# Operations Research Prelims Question Paper 1 – Vipin Saboo Tutorials

Prelim- Operations Research- Paper A

Solve both sections. Solve any 3 questions from section 2

Section 1

Q1. Explain the following concepts (3X5=15)

• Closed loop in transportation
• Decision tree
• Resource constrains in LPP
• Updating in networking
• Degeneracy in simplex

Q2. The following information is available for a network. Indirect cost id Rs 300 per day. Time give is in days (15 marks)

 Job 1—2 1–3 2—3 2–4 2–5 3–6 4–5 5–6 Normal time 9 15 7 7 12 12 6 9 Normal cost 1300 1000 1000 1200 1700 600 1000 900 Crash time 4 13 4 3 6 11 2 6 Crash cost 2400 1380 1540 1920 2240 700 1600 1200

Draw the network diagram and find the critical path and corresponding cost. What would be the impact on the cost if the deadline of 27days is imposed?

Section 2 (solve any 3. 10 marks each)

Q3. A company manufactures two products A and B. Profit per unit of A and B are Rs 3, 5 respectively. Each unit of A and B requires 3 and 2 units of labour hours. The company has a maximum of 18 labour hours available. Also the maximum demand for A and B is limited to 4 and 6 units respectively.  Formulate the above as LPP and solve by simplex.

Q4. The following cost, demand and supply information is available. Optimise the transport cost. No units can be transferred from P2 to M1. Would a 50% discount on route P3-M3 have an impact on the solution

Plant/Market     M1         M2         M3         Supply

P1                           6              9              8              120

P2                           –              4              2              80

P3                           11           5              4              80

Demand               150         70           60

Q5. Consider the problem of assigning 4 clerks to 4 tasks. Time in hours taken by each is given below.

 Tasks Clerks A B C D I 4 7 5 6 II 3 8 7 4 III 3 5 5 3 IV 6 6 4 2

Clerk II cannot be assigned A and Clerk III cannot be assigned B. Find the optimum allocation.

How do you find out that an alternate solution exists in the assignment sum.

Q6.A. For the following data compute EMV, EPPI, EVPI and EOL (4 marks)

 Probability S1 S2 S3 S4 S5 0.1 20 12 4 -4 -12 0.2 20 22 14 6 -2 0.4 20 22 24 16 8 0.2 20 22 24 26 18 0.1 20 22 24 26 28

B. A company is planning to buy a machine at Rs 50,000. It is anticipated that if the machine is purchased the demand can go up and hence the revenues gained would be Rs 75,000. If the demand is not good there is a loss of Rs 20,000. The company feels that there are 70% chances that demand being good and 30% chances of a bad demand. Construct a decision tree and help the company decide whether the machine should be purchased or no. (6 marks)

Prof Vipin Saboo can be contacted on 9820779873 for any further clarifications.

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#### vipin0785

Education Qualification: BMS- N M College (University Rank Holder) PGDBM- Sydenham College M Com- College topper Mr Vipin Saboo has been associated with the following institutes as a visiting faculty Lords college, Malad Patkar College, Goregoan Saraf college, Malad Dalmia college, Malad St Andrews College, Bandra Wilson College, Grant Road Thakur college, Kandivili L N College, Kandivili N K College, Malad Dhanukar College, Vile Parle St Xaviers College, Marine Lines Shroff College, Kandivili KES College, Khar Mr.Vipin Saboo also has more than 5 years of industry expertise with corporate like CRISIL, Motilal Oswal Investment Banking and Yes Bank. Mr. Saboo has also published a text book on Logistics and Supply Chain Management for TYBMS Students.

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