Question

The Advanced Tech Company has a project to design an integrated information data base for a major bank. Data for the project are given $150 per day. The company will incur a $100 per day penalty for each day the project lasts beyond day 15. the following table. Indirect project costs amount to Normal Time Crash Time Crash Cost Immediate Normal Cost (S) Activity Predecessor(s) (S) (days) (days) 1.200 A 6 800 4 6 1,000 2 2,200 600 900 C 1 A. B D 4 2,000 1,200 2 E 4 1,000 1,300 C. D .300 1,400 E 3 1 E 900 G 3 900 E 5 500 900 G H a. What is the project's duration if only normal times are used? day(s). (Enter your response as an integer.) The project duration is b. What is the minimum-cost schedule? With the minimum-cost schedule, the project duration is day(s). (Enter your response as an integer.) c. What is the critical path for the minimum-cost schedule? The critical path for the minimum-cost schedule is

Answer 1

Step 1: Network diagram is following: A F Start Finish B 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 unit time (Crash Cost Normal Cost) Max Crash time Max Crash cost Crash Normal Crash Normal Activity Predecessor ES Crash LS EF LF Slack /day Time Time Cost Cost Time 200 0 2 A 6 4 800 1,200 2 6 2 B 300 2 1,000 2,200 4 0 6 300 C A,B 2 1 600 900 1 6 8 10 2 D 1,200 400 6 10 10 B 4 2 2,000 2 C,D 4 1 1,000 1,300 100 10 10 14 14 1,300 50 14 17 F 1 19 2 G F 900 900 14 17 3 0 14 17 H 5 3 500 900 2 200 17 17 22 22 0 7,300 Step 3: Identify the alternative paths and Critical path. Critical path is the path of longest duration in the network A-C-E-F 15 20 A-C-E-G-H B-C-E-F 15 20 B-C-E-G-H B-D-E-F 17 Critical path B-D-E-G-H 22 Normal Time days 22 Total Direct Cost = 7,300 Indirect cost/day 150 (given) Penalty cost/day 100 (given) if project duration> days 15 시0이50이 c 6의의의 | |EL|6|:

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 Crash Path 1 Path 2 Path 3 Path 4 Path 5 Path 6 Activity Total Indirect Penalty Cumulativ TOTAL Iteration A-C-E-G-H B-C-E-F B-C-E-G-H B-D-E-I B-D-E-G-H Duration Crash Cost Crashed Time A-C-E-F e Crash Direct Cost Cost Cost COST 0 15 20 15 20 17 22 22 7,300 3.300 700 11,300 1 12 19 19 300 7,600 400 E 17 12 17 14 300 2,850 10,850 12 15 12 15 14 17 17 400 700 8.000 2,550 200 10,750 We see that only Activity B and D of critical path are remaining to be crashed. But the minimum crash cost per day is $ 300 for activity B, which is higher than the sum of indirect cost and penalty cost (=150+100 250). Therefore further crashing will not reduce cost, but will increase it. Therefore, minimum-cost schedule is achieved. Minimum-Cost Schedule Project Cost 10,750 Project Duration 17

a) Using normal times, The project duration is 22 days

b) Minimum-cost schedule:

With the minimum-cost schedule, the project duration is: 17 days

c) The critical path for the minimum-cost schedule is B-D-E-G-H