11-12 Sid Davidson is the personnel director of Babson and Willcount, a company that specializes in consulting and research. One of the training programs that Sid is considering for the middle-level managers of Babson and Willcount is leadership training. Sid has listed a number of activities that must be completed before a training program of this nature could be conducted. The activities and immediate predecessors appear in the following table:

Develop a network for this problem.

11-13 Sid Davidson was able to determine the activity times for the leadership training program. He would like to determine the total project completion time and the critical path(s). The activity times appear in the following table (see Problem 11-12):

11-14 A political campaign manager must coordinate several activities in order to be prepared for an upcoming election. The following table describes the relationships among the activities that need to be completed, as well as the estimated times.

1. Develop a project network for this problem.

2. Determine the ES, EF, LS, LF, and slack time for each activity. Also determine the total project completion time and the critical path(s).

11-15 A marketing firm is developing a new Web-based media campaign for a client. The following table describes the relationships among the activities that need to be completed.

1. Develop a project network for this problem.

2. Determine the ES, EF, LS, LF, and slack time for each activity. Also determine the total project completion time and the critical path(s).

11-16 Jean Walker is making plans for spring break at the beaches in Florida. In applying techniques she learned in her quantitative methods class, she has identified the activities that are necessary to prepare for her trip. The following table lists the activities and the immediate predecessors. Draw the network for this project.

11-17 The following are the activity times for the project in Problem 11-16. Find the earliest, latest, and slack times for each activity. Then find the critical path.

11-18 The Laurenster Corporation is getting into the construction business. A list of activities and their optimistic, most likely, and pessimistic completion times are given in the following table for the next construction project.

1. Develop a project network for this problem.

2. Determine the expected duration and variance for each activity.

3. Determine the ES, EF, LS, LF, and slack time for each activity. Also determine the total project completion time and critical path(s).

4. What is the probability that this job will finish in 38 days or less?

11-19 The Laurenster Corporation needs to set up an assembly line to produce a new product. The following table describes the relationships among the activities that need to be completed for this product to be manufactured.

1. Develop a project network for this problem.

2. Determine the expected duration and variance for each activity.

3. Determine the ES, EF, LS, LF, and slack time for each activity. Also determine the total project completion time and the critical path(s).

4. Determine the probability that the project will be completed in 34 days or less.

5. Determine the probability that the project will take longer than 29 days.

11-20 Monohan Machinery specializes in developing weed-harvesting equipment that is used to clear small lakes of weeds. George Monohan, president of Monohan Machinery, is convinced that harvesting weeds is far better than using chemicals to kill weeds. Chemicals cause pollution, and the weeds seem to grow faster after chemicals have been used. George is contemplating the construction of a machine that would harvest weeds on narrow rivers and waterways. The activities that are necessary to build one of these experimental weed-harvesting machines are listed in the following table. Construct a network for these activities.

11-21 After consulting with Butch Radner, George Monohan was able to determine the activity times for constructing the weed-harvesting machine to be used on narrow rivers. George would like to determine ES, EF, LS, LF, and slack time for each activity. The total project completion time and the critical path(s) should also be determined. (See Problem 11-20 for details.) The activity times are shown in the following table:

11-22 A project was planned using PERT with three time estimates. The expected completion time of the project was determined to be 40 weeks. The variance of the critical path is 9.

1. What is the probability that the project will be finished in 40 weeks or less?

2. What is the probability that the project will take longer than 40 weeks?

3. What is the probability that the project will be finished in 46 weeks or less?

4. What is the probability that the project will take longer than 46 weeks?

5. The project manager wishes to set the due date for the completion of the project so that there is a 90% chance of finishing on schedule. Thus, there would only be a 10% chance the project would take longer than this due date. What should this due date be?

11-23 Tom Schriber, the director of personnel of Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resumés, writing letters, making appointments to see prospective employers, and researching companies and industries. The information on these activities is shown in the following table:

1. Construct a network for this problem.

2. Determine the expected time and variance for each activity.

3. Determine ES, EF, LS, LF, and slack time for each activity.

4. Determine the critical path(s) and project completion time.

5. Determine the probability that the project will be finished in 70 days or less.

6. Determine the probability that the project will be finished in 80 days or less.

7. Determine the probability that the project will be finished in 90 days or less.

11-24 Using PERT, Ed Rose was able to determine that the expected project completion time for the construction of a pleasure yacht is 21 months and the project variance is 4.

1. What is the probability that the project will be completed in 17 months or less?

2. What is the probability that the project will be completed in 20 months or less?

3. What is the probability that the project will be completed in 23 months or less?

4. What is the probability that the project will be completed in 25 months or less?

11-25 The air pollution project discussed in the chapter has progressed over the past several weeks, and it is now the end of week 8. Lester Harky would like to know the value of the work completed, the amount of any cost overruns or underruns for the project, and the extent to which the project is ahead of or behind schedule by developing a table like Table 11.8. The revised cost figures are shown in the following table:

11-26 Fred Ridgeway has been given the responsibility of managing a training and development program. He knows the earliest start time, the latest start time, and the total cost for each activity. This information is given in the following table:

1. Using earliest start times, determine Fred’s total monthly budget.

2. Using latest start times, determine Fred’s total monthly budget.

11-27 General Foundry’s project crashing data are shown in Table 11.9. Crash this project to 13 weeks using CPM. What is the final time for each activity after crashing?

