JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III QUANTITATIVE ANALYSIS FOR BUSINESS DECISIONS Previous Question Paper (August - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Elaborate on the various techniques for solving problems in Operations Research.
Answer
Operations Research (OR) employs a variety of mathematical and analytical techniques to support decision-making. The primary techniques include:
- Linear Programming (LP): A mathematical method used to optimize a linear objective function subject to linear constraints, widely used in resource allocation.
- Transportation and Assignment Models: Specialized forms of LP used to minimize the cost of shipping goods from multiple sources to destinations or assigning tasks to resources.
- Queuing Theory: The study of waiting lines, used to balance the cost of providing service against the cost of customer waiting time.
- Inventory Control Models: Techniques like Economic Order Quantity (EOQ) that determine optimal inventory levels to minimize holding, ordering, and shortage costs.
- Game Theory: Used to model competitive situations where the outcome depends on the actions of two or more decision-makers.
- Simulation: The process of creating a model of a real-world system to observe its behavior under various conditions without disrupting the actual system.
- Network Analysis (PERT/CPM): Project management techniques used to plan, schedule, and control complex projects by identifying critical paths.
- Dynamic Programming: A method for solving complex problems by breaking them down into simpler sub-problems in a sequential manner.
Describe the nature and scope of OR.
Answer
The nature of Operations Research is interdisciplinary, scientific, and objective. It relies on the scientific method to provide a quantitative basis for decision-making, emphasizing the use of mathematical models to represent real-world systems. It is inherently team-oriented, requiring collaboration between subject matter experts and analysts.
The scope of OR is extensive and spans across various functional areas of management:
- Production Management: Facility layout, production scheduling, and quality control.
- Financial Management: Capital budgeting, portfolio management, and dividend policy.
- Marketing Management: Advertising media selection, sales force allocation, and product mix optimization.
- Personnel Management: Manpower planning, recruitment policies, and wage/salary administration.
- Logistics and Supply Chain: Distribution network design and inventory management.
Ampere Electric Company produces two products P1 and P2. Products are produced and sold on a weekly basis. The weekly production cannot exceed 25 for product P1 and 35 for product P2 because of limited available facilities. The company employs total of 60 workers. Product P1 requires 2 man-weeks of labour, while P2 requires one man week of labour. Profit margin on P1 is Rs.60 and on P2 is Rs.40. Formulate a linear programming problem with the above information and solve for maximum profit graphically.
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Explain duality principle with an illustration.
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A firm manufacturing a single product has three plants I, II and III. They have produced 60, 35 and 40 units respectively during this month. The firm had made a commitment to sell 22 units to customer A, 45 units to customer B, 20 units to customer C, 18 units to customer D and 30 units to customer E. Find the minimum possible transportation cost of shifting the manufactured product to the five customers. The net unit cost of transporting from the three plants to the five customers is given below:
| Plant | A | B | C | D | E |
|---|---|---|---|---|---|
| I | 4 | 1 | 3 | 4 | - |
| II | 2 | 3 | 2 | 3 | - |
| III | 3 | 5 | 2 | 4 | - |
Answer
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Write brief on application of transportation on model in OR.
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A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the times that each man would take to perform each task is given below in the matrix:
| Subordinates | I | II | III | IV |
|---|---|---|---|---|
| A | 8 | 26 | 17 | 11 |
| B | 13 | 28 | 4 | 26 |
| C | 38 | 19 | 18 | 15 |
| D | 19 | 26 | 24 | 10 |
How should the tasks be allocated to subordinates so as to minimize the total hours?
Answer
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Examine the importance of assignment model in OR.
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What is group replacement policy? Explain the rules governing group replacement policy.
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What are situations which make the replacement of items necessary?
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A manual stamper currently valued at Rs.1000 is expected to last two years and costs Rs.4000 per year to operate. An automatic stamper which can be purchased at Rs.3000 will last four years and can be operated at an annual cost of Rs.3000. If money carries a rate of interest of 10 per cent per annum, determine which stamper should be purchased.
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How do you describe the need of group replacement of low-cost items?
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Solve the following 3 × 5 game using dominance property.
| Player A | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| I | 6 | 15 | 30 | 21 | 6 |
| II | 3 | 3 | 6 | 6 | 4 |
| III | 12 | 12 | 24 | 36 | 3 |
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A repair shop attended by a single mechanic has an average of four customers an hour who bring small appliances for repair. The mechanic inspects them for defects and takes six minutes on an average. Arrivals are Poisson and service rate has the exponential distribution. You are required to:
- Find the proportion of time during which there is no customer in the shop.
- Find the probability of finding at least one customer in the shop.
- What is the average number of customers in the system?
- Find the average time a customer spent by a customer in the shop including service.
Answer
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