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Operations - Project Management

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Homework Assignment 6

1. For the problem in Q2 of Homework 5, the company decided that the project in the previous problem has to be expedited in order to optimize (minimize) the project cost. Expediting can be used to trade direct cost for indirect cost, since expediting the project reduces the indirect cost of the project by a fixed amount per day, while expediting an activity increases its total direct cost. The Accounting Department found that indirect costs amount to $100 per day, while activity direct costs as well as their normal and expedited times are given in the table below, from which you can compute the direct cost incurred by expediting an activity by one day.
Activity Normal
Time
(days) Expedited
Time
(days) Normal
Cost
($) Expedited
Cost
($)
A 32 26 200 500
B 21 20 300 375
C 30 30 200 200
D 45 40 200 800
E 26 20 700 1,360
F 28 24 1,000 1,160
G 20 18 400 550 Answer the following questions:
(a) (10 points) What is the optimal time to complete the project?
The optimal time to complete the project is 73 days. Consider the following information:

Activity Normal Time (days) Expedited Time (days) Normal Cost ($) Expedited Cost ($) Cost/ Week ($)
A 32 26 200 500 50
B 21 20 300 375 75
C 30 30 200 200 -
D 45 40 200 800 120
E 26 20 700 1,360 110
F 28 24 1,000 1,160 40
G 20 18 400 550 75

Cost/Week = (Expedited Cost – Normal Cost)/(Normal Time – Expedited Time)

Critical Paths = AP1EG and CFG

The company should first expedite Activity G by 1 day. This brings the completion time down to 77 days while adding $75 to the total cost of the project. This also adds AD as a critical path. Next, the company should expedite both A and F by 4 days, reducing the completion time to 73 days while adding an additional $90 per week to the total cost of the project.

(b) (5 points) What is the optimal project cost?

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