think it would be in Nokia's best interest to try to make these changes in how it runs this and future cell phone design projects? 109 Projects Chapter4 Work Breakdown Structure and Activities for the Cell Phone Design Project Major Subprojects/Activities Activity Identification Dependency Duration (weeks) Product specifications (P) Market research P1 2 Overall product specifications P2 P1 4 Hardware P3 P2 5 P4 P3 5 Supplier specifications (S) Hardware S1 P4 5 Software S2 P4 6 Product design (D) Battery D1 S1 Display D2 S1 2 Camera D3 S1 Outer cover D4 D1, D2, D3 4 Product integration (I) Hardware 11 D4 3 User interface 12 D2 4 Software coding 13 12 4 Prototype testing 14 11, 13 4 (V) Suppliers selection V1 S1,S2 10 Contract V2 14, V1 2 Practice Exam Name the term defined in each of the following state­ ments. Answers are listed at the bottom. 1. A project structured where a self-contained team works full time on the project. 2. Specific events that upon completion mark important progress toward completing a project. 3. This defines the hierarchy of project tasks, subtasks, and work packages. 4. Pieces of work in a project that consume time to complete. 5. A chart that shows both the time and sequence for completing the activities in a project. ·g1qu[!1lAu si\uM[u gJu sg:unosg~ ·01 llU!lJSUl;) "6 6. Activities that in sequence form the longest chain in a project. 7. The difference between the late and early start time for an activity. 8. When activities are scheduled with probabilistic task times. 9. The procedure used to reduce project completion time by trading off time versus cost. 10. A key assumption related to the resources needed to complete activities when using the critical path method. (J.~3d) ;mb!UlJ;)gJ. Mg!Ag~ puu uopun111A3 UllllllOld gqJ. ·g )PUIS ·l (s)lj1ud [ll;)!l!l;) "9 lllllj;) nuuo ·~ sgp!A!PV ·r :Jlll);)nJJS UMOp)[UgJq )[lOJ\ "£ SgUO)Sgl!W ·z S)[lOA\)[Ull)[S lO p;ifoJd gJnd ·1 WllX3 ;};Jn:m.Id OJ S.l