JNTU
JNTU MCA 2018 OPERATIONS RESEARCH Previous Question Paper (January - 2018 - 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
5 × 5 Marks = 25
Explain the limitations of operations Research.
Answer
Operations Research (OR) faces several limitations: 1) Models are often based on simplified assumptions that may not fully capture the complexity of real-world scenarios. 2) High costs associated with data collection, computation, and expert personnel can make it prohibitive for smaller organizations. 3) Mathematical models often struggle to incorporate qualitative factors like human behavior, morale, or political influences. 4) There is often a significant time lag between problem identification and the development of an optimal solution. 5) Solutions are only as accurate as the input data; poor quality or outdated data leads to unreliable results.
Give and explain Mathematical model of “Assignment problem”.
Answer
The assignment problem aims to assign n jobs to n machines at minimum cost. The mathematical model is defined as: Minimize Z = Σ Σ cij xij, subject to: Σ xij = 1 for each job i (i=1 to n), Σ xij = 1 for each machine j (j=1 to n), where xij = 1 if job i is assigned to machine j, and 0 otherwise. Here, cij represents the cost of assigning job i to machine j.
Explain the usefulness of sequencing modes.
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What is dynamic programming approach? Explain.
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What is EOQ(Economic order quantity)? What is its significance?
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Part B
Using two phase method solve the LPP:
s.t. 3x1 + 2x2 + x3 ≤ 3600
2x1 + 5x2 + 3x3 ≤ 2400
3x1 + 3x2 + 4x3 ≤ 4800
x1, x2, x3 ≥ 0
Problem Solution
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Explain the concept of unbound solution.
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With the Big-M method solve:
s.t. 3x1 + x2 ≥ 3
4x1 + 3x2 ≤ 6
x1, x2 ≥ 0
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Find the Initial Basic Feasible solution of the Transportation problem where cost matrix is given below
| Origin/Dest | A | B | C | D | Supply |
|---|---|---|---|---|---|
| I | 1 | 5 | 3 | 3 | 34 |
| II | 3 | 3 | 1 | 2 | 15 |
| III | 0 | 2 | 2 | 3 | 12 |
| IV | 2 | 7 | 2 | 4 | 19 |
| Demand | 21 | 25 | 17 | 17 | - |
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Explain Hungarian method for optimal solution through an example.
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There are 4 jobs each of which has to go through the machines M1, M2, M3, M4, M5, and M6, in order Processing Times are as given below. Determine a sequence of these four jobs which minimizes the total elapsed time T.
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Illustrate any two Replacement models with numerical examples.
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Solve using dynamic programming approach.
s.t. 2x1 + x2 ≤ 8
5x1 + 2x2 ≤ 15
x1, x2 ≥ 0
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Explain minimax method of optimal strategies.
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Explain the term competitive games, saddle point, value of the game with examples.
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Explain an inventory model where demand rate is uniform and production rate is uniform. Illustrate your answer with a numerical example.
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Explain the following Models (M/M/1):(FCFS/∞/∞) and (M/M/1):(FCFS/N/∞). Illustrate your answers with numerical examples.
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