DMBA 205 -OPERATIONS RESEARCH

Description

SESSION	JUL – AUG 2024
PROGRAM	MASTER OF BUSINESS ADMINISTRATION (MBA)
SEMESTER	II
COURSE CODE & NAME	DMBA205 OPERATIONS RESEARCH

 

 

Assignment Set – 1

 

1. What is Operations Research? Write in brief the advantages and limitations of Operations Research. 3+4+4

Ans 1.

Meaning of Operations Research

Operations Research (OR) is a scientific approach to problem-solving and decision-making that uses mathematical models, statistics, and algorithms to optimize outcomes. It focuses on analyzing complex situations to provide efficient and effective solutions to problems in business, engineering, and other fields. OR integrates various disciplines like mathematics, economics, and computer science to enhance productivity and reduce costs. It is often used in resource allocation, scheduling, logistics, and supply chain management to achieve organizational objectives

 

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2. Solve the given linear programming problem:

Maximize Z   =  3×1 + 2×2 + x3

    Subject to:     -3×1 + 2×2 + 2×3 = 8

                          -3×1 + 4×2 + x3 = 7

                        where x1, x2, x3 ≥ 0

 

Ans 2.

Problem is

Max Z = 3 x1 + 2 x2 + x3

subject to

– 3 x1 + 2 x2 + 2 x3 = 8 – 3 x1 + 4 x2 + x3 = 7

and x1,x2,x3≥0;

 

 

3. Find the Initial Basic Feasible Solution (IBFS) using VAM and Optimal solution using MODI method for the given transportation problem.

	D1	D2	D3	D4	Supply
S1	21	16	25	13	11
S2	17	18	14	23	13
S3	32	27	18	41	19
Demand	6	10	12	15

 

Ans 3.

To solve the transportation problem using Vogel’s Approximation Method (VAM) to find the Initial Basic Feasible Solution (IBFS) and then optimize it using the MODI method, follow these steps:

 

Step 1: Set up the Transportation Table

Source/ Destination	D1	D2	D3	D4	Supply
S1	21	16	25	13	11
S2	17	18	14	23	13
S3	32	27	18	41	19
Demand	6	10	12	15

Step 2: Solve

 

 

 

Assignment Set – 2

 

4. A company has four zones open and four salesmen available for assignments. The zones are not equally rich in their sales potentials. It is estimated that a typical salesman operating in each zone would bring in the following annual sales:

Zone A	Rs. 126000
Zone B	Rs. 105000
Zone C	Rs. 84000
Zone D	Rs. 63000

 

The four salesmen are also considered to differ in ability. It is estimated that working under the same conditions their yearly sales would be proportionately as follows:

Salesman P:7; Salesman Q: 5; Salesman R:5; Salesman S:4

If the criterion is maximum expected total sales, it is expected to assign the best salesman to the richest zone and the next best to the second richest zone and so on. Solve the given assignment problem using Hungarian Method.

Ans 4.

To solve the assignment problem using the Hungarian Method, follow these steps:

Step 1: Formulate the Assignment Table

The annual sales for each salesman in each zone can be calculated by multiplying the zone’s sales potential with the salesman’s proportional ability:

Zone/Salesman	P (7)	Q (5)	R (5)	S (4)
A (126000)	882000	630000	630000	504000
B (105000)	735000	525000	525000	420000
C (84000)	588000	420000	420000	336000
D (63000)	441000	315000	315000	252000

 

This table

 

5a. What is Queuing system? Briefly explain the important Operating characteristics of Queuing system.

1. A self-service store employs one cashier at its counter. An average of 9 customers arrives every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, find
2. Average number of customers in the system.
3. Average number of customers in queue or average queue length.

iii. Average time a customer spends in the system.

1. Average time a customer waits before being served.

Ans 5.

a. Queuing System and Its Operating Characteristics

A queuing system refers to a process where entities (customers, data packets, vehicles, etc.) arrive at a service facility, wait if necessary, and receive service. Queuing systems are widely used in areas like customer service counters, telecommunications, traffic management, and computer networks to analyze and optimize operations. A typical queuing system involves three main components: arrival process, service process, and queue discipline (order of service, such as FIFO –

 

6. What is Simulation? Write in detail the steps used in simulation processes. 4+6

Ans 6.

Meaning of Simulation

Simulation is a technique used to model and analyze real-world systems and processes in a controlled virtual environment. It involves creating a digital representation of a system to study its behavior under various conditions without affecting the actual system. This method is widely used in