11-28 Bowman Builders manufactures steel storage sheds for commercial use. Joe Bowman, president of Bowman Builders, is contemplating producing sheds for home use. The activities necessary to build an experimental model and related data are given in the following table:

1. What is the project completion date?

2. Formulate an LP problem to crash this project to 10 weeks.

11-29 The Bender Construction Co. is involved in constructing municipal buildings and other structures that are used primarily by city and state municipalities. This requires developing legal documents, drafting feasibility studies, obtaining bond ratings, and so forth. Recently, Bender was given a request to submit a proposal for the construction of a municipal building. The first step is to develop legal documents and to perform all steps necessary before the construction contract is signed. This requires that more than 20 separate activities be completed. These activities, their immediate predecessors, and their time requirements are given in Table 11.10.

As you can see, optimistic (a), most likely (m), and pessimistic (b) time estimates have been given for all of the activities described in the table. Using the data, determine the total project completion time for this preliminary step, the critical path(s), and the slack time for all activities involved.

11-30 Getting a degree from a college or university can be a long and difficult task. Certain courses must be completed before other courses may be taken. Develop a network diagram in which every activity is a particular course that must be taken for a given degree program. The immediate predecessors will be course prerequisites. Don’t forget to include all university, college, and departmental course requirements. Then try to group these courses into semesters or quarters for your particular school. How long do you think it will take you to graduate? Which courses, if not taken in the proper sequence, could delay your graduation?

11-31 Dream Team Productions was in the final design phases of its new film, Killer Worms, to be released next summer. Market Wise, the firm hired to coordinate the release of Killer Worms toys, identified 16 critical tasks to be completed before the release of the film. These tasks are shown in the following table:

1. (a) How many weeks in advance of the film release should Market Wise start its marketing campaign? What are the critical path activities?

2. (b) If tasks 9 and 10 were not necessary, what impact would this have on the critical path and the number of weeks needed to complete the marketing campaign?

11-32 The estimated times (in weeks) and immediate predecessors for the activities in a project are given in the following table. Assume that the activity times are independent.

1. Calculate the expected time and variance for each activity.

2. What is the expected completion time of the critical path? What is the expected completion time of the other path in the network?

3. What is the variance of the critical path? What is the variance of the other path in the network?

4. If the time to complete path A–C is normally distributed, what is the probability that this path will be finished in 22 weeks or less?

5. If the time to complete path B–D is normally distributed, what is the probability that this path will be finished in 22 weeks or less?

6. Explain why the probability that the critical path will be finished in 22 weeks or less is not necessarily the probability that the project will be finished in 22 weeks or less.

11-33 The following costs have been estimated for the activities in a project:

1. Develop a cost schedule based on earliest start times.

2. Develop a cost schedule based on latest start times.

3. Suppose that it has been determined that the $6,000 for activity G is not evenly spread over the 3 weeks. Instead, the cost for the first week is $4,000, and the cost is $1,000 per week for each of the last 2 weeks. Modify the cost schedule based on earliest start times to reflect this situation.

11-34 The Scott Corey accounting firm is installing a new computer system. Several things must be done to make sure the system works properly before all the accounts are put into the new system. The following table provides information about this project. How long will it take to install the system? What is the critical path?

11-35 The managing partner of the Scott Corey accounting firm (see Problem 11-34) has decided that the system must be up and running in 16 weeks. Consequently, information about crashing the project was put together and is shown in the following table:

1. If the project is to be finished in 16 weeks, which activity or activities should be crashed to do this at the least additional cost? What is the total cost of this?

2. List all the paths in this network. After the crashing in part (a) has been done, what is the time required for each path? If the project completion time must be reduced another week so that the total time is 15 weeks, which activity or activities should be crashed? Solve this by inspection. Note that it is sometimes better to crash an activity that is not the least cost for crashing if it is on several paths rather than to crash several activities on separate paths when there is more than one critical path.

11-36 The L. O. Gystics Corporation is in need of a new regional distribution center. The planning for this project is in the early stages, but the activities have been identified, along with their predecessors and their activity times in weeks. The table below provides this information. Develop a linear program that could be used to determine the length of the critical path (i.e., the minimum time required to complete the project). Solve this linear program to find the critical path and the time required to complete the project.

11-37 The Laurenster Corporation needs to perform the tasks in the following list. Develop the associated PERT network diagram, and determine the probability that the project will be complete in 16 weeks or less.

11-38 The Laurenster Corporation has determined the client will pay it a $10,000 bonus if it completes the project in Problem 11-37 in 14 weeks or less. The associated normal times and costs as well as the crash times and costs are shown below.

Considering the costs involved to crash the project, determine if the Laurenster Corporation should crash the project to 14 weeks to receive the bonus.