finalexam trial sem1 2011-1

7/29/2019 Finalexam Trial Sem1 2011-1

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Singapore Management University

OPIM 101 Management Science

Final Exam 1 (Trial)

Time allowed: 2 hours

Instructions to Candidates

1) Fill in your name, ID and Group number below.

2) Answer all 4 questions.

3) Write legibly; pencil may be used.

4) Write your answers in the blank spaces provided after each question (or part of a question)

5) This paper consists of11 pages. Formulas are given on page 11.

Name:

Student ID: ______________________________

Group: ______________________________

Question Marks Max Marks1 22

2 20

3 28

4 30

Total 100


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1a) An internet retailer has three warehouses and three major distribution centers located aroundits country. Items are shipped directly from the warehouses to the distribution centers. Thetransportation costs ($/unit) between warehouses and distribution centers, the supply at thewarehouses, and the demand at the distribution centers are shown in the following table:

Warehouse Distribution Centers Supply

A B C

1 $12 $11 $7 702 8 6 14 80

3 9 10 12 50

Demand 60 100 50

Formulate a linear programming model to minimize total transportation costs.(10 marks)

Solution:


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2a) Given the following network, with the indicated flow capacities along each branch,determine the maximum flow from source node 1 to destination node 7 and the flow along eachbranch:

(10 marks)

Solution:

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2b) Formulate the linear programming model to solve for the maximal flow problem in network3. (10 marks)

Solution:


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3) Max Textile Mill was inspected by OSHA and found to be in violation of a number of safetyregulations. The OSHA inspectors ordered the mill to alter some existing machinery to make itsafer (add safety guads, etc.); purchase some new machinery to replace older, dangerousmachinery; and relocate some machinery to make safer passages and unobstructed entrances andexits. OSHA gave the mill only 35 weeks to make the changes; if the changes were not made bythen, the mill would be fined $300,000.

The mill determined the activities in a CPM/PERT network that would have to be completedand then estimated the indicated activity times, as shown in the following table:

Activity Activity Description Activity

Predecessor

Time Estimates (weeks)

a m b

a Order new machinery - 1 2 3

b Plan new physical layout - 2 5 8

c Determine safety changes - 1 3 5

d Receive equipment a 4 10 25

e Hire new employees a 3 7 12

f Make plant alternations b 10 15 25

g Make changes inmachinery c 5 9 14

h Train new employees d,e 2 3 7

i Install new machinery d,e,f 1 4 6

j Relocate old machinery d,e,f,g 2 5 10

k Conduct employee safetyorientation

h,i,j 2 2 2

Determine the following:

a) Construct the project network for this project and expected activity times (5 marks)

b) Earliest and latest activity times, activity slacks and Critical path. (7 marks)

c) Expected project duration and variance. (3 marks)

d) The probability that the mill will be fined $300,000. (3marks)

e) In order to focus on certain safety regulations, Max Textile decided to abandon certainactivities. Ignoring activities b, c, f, g, j, draw the resultant network. Using the expected activitytimes computed in (i), formulate a linear programming model to find the minimum projectduration. (10 marks)

Solution:


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4a) John wants to open a new dealership. He has three offers:

1. from a foreign compact car company

2. from a full size car company

3. from a truck company

The success of each type of dealership will depend on availability of gasoline during the nextfew years. The profit from each type of dealership, given the probability of the availability of thegas is given in the following payoff table:

DealershipOffer

Gas Shortage0.6

Gas Surplus0.4

1 $300,000 $150,000

2 -$100,000 $600,000

3 $120,000 $170,000

i) John is a pessimistic person. Suppose he has no information on the probabilities of the statesof nature, which decision criterion will you suggest John to use and what will be his decision?

ii) Compute the expected opportunity loss for each decision.

iii) Considering the distribution of the gasoline availability, determine which type of dealershipJohn should purchase.

iv) Compute EVPI.(12 marks)

Solution:


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b) John is considering hiring a petroleum analyst to determine the future availability ofgasoline. The analyst will report either a shortage of surplus will occur. The probability that theanalyst will indicate a shortage, given that a shortage actually occurs is 0.90. The probabilitythat the analyst will indicate a surplus, given that a surplus actually occurs is 0.70. Given thatthe analyst indicates a shortage, there is a probability of 0.818 that there is an actual shortage.Given that the analyst indicates a surplus, there is a probability of 0.824 that there is an actualsurplus.

i) Present the decision tree. (12 marks)

ii) Determine the decision strategy John should follow, the expected value of this strategy, andthe maximum amount John should pay for the analyst's service. (6 marks)

Solution:


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Given Formulas

finalexam trial sem1 2011-1

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