ASSIGNMENT

Course Code   :    MS-51

Course Title   :   Operations Research

Assignment No.   :    MS-51/TMA/SEM-I/2019

Coverage       :    All Blocks

Note : Attempt all the questions and submit this assignment on or before 30

Th April, 2019 to the Coordinator of your study center.

1.  Solve the following problem through SIMPLEX method.

Minimize Z = -3x

1

+x2

+x3

Subject to

x

1

-2x

2

+x3

≤11

-4x

1

+x2

+2x3

≥3

-2x

1

+x3

=1

x

1

≥0, x2

≥0 and x3

≥0

2.  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.

3.  “ In a goal programming, we attempt to „satisfy‟ or come as close as possible to

satisfying the various goals,” Discuss.

4.  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?

5.  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