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Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Each question is followed by evaluation scheme.



1 Discuss the various stages involved in the methodology of Operations Research. Briefly explain the techniques and tools of Operations Research.

Answer : The basic dominant characteristic feature of operations research is that it employs mathematical representations or models to analyse problems. This distinct approach represents an adaptation of the scientific methodology used by the physical sciences. The scientific method translates a given problem into a mathematical




2 a. Explain the steps involved in linear programming problem formulation. Discuss in brief the advantages of linear programming.

Answer : The procedure for mathematical formulation of a linear programming problem consists of the following major steps:






b. Alpha Limited produces & sells two different products under the brand names black & white. The profit per unit on these products in Rs. 50 & Rs. 40 respectively. Both the products employ the same manufacturing process which has a fixed total capacity of 50,000 man-hours. As per the estimates of the marketing research department of Alpha Limited, there is a market demand for maximum 8,000 units of Black & 10,000 units of white. Subject to the overall demand, the products can be sold in any possible combination. If it takes 3 hours to produce one unit of black & 2 hours to produce one unit of white, formulate the model of linear programming.


Answer:-  A company has three operational departments (weaving, processing, and packing) with a capacity to produce three different types of clothes – suits, shirts, and woollens, yielding a profit of Rs.2, Rs.4, and Rs.3 per meter respectively. One meter of suiting requires 3 minutes of weaving, 2 minutes of processing, and 1 minute of packing. Similarly, one meter of shirting requires 4 minutes of weaving, 1 minute of processing, and 3 minutes of packing. One meter of woollen requires 3 minutes in each department. In a week, total run





3 a. What is degeneracy in transportation problem? How it can be resolved?

Answer : A basic solution to an m-origin, n destination transportation problem can have at the most m+n-1 positive basic variables (non-zero), otherwise the basic solution degenerates. It follows that whenever the number of basic cells is less than m + n — 1, the transportation problem is a degenerate one.

The degeneracy can develop in two ways:

Case 1 – The degeneracy develops while determining an initial assignment via any one of the initial assignment methods discussed earlier. To resolve degeneracy, you must augment the positive variables by as many zero-valued variables as is necessary to complete the required m + n — 1 basic variable. These zero-valued variables are selected in such a manner that the resulting m + n — 1 variable constitutes a basic solution.









b. Solve the following transportation problem using Vogel’s approximation method. Factories Distribution Centres Supply


Answer :  Computation/Solution to the problem

Since total demand = 135 = total supply, the problem is balanced. The initial basic feasible solution is obtained by Vogel’s approximation method.




4 a. Explain the steps in Hungarian method. Differentiate between Transportation and Assignment problem.

Answer : Steps in Hungarian method

Hungarian method algorithm is based on the concept of opportunity cost and is more efficient in solving assignment problems. The following steps are adopted to solve an AP using the Hungarian method algorithm.

Step 1: Prepare row ruled matrix by selecting the minimum values for each row and subtract it from the other elements of the row.




b. Find the optimal assignment of four jobs and four machines when the cost of assignment is given by the following table:



Answer :




5 Define Simulation. Explain the Simulation procedure. Discuss the use of Simulation with an example.

Answer : Simulation is the imitation of the operation of a real-world process or system over time.[1] The act of simulating something first requires that a model be developed; this model represents the key characteristics or behaviors/functions of the selected




6 Explain the following:

a. Integer programming model

Answer : Integer programming is concerned with optimization problems in which some of the variables are required to take on discrete values. Rather than allow a variable to assume all real values in a given range, only predetermined discrete values within the range are permitted. In most cases, these values are the integers giving rise



b. PERT and CPM

Answer : Project management is an important part of every business enterprise. Whenever a new product or service is launched; when embarking on a marketing campaign; or when organizing any new projects; project management is needed to make everything organized and successful.

As all projects consume resources such as





c. Operating Characteristics of a Queuing System

Answer : Characteristics of a queuing system that impact its performance, for example, queuing requirements of a restaurant will depend upon factors like:

  • How do customers arrive in the restaurant? Are customer arrivals more during lunch and dinnertime (a regular restaurant)? Or


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