A project may be defined as a series of related jobs usually directed toward some major output and requiring a significant period of time to perform. Project Management can be defined as planning, directing, and controlling resources (people, equipment, material) to meet the technical, cost, and time constraints of the project.
Tom Peters predicts that most of the world’s work will be “brainwork,” done in semi-permanent 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 pure project(nicknamed skunk works), where a self-contained team works full-time on the project.
- 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.
- 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 functional divisions.
- Because team members have no functional area home, they worry about life-after-project, and project termination is delayed
At the other end of the project organization spectrum is the functional project, housing the project within a functional division.
- A team member can work on several projects.
- Technical expertise is maintained within the functional area even if individuals leave the project or organization.
- 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.
- Aspects of the project that are not directly related to the functional area get short-changed.
- Motivation of team members is often weak.
- Needs of the client are secondary and are responded to slowly.
The classic specialized organizational form, “the matrix project,” 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 and when they will be performed, but the functional managers control which people and technologies are used.
- 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 worried 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.
- 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.
- Sub-optimization is a danger, as PM’s hoard resources for their own project, thus harming other projects.
Work Breakdown Structure
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 could also 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 sub-task 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 organizational 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, measures of performance, and specific events to be reached at points in time. These specific events are called project milestones. 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 work breakdown structure (WBDS) defines the hierarchy of project tasks, subtasks and work packages. Completion of one or more work packages results in the completion of a sub-task; 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.
Activities 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.
The two best-known network- planning models were developed in the 1950’s. The Critical Path Method (CPM) was developed for scheduling maintenance shutdowns at chemical processing plants owned by Du Pont.
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 missile project. This was a massive project involving over 3,000 contractors. Because most of the activities had never been done before, PERT was developed to handle uncertain time estimates. As years passed, features that distinguished CPM from PERT have diminished, so in our treatment here we just use the term CPM.
The critical path of activities in a project is the sequence of activities that form the longest chain in terms of their time to complete. If any one of the activities in the critical path is delayed, then the entire project is delayed.
CPM with a Single Time Estimate
Here is a procedure for scheduling a project. In this case, a single time estimate is used because we are assuming that the activity times are known. Later this will be expanded to the cases where there is uncertainty in the activity times.
The following are the appropriate steps:
- Identify each activity to be done in the project, and estimate how long it will take to complete each activity.
- Determine the required sequences of activities, and construct a network reflecting the precedence relationships.
- Determine the critical path.
- Determine the early start / finish and late start/ finish schedule. For each activity in the project, we calculate four points in time: the early start, early finish, late start, and late finish times. The early start and early finish are the earliest times that the activity can start and be finished. Similarly, the late start and late finish are the latest times the activities can start and finish. For some activities in a project there may be some leeway in when an activity can start and finish. This is called the slack time in an activity. The slack time is the time difference between the late and early start times of an activity which is the same as the time difference between the late and early finish times of an activity. The slack time is the time that an activity can be delayed without delaying the entire project.
A very simple project will be scheduled to demonstrate the basic approach. Consider that you have a group assignment that requires a decision on whether you should invest in a company. Your instructor has suggested that you perform the analysis in the following four steps:
A. Select a company.
B. Obtain the company’s annual report and perform a ratio analysis.
C. Collect technical stock price data and construct charts.
D. Individually review the data and make a team decision on whether to buy the stock.
Your group of four people decides that the project can be divided into four activities as suggested by the instructor. You decide that all the team members should be involved in selecting 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 your group: Two people will be responsible for the annual report and ratio analysis, and the other two will collect the technical data and construct the charts. Your group expects it to take two weeks to get the annual report and perform the ratio analysis, and a week to collect the stock price data and generate the charts. You agree that the two groups can work independently. Finally, you agree to meet as a team to make the purchase decision. Before you meet, you want to allow one week for each team member to review all the data. This is a simple project, but it will serve to demonstrate the approach. The following are the appropriate steps.
1. Identify each activity to be done in the project and estimate how long it will take to complete each activity. This is simple, given the information from your instructor. We identify the activities as follows: A(1), B(2), C(1), D(1). The numbers in parentheses are the expected duration of the activities in weeks.
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 immediate predecessors associated with an activity. The immediate predecessors 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:
Here is a diagram that depicts these precedence relationships:
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 longest. A–B–D has a duration of four weeks (1+2+1=4 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. For each activity in the project, we calculate four points in time: the early start , early finish, late start, and late finish times. The early start and early finish are the earliest times that the activity can start and be finished. Similarly, the late start and late finish are the latest times the activities can start and finish without delaying the project. 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.
