JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech IV Year OPERATIONS RESEARCH Previous Question Paper (July/August - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
What are the advantages and disadvantages of operations research models? Why is it necessary to test models and how would you go about testing a model?
Answer
Advantages of operations research models include the ability to provide a structured approach to decision-making, the capacity to handle complex systems with many variables, and the ability to predict the outcomes of different strategies without physical experimentation. They help in identifying optimal solutions and reducing costs or increasing efficiency. Disadvantages include the reliance on simplified assumptions that may not capture real-world complexities, the high cost and time required for data collection and model development, and the risk that the mathematical model may be misinterpreted or misused by non-experts.
Testing a model is necessary to ensure its validity, reliability, and accuracy before implementation. A model must be tested to verify that it correctly represents the system it is intended to simulate and that the output is logically consistent with the input data. The testing process involves: 1) Checking the model's structure for logical errors. 2) Conducting sensitivity analysis to see how changes in input parameters affect the output. 3) Comparing the model's predictions against historical data or known outcomes to assess its predictive power. 4) Performing a pilot run or simulation to observe real-time performance.
Use the graphical method to solve the following LP problem. Maximize Z = 15x1 + 10x2 subject to the constraints (i)
Answer
To solve the linear programming problem, we first determine the boundary lines for the constraints:
- 4x1 + 6x2 = 360: If x1=0, x2=60; if x2=0, x1=90.
- 3x1 = 180: x1 = 60.
- 5x2 = 200: x2 = 40.
The feasible region is bounded by the vertices (0,0), (60,0), (60,20), (30,40), and (0,40). Note that the intersection of 4x1 + 6x2 = 360 and 5x2 = 40 is 4x1 + 6(40) = 360, giving 4x1 = 120, so x1 = 30. The intersection of 4x1 + 6x2 = 360 and 3x1 = 60 is 4(60) + 6x2 = 360, giving 6x2 = 120, so x2 = 20.
Evaluating the objective function Z = 15x1 + 10x2 at the vertices:
| Vertex (x1, x2) | Z = 15x1 + 10x2 |
| (0, 0) | 0 |
| (60, 0) | 900 |
| (60, 20) | 1100 |
| (30, 40) | 850 |
| (0, 40) | 400 |
The maximum value of Z is 1100 at the point (60, 20).
Use two-phase simplex method to solve the following LP problem: Minimize Z = x1 + x2 subject to the constraints (i)
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A manufacturer wants to ship 22 loads of his product as shown below. The matrix gives the kilometres from sources of supply to the destinations. The shipping cost is Rs 10 per load per km. What shipping schedule should be used in order to minimize the total transportation cost?
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An airline company has drawn up a new flight schedule that involves five flights. To assist in allocating five pilots to the flights, it has asked them to state their preference scores by giving each flight a number out of 10. The higher the number, the greater is the preference. A few of these flights are unsuitable to some pilots, owing to domestic reasons. These have been marked with ‘×’. What should be the allocation of the pilots to flights in order to meet as many preferences as possible?
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What is replacement? Describe the problem of replacement of items whose maintenance cost increase with time. Assume that the value of money remains constant. Machine A costs Rs 45,000 and its operating costs are estimated to be Rs 1,000 for the first year increasing by Rs 10,000 per year in the second and subsequent years. Machine B costs Rs 50,000 and operating costs are Rs 2,000 for the first year, increasing by Rs 4,000 in the second and subsequent years. If at present we have a machine of type A, should we replace it with B? If so when? Assume that both machines have no resale value and their future costs are not discounted.
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We have five jobs each of which must go through the machine A, B and C in the order ABC. Determine a sequence for the jobs that will minimize the total elapsed time.
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Solve the following game by using maximin (minimax) principle, whose payoff matrix are given below: Include in your answer: (a) strategy selection for each player, (b) the value of the game to each player. Does the game have a saddle point?
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A television repairman finds that the time spent on his jobs has an exponential distribution with mean of 30 minutes. If he repairs sets in the order in which they came in, and if the arrival of sets follows a Poisson distribution approximately with an average rate of 10 per 8-hour day, what is the repairman’s expected idle time each day? How many jobs are ahead of the average set just brought in? What is the average time for a job to be in the system? What is the average time a job has to wait before being repaired?
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