MTH601 Midterm Past Paper Spring 2005

MIDTERM EXAMINATION · SEMESTER SPRING 2005 · MTH601 – Operational Research

2. 2. Paste the bitmap image for the tables, diagrams etc while solving your questions
3. The duration of this examination is 90 minutes.
4. This examination is closed book, closed notes, closed neighbors.
5. Calculator is allowed

Descriptive Multiple Choice Questions Total Question

Q10. Question No: 1

Marks: 10

For the following project diagram find out Earliest Start Time (EST), Earliest Finish Time (EFT), Latest Start Time (LST), Latest Finish Time (LFT) for each activity. Also find the Critical path.

NOTE: There is no need of making diagram corresponds to each step, you have to write down only the required terms correspond to each activity and the justification for the critical path.

Solution: · Activity · EST · EFT · LST · LFT

A(1 – 2) B(1 – 3) D1(2 – 3) C(2 – 4) D(3 – 5) E(4 – 5) F(4 – 6) G(5 – 6)

To find the Critical Path we’ll find the Slack (Float) of each activity.

Activity

Slack

A(1 – 2) B(1 – 3) D1(2 – 3) C(2 – 4) D(3 – 5) E(4 – 5) F(4 – 6) G(5 – 6)

Critical Path: A – C – E – G

Q2. Marks: 10

Suppose the following estimates of activity times of a project,

Activity · Optimistic · Most likely · Pessimistic

A B C D E F G

If the critical path of the project is B, D, E, F, then calculate the Expected Completion Time (Length of the path) and Variance for the project

Solution: · Critical · Activities · Optimistic · Time (t0) · Most · Likely · Time (tm) · Pessimistic · Time (tp) · Expected · (te) · Variance

B 0.11 D 0.44 E 1.78 F

Expected Completion time = 4 + 5 + 7 + 7 = 23 Variance (of the project) = 0.11 + 0.44 + 1.78 + 1 = 3.33

Q3. Demand for the product is 600 units per week, and the items are withdrawn at a constant rate. The setup cost for placing an order to replenish inventory is $25. The unit cost of each item is $3, and the inventory holding cost is $0.05 per item per week.

(a). Assuming shortages are not allowed, determine how often to make a production run and what size it should be. (b). If shortages are allowed but cost $2 per item per month, determine how often to order and what size the order should be.

Solution:

Demand (D) = 600 unit/week Ordering Cost (C2) = $25/order Item Cost (C1) = $3/item