Question

Development of a new deluxe version of a particular toy is being considered by T-O-Y Inc. The activities necessary for the completion of this project along with the relevant information for each activity are listed in the following table. The Total Crash Time represents the time for that activity after it has been crashed the maximum crash time allowed for that activity. For example, we can reduce the time for Activity A by one week to 3 weeks after crashing it.

Activity	Time to complete using Normal Time (Weeks)	Time activity is completed using Crash Time (Weeks)	Total Normal Cost	Crash Cost per period	Immediate Predecessors
A	4	3	$2,000	$600	--
B	2	1	2,200	$800	--
C	3	3	500	$0	--
D	8	4	2,300	$750	A
E	6	3	900	$100	B
F	3	2	3,000	$1,200	C
G	4	2	1,400	$300	D,E

a) Using the normal time, what is the critical path, the project completion time, the total time required to complete all of the activities, and the slack time for each path and each activity? (The slack time for each path should be relative to the time to complete the critical path.)

b) If you wish to reduce the time required to complete this project by one week, which activity should be crashed, and how much will this increase the total cost?

c) Now, we want to crash the project to the minimum possible time crashing any and all activities necessary to do this using the crash cost per period rule we have studied. What is the project completion time now? How much would the total cost increase?

d) Let’s return to the results found in a). Suppose the company believes that reducing the project completion time from the time reported in part a), will help the company realize an additional $700 per week in revenue for the first two weeks the project time is reduced, $650 per week in revenue for the next two weeks the project is reduced and $500 per week in revenue after that for every week the project is reduced. How many weeks should the company reduce the project completion time and what is the resulting cost of the project considering the additional revenue as an offset to the cost associated with crashing the project? The company is interested in selecting the project duration and reduced activity times that minimize the cost of the project.

Answer 1