GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER-VII (NEW) EXAMINATION - WINTER 2020
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Subject Code:2171901
Subject Name:Operation Research
Date:25/01/2021
Time:10:30 AM TO 12:30 PM
Total Marks: 56
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Instructions:
- Attempt any FOUR questions out of EIGHT questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q.1
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(a) Discuss various areas for the application of operations research techniques. (03 MARKS)
(b) Differentiate CPM & PERT. (04 MARKS)
(c) Explain the set of assumptions for Linear Programming in details. (07 MARKS)
Q.2
(a) Graphically represent following cases in linear programming. (03 MARKS)
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(1) Un-bounded solution (2) Multiple optimal solution
(b) A company is manufacturing two different types of products, A and B. Each product has to be processed on two machines M1 and M2. Product A requires 2 hours on machine M1 and 1 hour on machine M2, Product B requires 1 hours on machine M1 and 2 hour on machine M2. The available capacity of machine M1 is 104 hours and that of machine M2 is 76 hours. Profit per unit for product A is Rs.6 and that for B is Rs.11.Formulate the problem. (07 MARKS)
(c) Maximize Z=40x1+35x2 (07 MARKS)
Subject to constraints, 2x1 + 3x2 < 60,
4x1 + 3x2 <96,
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x1,x2>0
Q.3
(a) What is assignment problem? Show the assignment problem is special case of transportation problem. (03 MARKS)
(b) Describe the various steps in Hungarian method used for solving the assignment problem. (04 MARKS)
(c) The captain of a cricket team has to allot five middle order batting positions to 5 batsmen available for selection. The average runs scored by each batsman at these positions are summarized in a table below. Using Assignment model, determine the assignment of batsmen to positions which would give maximum runs in favor of team. (07 MARKS)
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Batsman Batting positions
| I | II | III | IV | V | |
|---|---|---|---|---|---|
| A | 40 | 46 | 48 | 36 | 48 |
| B | 48 | 32 | 36 | 29 | 44 |
| C | 49 | 35 | 41 | 38 | 45 |
| D | 30 | 46 | 49 | 44 | 44 |
| E | 37 | 41 | 48 | 43 | 47 |
Q.4
(a) What is degeneracy in transportation problem? (03 MARKS)
(b) Discuss group replacement policy with suitable example. (04 MARKS)
(c) A small machine shop has five jobs available to be assigned to five machines. The time (in hours) that each machine requires to perform each job is given below. Find the optimum assignment. (07 MARKS)
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Employees
| I | II | III | IV | V | |
|---|---|---|---|---|---|
| A | 10 | 5 | 13 | 15 | 16 |
| B | 3 | 9 | 18 | 13 | 6 |
| C | 10 | 7 | 2 | 2 | 2 |
| D | 7 | 11 | 9 | 7 | 12 |
| E | 7 | 9 | 10 | 4 | 12 |
Q.5
(a) What is inventory? Classify the inventory. (03 MARKS)
(b) Write a short note on “ABC analysis” of inventory control technique. (04 MARKS)
(c) The annual demand for an item is 3200 units. The unit cost is Rs.6 and inventory carrying charges 25 % per annum. If the cost of one procurement is Rs.150, then determine the 1) EOQ 2) No. of order per year 3) Time between two consecutive order 4) The optimal cost. (07 MARKS)
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Q.6
(a) Define the following terms relating the customer’s behavior in Queue. (03 MARKS)
(A) Balking (B) Jockeying (C) Reneging
(b) Explain Kendall’s notation for queuing system. (04 MARKS)
(c) In a bank counter, customers arrive at a rate of 30 customers per day. Assuming that the inter arrival time follows an exponential distribution and service time distribution is also exponential with an average of 36 minutes. Calculate: (07 MARKS)
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Expected queue size
Probability that the queue size exceeds 10
Q.7
(a) What is “Strategy”? Explain the difference between pure strategy and mixed strategy. (03 MARKS)
(b) Discuss various costs involved in an Inventory model. (04 MARKS)
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(c) Explain the steps of a Travelling Salesman Problem. (07 MARKS)
Q.8
(a) What is replacement? Describe some important replacement situations. (03 MARKS)
(b) How would you deal with assignment problems, where (a) the objective Function is to be maximized? (b) Some assignments are prohibited? (04 MARKS)
(c) Explain the different methods useful for decision making under certainty. (07 MARKS)
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