Algorithms to determine the early start/finish and late start/finish schedule:
- Forward algorithm to calculate the early start and early finish times:
For each path, start at the left side of the diagram and work toward the right side.
For each beginning activity, Early start time =0; Early finish time =Early start time (ES) + activity time
For each other activity, Early start time =Early finish time of the immediate predecessor (immediate preceding activity); if an activity has multiple immediate predecessors, set its early start time equal to the largest early finish time of its immediate predecessors; Early finish time=Early start time+activity time;
- Backward algorithm to calculate the late start and late finish times after forward algorithm:
For each path, start at the right side of the diagram and work toward the left side.
Use the largest early finish times as the late finish time for all ending activities. For each ending activity, Late start time = late finish time- activity time
For each other activity: Late finish time = late start time of the immediate following activity. Note: If an activity has multiple immediately following activities, set the activity’s Late finish time equal to the smallest late start times of the following activities. Late start time = late finish time- activity time
To calculate the early start and early finish times for our project, start from the beginning of the network and work to the end (forward algorithm). Activity A is a beginning activity and has an early start of 0. Its early finish time= early start time + activity time =0+1=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 (early start time of B plus the activity time of B), and the early 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 which is the largest early finish time of its immediate predecessors B and C. The early finish for D is 4 (early start time + activity time of D). Our diagram now looks like this.
To calculate the late finish and late start times, start from the end of the network and work toward the front (backward algorithm). Consider activity D. The earliest that it can be done is at time 4; and if we do not want to delay the completion of the project, the late finish needs to be set to 4. With a duration of 1, the late start time for D is 3 ( late finish time – activity time of D).
Now consider activity C. C must be done by time 3 so that D can start, so C’s late finish time is 3 (Late finish time = late start time of the immediate following activity). Correspondingly, C’s late start time is 2 (Late start time = late finish time- activity time of C). Notice the difference between the early and late start and finish times: Activity C has one week of slack time (slack time=late finish time – early finish time). This means if all of the activities on the same path will be started as early as possible and not exceed their expected times, activity C can be postponed by 1 week without delaying the duration of the project.
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.
To summarize, the critical path for this project is A–B–D. The early start/finish and late start/finish schedules for all activities are summarized as in the table below:
|Activity||Early Start time (ES)||Early finish time (EF)||Late Start time (LS)||Late Finish time (LF)||Slack Time|
CPM with Three Activity Time Estimates
If a single estimate of the time required to complete and 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.
1. Identify each activity to be done in the project.
2. Determine the sequence of activities and construct a network reflecting the precedence relationships.
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 discussed later.
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 percent, that it would take longer.)
In this case, an activity time is assumed to have a beta distribution which is characterized by the three estimates above. Typically, the three estimates are gathered from those people who will perform the corresponding activity.
4. Calculate the expected time (ET) for each activity. The formula for this calculation is:
5. Determine the critical path. Using the expected time (ET) for each activity from step 4, a critical path is calculated in the same way as the single time case.
6. Calculate the variances (𝜎2σ2) of the activity times. Specifically, this is the variance ,𝜎2σ2, associated with each ET and is computed as follows:
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. 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
Determine the probability of completing the project on the given date, based on the application of the standard normal distribution.
D = Desired completion date for the project
𝑇𝐸TE = Expected completion time for the project
∑𝜎2𝑐𝑝∑σcp2 = 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, ind 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.
Given the following project and three time estimates,
we can calculate the activity expected times and variances using the formula in steps 4 and 6 as follows:
we create the project network and determine the critical path the same way we did previously. The only difference is that we are using the expected times (ETs) to determine the critical path and the early start/finish and late start/finish time schedule. The following graph shows the network and the critical path.
Because there are two critical paths in the network (both A-C-F-G and A-B-D-F-G are critical paths), 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 associated with activities A, C, F, and G would be used to ind the probability of completion. Thus ∑𝜎2𝑐𝑝∑σcp2= sum of the variances along the critical path A-C-F-G =9+2.7778+0.1111+ 0 =11.8889. Suppose management asks for the probability of completing the project in 35 weeks. D, then, is 35. The expected completion time is the length of the critical path based on the expected times. Hence the expected completion time is 21+7+8+2=38 (the length of critical path A-C-F-G based on the expected times). Substituting into the Z equation and solving, we obtain
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 critical 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.
Prepare a CPM-type network diagram.
Determine the cost per unit of time (assume days) to expedite each activity.
Compute the critical path.
Shorten the critical path at the least cost.
Plot project direct, indirect, and total-cost curves and find the minimum cost schedule.
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