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Operations Project Management Essay

693 words - 3 pages

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
...view middle of the document...

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?
The optimal project cost is $3,435.

Computation:
Project cost = Original cost + (cost of expediting G) + (cost of expediting A) + (cost of expediting F)
Project cost = $3,000 + ($75)(1) + ($50)(4) + ($40)(4)
Project cost = $3,435

2. A company decides to plan a project, with activities, precedence and random duration statistics given in the following table:
Activity Immediate
Predecessors Duration
Minimum
(weeks) Duration
Mode
(weeks) Duration
Maximum
(weeks) Duration Mean Duration Variance
A none 2 5 9 5.17 1.36
B A 1 6 8 5.50 1.36
C A 3 5 12 5.83 2.25
D B 2 4 12 5.00 2.78
E B, C 4 6 8 6.00 0.44
F B 6 7 8 7.00 0.11
G D, E 1 2 6 2.50 0.69
H F, G 4 6 16 7.33 4.00

Answer the following questions:
(a) (5 points) Using the PERT method, compute the mean and variances for each activity and add them to the table above.
Mean duration = (ai + 4mi + bi)/6
Duration variance = [(bi – ai)/6]2
Activity Immediate
Predecessors Duration
Minimum
(weeks) Duration
Mode
(weeks) Duration
Maximum
(weeks) Duration Mean Duration Variance
A none 2 5 9 5.17 1.36
B A 1 6 8 5.50 1.36
C A 3 5 12 5.83 2.25
D B 2 4 12 5.00 2.78
E B, C 4 6 8 6.00 0.44
F B 6 7 8 7.00 0.11
G D, E 1 2 6 2.50 0.69
H F, G 4 6 16 7.33 4.00

(b) (5 points) Draw the project network and label the arcs with the activity name.


(c) (5 points) Assuming that the critical path is ABP1EGH, compute the probability that this path duration is between 28 weeks and 32 weeks.

Pr(28 weeks

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