JNTU
JNTU MCA 2023 OPERATIONS RESEARCH Previous Question Paper (March - 2023 - R15)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
PART - A
Discuss the role of OR model in decision making.
Answer
An Operations Research (OR) model serves as a simplified representation of a real-world system, allowing decision-makers to analyze complex problems through mathematical abstraction. Its primary role is to provide a structured framework for evaluating alternatives, predicting outcomes under various conditions, and identifying the optimal course of action. By quantifying relationships between variables, OR models reduce uncertainty, minimize risks, and assist management in making objective, data-driven decisions that maximize efficiency or minimize costs.
What is assignment problem? Give the areas of its application.
Answer
An assignment problem is a special type of linear programming problem where the objective is to assign a number of tasks to an equal number of resources (such as workers, machines, or locations) on a one-to-one basis such that the total cost or time is minimized. It is a specific case of the transportation problem where supply and demand are each equal to one.
Key areas of application include:
- Assigning jobs to machines to minimize total processing time.
- Allocating sales personnel to different territories to maximize sales.
- Scheduling teachers to specific class periods.
- Assigning tasks to employees based on skill sets to optimize productivity.
What is replacement? Describe some important replacement situations and replacement policies.
Answer
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Briefly explain dominance property in game theory.
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Write notes about the controlled variable in inventory.
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PART - B
Write the phases and characteristics of OR.
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A resourceful home decorator manufactures two types of lamps say A and B. Both lamps go through two technicians first a courter, second a finisher. Lamp A requires 2 hours of the courters time and 1 hour of the finisher time. Lamp B requires 1 hour of the courter and 2 hours of the finisher time. The courter has 104 hours and finisher has 76 hours of time available each. Profit on one lamp A is Rs.6/- and on lamp B is Rs.11/-. Form the LPP and maximize.
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What is the difference between artificial and slack variables?
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Use the Big-M method to solve the following LPP:
Subject to 6x1 + 8x2 > 100
7x1 + 12x2 > 120
x1, x2 > 0
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Briefly explain unbalanced transportation problem.
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Solve the following Assignment Problem for maximization.
70 85 60 75 55
88 96 118 85 71
48 64 87 77 80
60 70 98 66 83
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To minimize the cost per cycle, solve the following travelling salesman problem.
1 ∞ 10 25 25 10
2 1 ∞ 10 15 2
3 8 9 ∞ 20 10
4 14 10 24 ∞ 15
5 10 8 25 27 ∞
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Find the cost per period of individual replacement policy of an installation of 300 bulbs given.
Cost of replacing individual bulb is Rs.3/-
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Conditional probability of failure is given below:
Conditional Prob of failure 0 1/10 1/3 2/3 1
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Find the sequence that minimizes the total time required in performing the following jobs on three machines in the order A-B-C as shown in the below table. Also, find the total elapsed time.
A 8 3 7 2 5 1
B 3 4 5 2 1 6
C 8 7 6 9 10 9
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Describe the minmax principle of the game theory.
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Solve the game whose payoff matrix for the player A is given in table.
I | -2 | 15 | -2
II | -5 | -6 | -4
III | -5 | 20 | -8
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In a game matching coins with two players suppose A wins one unit of value when there are two heads, wins nothing when there are two tails and losses 1/2 unit of value when there are one head and one tail. Determine the payoff matrix the best strategies for each player and the value of game to A
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Explain the importance of dynamic programming approach for priority management employment smoothening.
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What are the costs that are involved in inventory? Explain them in detail.
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Find the optimum order quantity for a product for which the price breaks are as follows:
Unit cost (Rs) 10 9.25
The monthly demand for a product is 200 units. The cost of storage is 2% of unit cost per month and the cost of ordering is Rs 350.
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A self – servicing store employs one cashier at its counter. Nine customers arrive at an average 5 minutes while the cashier can service 10 customers in 5 minutes. Assuming the Poisson distribution for arrival rate find.
- The average number of customers in the system.
- The average number of customers in the queue.
- The average time a customer spends in the system.
- The average time a customer waits before being serviced.
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