Exam 13: Project Scheduling: Pertcpm

Use the following network of related activities with their duration times to complete a row for each activity under the column headings below. Activity Immectate Predecessors Activity Time ES LS EF LF Sack Critical Path? A B C D E F G H I J

Precedence relationships among activities is critical in CPM analysis but not in PERT.

A project has the following activities,durations,costs,and precedence relationships: Present Duration (Weeks) Accelerated Duration (Weeks) Immediate Predecessor Activities Present Cost Accelerated Cost A 10 9 \@cdots \ 11,000 \ 15,000 B 15 13 \@cdots 20,000 25,000 C 10 6 A 9,000 20,000 D 20 18 A 25,000 30,000 E 15 10 C 20,000 35,000 F 17 15 B 20,000 30,000 G 12 10 B 15,000 25,000 H 9 8 D,F 12,000 18,000 I 7 6 G, H 10,000 15,000 Develop a cost-time trade-off analysis.Detail the steps that you would use to accelerate or crash the project to its minimum duration at the lowest cost.Determine each step's cost and the duration of the project.

Critical activities are those that can be delayed without delaying the entire project.

Name at least three managerial situations where answers are provided by project management solutions.

The variance in the project completion time is the sum of the variances of all activities in the project.

The latest finish time for an activity is the largest of the latest start times for all activities that immediately follow the activity.

National Oil Company (NATOCO)must plan the shutdown of its Houston refinery for routine preventive maintenance.Each hour of downtime is lost production time and is very costly,so NATOCO wants the maintenance project completed in 22 hours.The PERT network below shows the precedence relationships of the activities involved in the project.The table gives the activity times and costs under normal operations and maximum crashing. NATOCO wants to know the minimum cost of completing the maintenance project within the 22-hour period.Formulate and solve a linear program that will yield this information. Activity Normal Time (hr) Normal Cost Crash Time (hr) Crash Cost A 2 \ 2,000 1.5 \ 3,000 B 4 3,000 3 3,500 C 1 1,500 1 1,500 D 4 5,300 2.5 8,000 E 6 5,400 5 7,000 F 10 6,000 8 9,000 G 8 4,800 5 9,900 H 2 2,800 1 2,900 I 5 4,500 4 5,000 J 12 6,000 6 9,600 K 7 7,000 4 9,700 L 11 8,800 9 9,200 M 4 1,000 1 7,000

From this schedule of activities,draw the PERT/CPM network. Activity Immediate Predecessor A \@cdots B A C B D B E A F C, D G E, F

Constraints in the LP models for crashing decisions are required to compare the activity's earliest finish time with the earliest finish time of each predecessor.

PERT and CPM are applicable only when there is no dependence among activities.

PERT and CPM

A project consists of five activities.Naturally the paint mixing precedes the painting activities.Also,both ceiling painting and floor sanding must be done prior to floor buffing. Activity Optimistic Time (hr) Most Probable Time (hr) Pessimistic Time (hr) Floor sanding 3 4 5 Floor buffing 1 2 3 Paint mixing 0.5 1 1.5 Wall painting 1 2 9 Ceiling painting 1 5.5 7 a.Construct the PERT/CPM network for this problem. b.What is the expected completion time of this project? c.What is the probability that the project can be completed within 9 hr.?

A senior MIS design class project team has developed the following schedule of activities for their project,using their best estimate of completion times.Both written and oral reports are required.Draw the project network.Can they complete the project in the 38 class days remaining until the end of the semester? Activity Time Immediate Predecessor A. Find dient 4 \@cdots B. Write prospectus 2 A C. Obtain approval from client and professor 3 D. Complete programming 12 E. Do industry background research 10 \@cdots F. Write final paper 6 D, E G. Write oral report 5 D, E

When activity times are uncertain,an activity's most likely time is the same as its expected time.

Mary Yetter,a staff analyst at the Los Angeles plant of Computer Products Corporation,is assigned to the team that is developing the process design for producing the bar code scanner of Example 1.The corporate planning group in San Jose,California has contacted her and has asked how confident the design group is about completing the project in 60 days.She has developed these estimated time durations in days for the project: Activity Immediate Predecessor Activities Optimistic Time Most Likely Time Pessimistic Time A - 10 12 15 B A 6 10 14 C A 10 15 20 D A 9 9 18 E B 5 6 8 F C,E 10 12 13 G B 12 14 16 H B,D 18 21 24 I B,D 10 15 20 J F.G.H 8 10 14 a. Compute the expected time and variance for each activity. b. Determine the critical path and the expected duration of the project. c. What is the probability that the project will take longer than 58 days to complete? d. Which path in the project network offers the greatest risk of overrunning a new deadline of 56 days?

Arcs in a project network indicate

Slack equals

Joseph King has ambitions to be mayor of Williston,North Dakota.Joe has determined the breakdown of the steps to the nomination and has estimated normal and crash costs and times for the campaign as follows (times are in weeks). Joe King is not a wealthy man and would like to organize a 16-week campaign at minimum cost.Write and solve a linear program to accomplish this task.

The project manager should monitor the progress of any activity with a large time variance even if the expected time does not identify the activity as a critical activity.