MB0048 - OPERATIONS RESEARCH

              

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ASSIGNMENT

DRIVE	SUMMER 2017
PROGRAM	MBA/ MBADS/ MBAFLEX/ MBAHCSN3/ PGDBAN2
SEMESTER	II
SUBJECT CODE & NAME	MB0048 - OPERATIONS RESEARCH
BK ID	B1632
NUMBER OF ASSIGNMENTS, CREDITS &  MARKS	2, 4 Credits, 30 marks each

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.

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. Define various Characteristics & Scope of operations research

Answer:

Characteristics of operations research:

·       OR is system-oriented. OR scrutinises the problem from an organisation’s perspective. The results can be optimal for one part of the system, while the same can be unfavourable for another part of the system.

·       OR imbibes an inter–disciplinary team approach.

2 a. Elaborate various Rules for Writing a Dual Problem in linear programming.

Answer:

Consider the following linear programming problem:

Maximise Z = c1x1 +c2x2 + . . . +cnxn

Subject to the constraints

a11 x1 + a12 x2 + . . . + a1n xn ≤ b1

a21 x1 + a22 x2 + . . . + a2n xn ≤ b2

am1 x1 + am2 x2 + . . . + amn xn ≤ bm

x1, x2, . . ., xn ≥ 0

To construct a dual problem, we must adopt the following guidelines:

·       The maximisation problem in the primal becomes a minimization problem in the dual and vice versa.

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 ≤ 240

2X1 + 4X2

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

b. Solve the following transportation problem using Vogel’s Approximation method.

Answer:

olution:
TOTAL no. of supply constraints : 3
TOTAL no

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.

Answer1.

The Processing time for the new problem is given below:

 

The optimal sequence is

2

1

4

3

Total elapsed time = 61

Idle time for

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

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

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

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 has

Question6. Explain the following:

a. Economic Order Quantity (EOQ)

Answer 6(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 costs and

 b. PERT and CPM

Answer 6(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 developed for

c.  Applications of queuing models

Answer 6(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

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