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University: IGNOU

Course: Master of Business Administration

**Q&A of Mba MS-51 Solved Assignment 2019 - Operations Research**

Q. Solve the following problem through SIMPLEX method.

Minimize Z = -3x1+x2+x3

Subject to

x1-2x2+x3≤11

-4x1+x2+2x3≥3

-2x1 +x3=1

x1≥0, x2≥0 and x3≥0

Answer......

Q. A refueling station is served by a single pump machine for providing service to the petrol
vehicles. The arrival process has shown that the distribution of times between arrivals is
negative exponential with a mean of 10 minutes. Similarly, service times were found to
be adequately described by a negative exponential distribution with a mean of 6 minutes.
Waiting space is unlimited. Determine:

(i) Probability that the customer has to wait.

(ii) Mean number of customer in the system.

(iii) Percentage utilization of the service station.

(iv) Steady-state probability of having four customers in the system.

Answer.......

Q. "In a goal programming, we attempt to 'satisfy' or come as close as possible to satisfying the various goals," Discuss.

Answer......

Q. What is simulation? Describe the simulation process. State the major two reasons for using simulation to solve a problem. What are the advantages and limitations of simulation?

Answer......

Q. Write short notes on any five of the following:

(a) GOAL Programming

(b) GOMORY‟s cutting plane Algorithm

(c) Selective Inventory Control

(d) Pure and Mixed Strategy

(e) Sensitivity Analysis

(f) Monte Carlo Simulation

Answer......

## Product Details: Mba MS-51 Solved Assignment 2019

Course: Ignou MBA (Master of Business Administration)

Session: Jan - June 2019

Subject: Operations Research

### Old Sample Answers of Mba Ignou MS-51 Assignments

Q. What is Operations Research?

Answer. Operations research (OR) has its beginning in World War II. The term, operations research, was coined by McClosky and Trefthen in 1940 in the UK........ British scientists set up the first field installations of radars during the war and observed the air operations. Their analysis of these led to suggestions that greatly improved and increased the effectiveness of British fighters, and contributed to the success of British defence.......

Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems...........

Operations research overlaps with other disciplines, notably industrial engineering and operations management. It is often concerned with determining a maximum (such as profit, performance, or yield) or minimum (such as loss, risk, or cost.).........

Today, almost every large organization or corporation in affluent nations has staff applying operations research, and in government the use of operations research has spread from military to widely varied departments at all levels........ This general acceptance to OR has come as the managers have learned the advantage of the scientific approach on which OR is based. Availability of faster and flexible computing facilities and the number of qualified OR professionals has enhanced the acceptance and popularity of the subject. The growth of OR has not been limited to the USA and the UK...... It has reached to many countries of the world......

Q. What is linear programming?

Answer. Linear programming (LP) is a mathematical optimization technique that allows us to define objectives and constraints. LP provides a procedure to optimize the process to meet the objective. Optimization includes either maximization (e.g., revenue or profit) or minimization (e.g., cost and tardiness). The solution is derived by a procedure called simplex programming.......

The general LPP calls for optimising (maximising/minimising) a linear function of variables called the 'objective function' subject to a set of linear equations and/or inequalities called the constraints or restrictions......

In most linear programming problems, the decision variables are permitted to take any non-negative values that satisfy the constraints. There are some problems in which the variables have integral values only. These problems are not LPP, but very often they can be solved by LPP techniques and the values are then approximated to nearest integers to satisfy the constraints....... Ignou Mba MS-51 Solved Assignment 2019 Jan - June Operations Research..........

Mathematically, the constraints that restrict the decision variables to be non-negative do not differ from other constraints. However, while solving the problems they are handled differently from the other constraints, they have been termed as non-negative restrictions, and the term constraints has been used to represent constraints other than the non-negativity restriction.....

The procedure for mathematical formulation of LPP consists of the following steps:

Step 1: Identify the decision variables of the problem.

Step 2: Formulate the objective function to be optimised (maximised or minimised) as a linear function of the decision.........

Step 3: Formulate the constraints of the problem such as resource limitations, market conditions, interrelation between variables and others as linear equation or.....

Q. Write a short note goal programming

Answer. In today's business environment, profit maximization or cost minimization are not always the only objectives that a service organization sets forth....... Often, maximizing total profit is just one of several goals, including such contradictory objectives as maximizing market share, maintaining full employment, providing quality ecologic management, minimizing noise level in the neighborhood, and meeting numerous other noneconomic goals......

In typical decision-making situations, the goals set by management can be achieved only at the expense of other goals. It is necessary to establish a hierarchy of importance among these goals so that lower-priority goals are tackled only after higher-priority ones are satisfied....... Because it is not always possible to achieve every goal to the extent the decision maker desires, goal programming attempts to reach a satisfactory level of multiple objectives.......

Linear programming technique that has been applied quite extensively to various decision problems has a limited value for problems involving multiple goals...... The difficulty in using linear programming lies in the uni-dimensionality of the objective function, which requires maximisation or minimisation of one objective function....... However, in real life situations multiple goals and subgoals must be taken into account. Various goals may be expressed in different units of measurement such as rupees, hours, tons and others.