AY 2012-13 Term 1 Final Examinations

Date / Start Time 30 Nov 2012 / 8.30am

Course OPIM 101 MANAGEMENT SCIENCE

Groups G8, G10

Instructor Dr. Joyce M.W. Low

INSTRUCTIONS TO CANDIDATES 1 The time allowed for this examination paper is 2 hours. 2 This examination paper contains a total of Six (6) questions and comprises Fifteen (15)

pages including this instruction sheet. 3 You are required to answer ALL questions. 4 A one-sided (A4 size) cheat sheet is allowed

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Question 1 (8 marks) Lion Motors is a Singapore car manufacturer. At its largest manufacturing facility, the company produces subcomponents at a rate of 300 per day, and it uses these components at a rate of 12,500 per year (of 250 working days). Holding costs are $2 per item per year, and ordering costs are $30 per order. a) What is the economic production quantity? b) How many production runs per year will be made? c) What will be the maximum inventory level? d) What is the percentage of time will the facility be producing components? e) What is the annual cost of ordering and holding inventory?

(1m for a & b, 2 m each for c-e)

Answer:

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Question 2 (12 marks) Kopi coffee shop in Stamford Road is opened 200 days per year and sells an average of 75 pounds of Ipoh coffee beans a day. Demand can be assumed to be distributed normally with a standard deviation of 15 pounds per day. After ordering (fixed cost = $16 per order), beans are always shipped from Malaysia within exactly 4 days. Per-pound annual holding costs for the beans are $3.

a) What is the economic order quantity (EOQ) for Ipoh coffee beans? b) What are the total annual holding costs of stock for Ipoh coffee beans? c) What are the total annual ordering costs of stock for Ipoh coffee beans? d) Assume that OPIM 101 consultant has specified that no more than a 1%

risk during stock-out is acceptable. What should the reorder point (ROP) be?

e) What is the safety stock needed to attain a 1% risk of stock-out during lead time?

f) What is the annual holding cost of maintaining the level of safety stock needed to support a 1% risk?

g) If the consultant specified that a 2% risk of stock-out during lead time would be acceptable, would the safety stock holding costs decrease or increase?

(1 m each for a and g, 2 m for b-f)

Answer:

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Question 3 (7 marks) The activities needed to build an experimental chemical contaminant tracking machine at Singapore Management University School of Tomorrow Technology are listed shown in the AON network below:

Professor Smart was able to determine the activities times for constructing his chemical contaminant tracking machine. He would like the students taking Management Science in the School of Business to help him determine ES, EF, LS, LF and slack for each activity. The total project completion time and the critical path should also be determined. Here’s are the activity times:

Activity Time (weeks) Activity Time (weeks)

A 6 E 4

B 7 F 6

C 3 G 10

D 2 H 7

(ES, EF, LS. LF: 4 m; Slack: 1m; critical path and time: 2 m) Answer:

Activity Time ES EF LS LF Slack

A

B

C

D

E

F

G

H

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The projection completion time is ______________________

The critical path is ___________________________________

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Question 4 (9 marks) Papa smurf, the head of Smurf family, has developed the tasks, durations and predecessor relationships in the following table for building new villages.

Time Estimates (in weeks)

Activity Immediate Predecessors(s)

Optimistic Most Likely Pessimistic

A - 4 8 10

B A 2 8 24

C A 8 12 16

D A 4 6 10

E B 1 2 3

F E,C 6 8 20

G E,C 2 3 4

H F 2 2 2

I F 6 6 6

J D,G,H 4 6 12

K I,J 2 2 3

The AON network is given as follows:

a) What is the expected time for activity C? (1m) b) What is the variance for activity C? (1m) c) Based on the calculations of estimated times, what is the critical path? (3m) d) What is the activity variance along the critical path? (2m) e) What is the probability of completion of the project before week 36? (2m)

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Answer:

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Question 5 (6 marks)

Bolling Electronics manufactures DVD players for commercial use. W. Blaker Bolling, president of Bolling Electronics, is contemplating producing DVD players for home use. The activities necessary to build an experimental model and related data are given in the following table:

Activity Normal time

(weeks)

Crash Time

(weeks)

Normal cost ($)

Crash Cost ($)

Immediate Predecessor

A 3 2 1000 1600 -

B 2 1 2000 2700 -

C 1 1 300 300 -

D 7 3 1300 1600 A

E 6 3 850 1000 B

F 2 1 4000 5000 C

G 4 2 1500 2000 D,E

a) What is the project completion date? b) Crash this project to 10 weeks at the least cost? c) Crash this project to 7 weeks (which is the maximum it can be crashed) at the

least cost. (2 marks each)

Answer:

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Question 6 (8 marks)

A Finance Professor is considering four different opportunities, A, B, C, or D.

The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below. Economic Condition Poor Average Good Excellent Investment (S1) (S2) (S3) (S4)

A 50 75 20 30 B 80 15 40 50 C -100 300 -50 10 D 25 25 25 25

a) What decision would be made under maximax? (1m) b) What decision would be made under maximin? (1m) c) What decision would be made under minimax regret? (2m) d) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what investment would be made using the expected value criterion? (2m) e) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what is the expected value of perfect information? (2m)

Answer:

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- End of Paper –

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Normal Table