DOMS308 MBA APPLICATIONS OF OPERATIONS RESEARCH

Description

SESSION	JAN – FEB 2026
PROGRAM	MASTER OF BUSINESS ADMINISTRATION (MBA)
SEMESTER	III
COURSE CODE & NAME	DOMS308 APPLICATIONS OF OPERATIONS RESEARCH

 

 

Assignment Set – 1

 

Q.1. What is operations research? Write the Characteristics and limitations of O.R. (4+3+3 = 10 Marks)

Ans 1.

Operations Research is an interdisciplinary research-based approach to making decisions which employs advanced analytical techniques to assist organizations in solving complicated management challenges and enhance efficiency of operations. It was developed in World War II when military planners required a rigorous method to manage scarce resources and manage huge-scale operations. After the war these methods were adopted by both industry and government agencies to help improve the

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Q.2. Solve the given LPP using Revised Simplex Method: Maximize Z = x1 + 2×2, Subject to: x1+x2<=3, x1+2×2<=5, 3×1+x2<=6, x1,x2>=0. (10 Marks)

Ans 2.

It is the Revised Simplex Method is a more efficient computational version of the conventional Simplex Method for solving linear programming challenges. Although the traditional Simplex Method maintains the full simplex table and update the columns with each repetition The Revised Simplex Method works only using the inverse basis matrix and only computes the data necessary at each stage. This makes it much better suited to large-scale issues as it doesn’t require storing or changing irrelevant columns in the tableau.

The process begins by changing the LPP to a standard format through the introduction of slack variables that

 

 

Q.3. What is Principles of Duality? Solve the given LPP using its dual. Minimize Z = x1 – x2 + x3, Subject to: x1-x3>=4, x1-x2+2×3>=3, x1,x2,x3>=0. (3+7 = 10 Marks)

Ans 3.

The Principle of Duality states that each linear programming issue known as the Primal is a double problem that is derived from same information. Both are mirror images of the their counterparts: a reduction of primal with constraints that are greater to a maximumization dual that has constraints that are less than, and the reverse is true. A Weak Duality Theorem says that a dual approach to any problem can be used to determine the ideal primal objective value. In the case of maximization primals it is the case that any dual solution will always be higher in comparison to or greater than any possible primal value.

The Strong Duality Theorem states that where both the primal as well as dual solutions are optimal and their ideal objective values are identical. If the primal is not bounded and the dual cannot be achieved or incompatible, the reverse is true. Every dual variable is one constraint in the primal and shows the shadow value of the constraint. This shows how much it is worth loosening it by a single unit. Duality

 

 

Assignment Set – 2

 

 

Q.4. Solve the assignment problem using Hungarian method to maximize profit. Find which job should be declined. (10 Marks)

Ans 4.

The Hungarian Method is an efficient algorithm that uses combinatorial optimization to solve problem of assignment. A problem of assignment involves the assignment of a group of agents to jobs on a one-to-1 basis in order to reduce costs or maximise profits. The method works by decreasing the cost matrix using reductions in columns and rows until a suitable assignment is derived by removing the non-zero elements from the matrix.

In the case of a maximization challenge it is changed to a minimization challenge by subtracting all the elements of the largest

 

 

 

Q.5. A company has six salesmen and three market areas (A, B, C). Use dynamic programming to determine the optimal allocation to maximize profit. (10 Marks)

Ans 5.

Dynamic Programming is an method of mathematical optimization that was created by Richard Bellman for solving problems which can be broken down into interconnected sub-decisions. The fundamental principle of Bellman’s Principle of Optimality. It states that an optimal strategy has the advantage that no matter what the starting point and choice is in the future, all subsequent decisions should

 

 

Q.6. Write short notes on: (1) Sensitivity Analysis, (2) Integer Programming Problem, (3) Quadratic Programming Problem. (10 Marks)

Ans 6.

(1) Sensitivity Analysis

Sensitivity Analysis (also known as post-optimality analysis, is a investigation of how the ideal solution for linear programming issues is affected when input data changes. Because the information used in any LP model is often uncertain or based on estimates it is essential for decision makers to know how resistant the ideal solution is to variations in objective function coefficients right-hand side coefficients as well as constraints coefficients. This information is provided by sensitivity analysis without having to require to re-work the LP to be re-constructed with