DOMS304 MBA APPLICATIONS OF OPERATIONS RESEARCH

Description

SESSION	FEBRUARY – MARCH 2024
PROGRAM	MASTER OF BUSINESS ADMINISTRATION (MBA)
SEMESTER	III
COURSE CODE & NAME	DOMS304 – APPLICATIONS OF OPERATIONS RESEARCH

 

 

Assignment Set – 1

 

1. Write short notes on the following:
2. a) Importance of Operations Research to decision-maker?
3. b) Sensitivity Analysis
4. c) Dynamic programming Problem

Ans 1.

Importance of Operations Research to Decision-Maker

Operations Research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In a competitive business environment, decision-makers rely on OR to improve operational efficiency, optimize resources, and make data-driven decisions. The significance of OR to decision-makers lies in its ability to model complex scenarios

 

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2. Solve the following linear programming problem using Revised Simplex Method:

    Maximize Z   = x1 + x2+ 3×3

    Subject to:           3×1+2×2+ x3 ≤ 3

   2×1 + x2+ 2×3≤ 2

where x1, x2, x3≥ 0

 

Ans 2.

Problem is

Max Z = x1 + x2 + 3 x3

 

 

3. Consider the following profit matrix of the Transportation Problem:

	A	B	C	D	E	Supply
1	19	21	16	15	15	150
2	9	13	11	19	11	200
3	18	19	20	24	14	125
Demand	80	100	75	45	125

 

Find the optimum solution to get Maximum profit.

Ans 3.

TOTAL number of supply constraints : 3
TOTAL number of demand constraints : 5
Problem Table is

	D1	D2	D3	D4	D5		Supply
S1	19	21	16	15	15		150

 

Assignment Set – 2

 

 

4. Use Branch and Bound method to solve the following Integer programming problem:

Minimize Z = 4×1 + 3×2

Subject to

  5×1 + 3×2 ≥ 30

  x1 ≤ 4

  x2 ≤ 6

and x1, x2 ≥ 0 and are integers.

Ans 4.

Step 1: Reformulate the problem

First, let’s convert the inequality constraints into equalities by adding slack variables:

Minimize Z = 4×1 + 3×2 Subject to:

5×1 + 3×2 – S1 = 30 x1 – X1 = 0 x2 – X2 = 0 x1 ≤ 4 x2 ≤ 6 x1, x2 ≥ 0, X1, X2 ≥ 0 (slack variables) x1, x2 are integers

Step 2: Create an initial upper bound

The upper bound

 

 

5. Solve the given Non-Linear Programming Problem using Kuhn-Tucker conditions:

Maximize Z = 21×1 +12×2 +2x1x2 -2×12 – 2×22

Subject to:      x2 ≤ 8

                       x1 + x2 ≤ 10

                    and x1, x2 ≥ 0

 

Ans 5.

Problem is

Max z = 21 x1 – 2 x12 + 2 x1x2 + 12 x2 – 2 x22

subject to

→:x2 ≤ 8 x1 + x2 ≤ 10

 

 

6a. What do you mean by the Metaheuristic Method? Write the Fundamental Properties of Metaheuristics.

1. b) Write short notes on the following:
2. i) Simulation Annealing Method
3. ii) Genetic Algorithm

Ans 6.

1. Metaheuristic Method and Its Fundamental Properties

Metaheuristic methods are advanced optimization techniques used to find near-optimal solutions to complex problems that are difficult to solve through traditional optimization methods. These methods are designed to explore the search space efficiently and effectively, avoiding the pitfalls of local optima and ensuring a broader exploration to find the best possible solution. Metaheuristics are particularly useful for solving large-scale and combinatorial problems where the