Assignment_dmba205_mba-2_set-1-and-2_nov_2021

Q1. What is Operations Research (O.R.)? Discussed the significance and scope of O.R. 3+3+4               10

Ans.

Operations Research (O.R.): Churchman, Aackoff, and Aruoff defined operations research as “the application of scientific methods, techniques and tools to the operation of a system with optimum solutions to the problems” where ‘optimum’ refers to the best possible alternative.

The objective of OR is to provide a scientific basis to the decision-makers for solving problems involving interaction with various components of the organisation. This can be achieved by employing a Its Half solved only

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Q2. a) Solve the following linear programming problem:

Max. Z  = 20×1 + 10×2

Subject to:  x1 + x2 = 150

x1 ≤ 40

x2 ≥ 20

where  x1, x2 ≥ 0       5 marks

Ans:

Solution:
Problem is

b) Discuss in brief “Duality” in linear programming problems. How to interpret the primal-dual relationship?            2+3

Ans:

Duality: Every Linear Programming Problem (LPP) is associated with another linear programming problem involving the same data and optimal solutions. The two problems are said to be duals of each

3. a) A car hire company has one car at each of the five depots D1, D2, D3, D4 & D5.

Customers in each of the five towns A, B, C, D & E requires a car. The distance (in miles)

between the depots (origins) and the towns (destinations) where customers are given in the following distance matrix:

Depots            5          10

                  D1      D2       D3       D4       D5             

            A    160     130       175       190       200                    

            B    135     120       130       160       175                    

Person C    140     110       155       170       185                   

            D     50      50        80        80       110            

            E     55      35        70        80       105            

            How should the cars be assigned to the customers so as to minimize the distance

travelled?      

Ans 3a.

This problem could be solved using the transportation technique. However, only five of the routes will be used and so an additional four routes would have to be included at zero level in order to determine shadow costs and thus test for optimality. The problem is to select five elements from the matrix of Table 1 such that there is one element in each row, one in each column, and the sum is the

 b) Solve the following transportation problem using Vogel’s Approximation Method:

Destination     5         

                             D1      D2      D3      D4    Supply            

Source   S1           7          3        8           6       60                 

               S2           4          2        5          10     100                

               S3           2          6        5           1       40                 

        Demand    20      50      50      80                       

Ans:

Solution:
TOTAL number of supply constraints : 3
TOTAL number of demand constraints : 4
Problem Table is

Table-1

Set – II

Q4.a) Solve the following Integer programming problem using Gomory’s Fractional

Algorithms:

Maximize Z = 5×1 + 7×2

Subject to: -2×1 + 3×2 ≤ 6

6×1 + x2 ≤ 30

where x1, x2 ≥ 0 are integers.                      

Answer:

Solution:
Problem is

b) Solve the following game using Dominance rule:

Player B

                       B1  B2  B3

                 A1  5   20  -10

Player A  A2  10   6    2

                 A3  20   15   18     

Solution:

Q5. Write short notes on the following concepts:

a) Erlang M/M/1: ∞/FCFS Queuing Model

b) Program Evaluation and Review Technique [PERT]  5+5      10

Ans:

a) Erlang M/M/1: ∞/FCFS Queuing Model:

The queueing system where the distribution of arrival and the departure both are assumed to be Poisson or the distribution of inter-arrival time and service time are assumed to be Exponentially distributed are called as the Poisson queuing system. The main Poisson queuing

Q 6. The Cargo Honda Ltd. Manufactures around 150 scooters. The daily production

varies from 146 to 154 depending upon the availability of raw materials and other working conditions:

Production  146   147   148   149   150   151   152   153   154

Per day

Probability  0.04   0.09   0.12   0.14   0.11   0.10   0.20   0.12   0.08

The finished scooters are transported in a specially arranged lorry accommodating

150 scooters. Using following random numbers: 80, 81, 76, 75, 64, 43, 18, 26, 10,

12, 65, 68, 69, 61, 57. Simulate the process to find out:

i) the average number of scooters waiting in the factory. ii) the average number of empty spaces on the lorry.            10       

Ans:

The random numbers are given in the table below: