Wilson College Operations Research Prelims Question Paper 2014

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Operation Research Management

1. Section I is compulsory
2. Attempt any three questions from Section II
3. Use of Simple calculator is allowed.

Section I

Q1. Answer the following questions briefly:                           (3 X 5 = 15 Marks)

1. What are the limitations of Linear Programming?
2. Explain Slack Variable in Simplex .
3. Why is a non-degenerate solution a pre-requisite for optimality test of transportation solution?
4. What is Network Analysis?
5. What is meant by project crashing?

Q2. A company has three plants and three warehouses. The supply and demand in units and corresponding transportation costs in Rs. per unit are given below. On the basis of the past experience, the following transportation schedule has been finalised.

 Plant Warehouses (Transportation costs in Rs./unit) Sypply (in Units) I II III A 40 70 90 300 (300) B 12 8 30 400 (300) (100) C 60 90 45 200 (200) Demand (in Units) 300 300 300 900

1. Improve the above solution to optimality.                                                            (7 Marks)
2. Study the solution found by you and answer the following questions with justification:

i.              Is there any alternate optimal solution?                                       (2 Marks)
ii.            Find the total minimum transportation cost.                                (2 Marks)
iii.           If the route C to II is used, by how much amount the total transportation cost would go up for every unit transported?                                     (2 Marks)
iv.           What should be the minimum decrease in the unit cost of the cell A –II so that the company will be using this route?                             (2 Marks)

Section II

Q3. A company manufactures two products A & B. Both products are processed on two machines M1 & M2.

 Products / Machines M1 M2 A 6 hours / unit 2 hours / unit B 4 hours / unit 4 hours / unit Availability 7200 hours / month 4000 hours / month

Profit per unit for A is Rs.100 and for B is Rs.80. Find out monthly production of A and B to maximise profit using the graphical method or the simplex method. (10 Marks)

Q4. In a factory there are 5 employees and 5 jobs are to be completed on one to one basis. Time required in minutes is given for each employee job combination. Find the optimal assignment of employees and jobs to minimize the total time.       (10 Marks)

 Jobs A B C D E Employees I 160 130 175 190 200 II 135 120 130 160 175 III 140 110 155 170 185 IV 50 50 80 80 110 V 55 35 70 80 105

Q5. A small project consists of seven activities. Optimistic time, most likely time and pessimistic time estimates are given for each activity.

 Activity Preceding Activity Time in Days Optimistic Most Likely Pessimistic A – 2 5 8 B – 2 5 14 C A 4 6 14 D A 5 7 15 E B,C 2 3 10 F D 3 3 3 G E 1 2 3

1. Draw the PERT Network and find expected completion time of the project.
2. What is the probability that the project will be completed in?
1. 18 days
2. 21 days
3. 16 days
1. If the project manager wants an assurance of 95% that the project is completed on time, how many days before the scheduled date he should start the project.                                                                                                 (10 Marks)

(Area under standard normal curve for z=1.26 is 0.3962 and for z=0.84 is 0.2996.

For Probability 0.4505 value of z=1.65)

Q6. A dealer buys a product from a manufacturer at a cost of Rs.70 per unit. He sells the product to retailers at Rs.100 per unit. The product has an expiry date of one year. At the end of the year, unsold quantity of the products can be sold as scrap at a price of Rs.20 per unit.

The market demand fluctuates between 6 to 10 units. The order for the product should be placed at the beginning of the year only. The dealer wants to decide how many units to order. Prepare pay-off table and regret table.                               (5 Marks)

If the following probabilities are assigned to various possible events:

Event                                     Probability

E1: Demand = 6 units                     P1 = 0.1

E2: Demand = 7 units                     P1 = 0.2

E3: Demand = 8 units                     P1 = 0.3

E4: Demand = 9 units                     P1 = 0.25

E5: Demand = 10 units                   P1 = 0.15

Find:

1. Expected Monetary Value                                                                          (2 Marks)
2. Expected Opportunity Loss                                                                        (1 Mark)
3. Expected Pay off with PI                                                                            (1 Mark)
4. Expected value of PI                                                                                   (1 Mark)

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