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
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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;
The problem is converted to canonical form by adding slack, surplus and artificial variables
as appropiate
1. As the constraint-1 is of type ‘=’ we should add artificial variable A1
2. As the constraint-2 is of type ‘=’ we should add artificial variable A2
After introducing artificial variables
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 Using VAM
Step 2.1: Calculate Penalty Values
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 represents the expected annual sales for each combination of salesman and zone.
Step 2: Apply the Hungarian Method
The Hungarian method involves minimizing cost, so we convert the problem into a
5a. What is Queuing system? Briefly explain the important Operating characteristics of
Queuing system.
b. 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
i. Average number of customers in the system.
ii. Average number of customers in queue or average queue length.
iii. Average time a customer spends in the system.
iv. 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 th
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 operations research, engineering, and management to predict outcomes,
improve processes, and support decision-making.
Simulation is particularly beneficial for studying systems that are complex, dynamic, or too
costly and time-consuming to experiment with directly. For example, it can be used to optimize