JNTU
JNTU B.Tech IV OPERATIONS RESEARCH Previous Question Paper (December - 2019 - R15)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
Part A
(25 Marks)
What is Operations research?
Answer
Operations Research is the scientific approach to decision-making that involves the application of advanced analytical methods, such as mathematical modeling, statistics, and optimization, to help make better decisions in complex organizational systems.
What are the limitations of LP problem?
Answer
- Linearity assumption: Real-world problems often involve non-linear relationships between variables.
- Certainty assumption: It assumes parameters are known constants, whereas they are often probabilistic.
- Divisibility assumption: It assumes variables can take fractional values, which is not always physically possible in reality.
Formulate the travelling – Salesman problem as an assignment problem.
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What is a degenerate transportation problem and how do you resolve it?
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What are the situations which make the replacement of items necessary?
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Write three assumptions of job sequencing.
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What are the characteristics of game theory?
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What are the functions of inventory management?
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What are major limitations of simulation?
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What are the applications of dynamic programming?
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Part B
(50 Marks)
Use penalty (or Big-M) method to maximize z = 3x1 - x2. Subject to the constraints 2x1 + x2 ≥ 2; x1 + 3x2 ≤ 3; x2 ≤ 4; x1, x2 ≥ 0
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A person requires 10, 12, and 12 units of chemicals A, B and C respectively for his garden. The liquid product contains 5 units, 2 units and 1 unit of A, B and C respectively per jar. The dry product contains 1 unit, 2 units and 4 units of A, B and C per jar. If the liquid product sells for Rs.3 per jar and dry product sells for Rs.2 per jar, how many of each should be purchased to minimize the cost and meet the requirements.
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Solve the following transportation problem by Least Cost method and check the feasibility of the solution. The unit costs of shipment are given in the cells below
| D | E | F | Supply | |
|---|---|---|---|---|
| A | 6 | 4 | 1 | 50 |
| B | 3 | 8 | 7 | 40 |
| C | 4 | 4 | 2 | 60 |
| Demand | 20 | 95 | 35 | 150 |
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A company has one surplus truck in each of the cities A, B, C, D, and E and one deficit truck in each of the cities 1, 2, 3, 4, 5 and 6. The distance between the cities in Kilometers is shown in the matrix below. Find the assignment of trucks from cities in surplus to cities in deficit so that the total distance covered by the vehicles is minimum.
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| A | 12 | 10 | 15 | 22 | 18 | 8 |
| B | 10 | 18 | 25 | 15 | 16 | 12 |
| C | 11 | 10 | 3 | 8 | 5 | 9 |
| D | 6 | 14 | 10 | 13 | 13 | 12 |
| E | 8 | 12 | 11 | 7 | 13 | 10 |
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Find the Sequence for the following eight jobs that will minimize the total elapsed time for the completion of all jobs. Each job is processed in the same order ABC. The following entries give the time in hours on the machines. Find the total elapsed time and the idle line on each machine.
| Jobs | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| A | 4 | 6 | 7 | 4 | 5 | 3 | 6 | 2 |
| B | 8 | 10 | 7 | 8 | 11 | 8 | 9 | 13 |
| C | 5 | 6 | 2 | 3 | 4 | 9 | 15 | 11 |
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Find the cost period of individual replacement of an installation of 300 lighting bulbs, given the following:
Cost of replacing individual bulb is Rs. 3. The cost of individual replacement is Rs 1.25.
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Conditional probability of failure is given below:
| Week number | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Conditional probability of failure | 0 | 1/10 | 1/3 | 2/3 | 0 |
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Solve the following game by dominance method.
| B1 | B2 | B3 | B4 | B5 | B6 | |
|---|---|---|---|---|---|---|
| A1 | 4 | 2 | 0 | 2 | 1 | 1 |
| A2 | 4 | 3 | 1 | 3 | 2 | 2 |
| A3 | 4 | 3 | 7 | -5 | 1 | 2 |
| A4 | 4 | 3 | 4 | -1 | 2 | 2 |
| A5 | 4 | 3 | 3 | -2 | 2 | 2 |
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Explain Different inventories.
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Find the economic lot size that associates with total cost and the length of time between two orders, given that the set-up cost is Rs.100, daily holding cost per unit of inventory is 5 paise and daily demand is approximately 30 units.
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Jobs arrival at a workstation in a manufacturing plant is in a Poisson fashion at an average rate of five per hour. The time to machine one job is an exponential distribution with a mean time of 10 minutes. What is the expected time a job has to wait at the workstation? What will be the average number of jobs waiting at the workstation at any time? What is the probability that there will be more than four jobs?
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State the Bellman’s principle of optimality in dynamic programming and give a mathematical formulation of a dynamic programming problem?
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Explain the Process of simulation and give its applications.
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