MB0048 OPERATIONS RESEARCH

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DRIVE	SUMMER 2016
PROGRAM	MBA
SEMESTER	II
SUBJECT CODE & NAME	MB0048 OPERATIONS RESEARCH
BK ID	B2068
CERDIT	4
MARKS	60

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ASSIGNMENT

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.

Question1. 1 Explain the process of OR

Answer1. “Operations Research is “the use of mathematical models, statistics and algorithms to aid in decision-making. It is most often used to analyze complex real-world systems, typically with the goal of improving or optimizing performance. It is one form of applied mathematics.”

 (1) Recognize the Problem

(2) Formulate the Problem

(3) Construct a Model

(4) Find a Solution

(5) Define the Process

(6) Implement the Solution

(7) Repeat and Refine

Essentially, the operations research process is your basic problem solving process, like the introductory problem solving process you might encounter if you were studying (cognitive) psychology, the art of mathematics,

Question2.  a. Discuss any four applications of linear programming.

Answer2a. Four applications of linear programming are as follows:

1.      Marketing applications:

·         Main application of linear programming in marketing is “media selection”.

·         Linear programming can be used to help marketing managers allocate a fixed budget to various advertising media.

·         The main objective is to maximize frequency and quality of exposure.

·         Restrictions on the

b. An organisation produces X1 and X2 units of products R and S, respectively. In this case, the objective function and constraints are expressed as follows:

Maximise                        Z = 60X1 + 120X2

 Subject to,                     3X1 + 6X2   ≤   240         Raw material constraint                    

                                          2X1 + 4X2   ≤   800        Labour hours constraint             

                                          X1, X2         ≥   0            Non-negativity condition

Use graphical method to determine how many units of products R and S the organisation should produce to maximise its profits.

Answer 2(b) - Here,

We have to maximise Z = 60X1 + 120X2

Subject to,

3X1 + 6X2 ≤

Question3.a. Explain the concept of Trans-shipment.

Answer3(a). Transhipment is the act of off-loading a container from one ship and loading it onto another ship. In any service operated by any line there are practical restrictions in terms of coverage of ports.. There is no shipping line that can cover all ports around the world on a single service and therefore the services are segregated into trade lanes.

Let’s say there is a liner service that connects Durban to Far East with Singapore, Hong Kong, and Port Kelang being the ports of call on the voyage from South Africa to Far East. Let’s call this vessel A.

Let’s say that there is a shipment from

b. Solve the following transportation problem using North-west corner method & Matrix minimum method.

Answer3(b).

The transportation problem given is :

The north-west corner method generates an initial allocation according to the following

Procedure:

1. Allocate the

Question4. The processing time of four jobs and five machines (in hours, when passing is not allowed) is given in following table

a. Find an optimal sequence for the above sequencing problem.

b. Calculate minimum elapsed time & idle time for machines A, B, C, D & E.

Answer4.

The Processing time for the

Question5. Define following criteria’s used for decision making under Uncertainty

a. Optimism (maximax or minimin) criterion

Answer 5(a).

Maximax (Optimist)

The maximax looks at the best that could happen under each action and then chooses the action with the largest value. They assume that they will get the most possible and then they take the action with the best case scenario. The

b. Pessimism (maximin or minimax) criterion

Answer5(b).

Maximin (Pessimist)

The maximin person looks at the worst that could happen under each action and then choose the action with the largest payoff. They assume that the worst that can happen will, and then they take the action with the best worst

c. Equal probabilities (Laplace) criterion

Answer5(c).

Laplace criterion is also called as law of equal probabilities criterion or criterion of rationality, since probability of states of nature are not known it is assumed that all states of nature will occur in equal probability. I.e. assign an

d. Coefficient of optimism (Hurwicz) criterion

Answer5(d).

A compromise between the maximax and maximin criteria. The decision maker is neither totally optimistic (as the maximax

e. Regret (salvage) criterion

Answer5(e).

The minimization of regret that is highest when one decision has been made instead of another. In a situation in which a decision

Question6. Explain the following:

a. Economic Order Quantity(EOQ)

Answer6(a).

Economic order quantity (EOQ) is an equation for inventory that determines the ideal order quantity a company should purchase for its inventory given a set cost of production, demand rate and other variables. This is done to minimize variable inventory costs, and the formula takes into account storage, or holding, costs, ordering

 b. PERT and CPM

Answer6(b).

PERT stands for Program Evaluation Review Technique, a methodology developed by the U.S. Navy in the 1950s to manage the Polaris submarine missile program. A similar methodology, the Critical Path Method (CPM) was

c.  Applications of queuing models

Answer6(c).

Queueing Theory has a wide range of applications, and this section is designed to give an illustration of some of these.  It has been divided into 3 main sections, Traffic Flow, Scheduling and Facility Design and Employee Allocation.  The given examples are certainly not the only applications where queuing theory can be put to good

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