Question

Assume that Indirect project costs are $75,000 per week Crash the network (one week at a time) until you reach the optimum cost-time point. Document your crashes clearly. d. What is the project length at the optimum point?

MGMT 4143 Ch 9 HomeworkDue 3/27, 9pm NOTE due date is changed All work must be done in Excel Put each problem on a separate worksheet tab Label the worksheet tabs, put your name on each worksheet. Note: Crash the networks as demonstrated in the Project Crashing notes andpodcast. You must draw and solve the networks in Excel using the method that we have previously mastered - showing ES, EF, LS, LF,slack on each activity ATEACH STEP Show your crashes in a clear and systematic manner, redrawing the network and documenting the results for each crash. Use complete sentences, proper gram If you draw diagrams as shown in the text, you will get 0 credit Answer any questions underneath the appropriate network diagram. mnar The following table gives information on a project (T in weeks) Normal Crash Activity PredecessorsSlop Ta (weeks) Ca (S000) Tc (weeks)Ce (S000) Start Start 50 80 180 70 50 100 160 190 80 B, C D, E 200 400 H. I Draw the network, solve according to the prescribed method. a. Under normal conditions, what is the earliest the project can be completed? b. What is the critical path? c. What is the total direct cost? Assume that Indirect project costs are $75,000 per week Crash the network (one week at a time) until you reach the optimum cost-time point. Document your crashes clearly d. What is the project length at the optimum point? e. What is the total project cost at the optimum point?

Answer 1

Step 1: Network Diagram (Activity on Node) is as follows Step 2: Draw the table listing Max crash time and Crash cost per unit time Max Crash time Normal time - Crash time Crash cost per week (Crash Cost Normal Cost) Max Crash time Max Crash cost ES / weekES Normal Crash N Normal Crash Activity Predecessor LS EF Cost Cost 90 180 Time Time 40 50 60 70 50 100 60 60 160 190 80 10 60 100 20 12 14 14 16 21 23 23 24 B,C D,E 14 16 21 16 23 14 16 21 20 23 14 16 21 23 19 24 60 60 200 400 200 H,I 745 Step 3: Identify the alternative paths and Critical path. Critical path is the path of longest duration in the network A-B-E-F-G-H- A-C-E-F-G-H- A-D-F-G-H-J A-B-E-F-I-J A-C-E-F-I-J A-D-F-I-J 23 24 Critical path 17 19 20 13 Normal Time - Total Direct Cost = 24 weeks 745 Indirect cost/wk 75 (given)

Step 4: Project Crashing using least cost method 1. Identify and list the various alternative paths through the network and their respective duration 2. Determine Max crash time (-Normal time - Crash time) and Crash cost per unit time (Crash cost - Normal cost)/Max Crash Time for each activity. Also determine whether the crash cost rate remains constant as the activity is crashed, or it changes. Determine the variable crash costs by time, if they are variable. 3. Determine the critical path, i.e. the path of longest duration. Only activities along the critical path need to be crashed 4. Identify the eligible activity on the critical path having the least crash cost per unit time. and reduce by 1 time unit at a time. See if the critical path changes as the activities along the critical path are crashed 5. If there are multiple critical paths at any stage during the crashing. Then determine whether there is any of the activites common to the critical paths Then calculate whether the crash cost of common activity is less than the combined crash costs of the least cost crash cost activities along the critical paths 6. Continue crashing as long as the total benefit of crashing is more than the cost of crashing, if the objective is to minimize cost. Or continue crashing, if all the activities of the critical path are fully crashed, if the objective is to minimize project duration, irrespective of cost. Project Activity Cumulativ e Crash Path 4 Path 1 A-B-E-F- G-H-J 23 Path 2 A-C-E-F- G-H-J Path 3 A-D-F-G- H-J 17 Path 5 Path 6 Activity Crashed Iteration TOTAL COST 1 Time A-B-E-F-I- A-C-E-F-I- A-D-F-I- Duration Crash Cost Direct Cost Cost 19 19 18 17 13 13 12 12 24 745 765 805 1,800 1,725 1,650 1,575 2,545 2,490 2,455 21 15 19 21 15 18 21 120 We see that all the activities of the critical path, except F are fully crashed. The crash cost of per week of activity F is 100 ($000), which is more than indirect cost of 75 ($000). There it is not economical to crash activity F. So, optimum cost-time point is reached Therefore, minimum-cost schedule is achieved Minimum Cost-Time Schedule Project Cost Project Duration 2,440 21

a) Under normal conditions, earliest project completion time = 24 weeks

b) Critical path is: A-C-E-F-G-H-J

c) Total direct cost = 745 ($000)

d) Project length at optimum point = 21 weeks

e) Total project cost at the optimum point = 2440 ($000) (this is reduced after crashing from original total project cost of 2545)