Description

SESSION FEBRUARY – MARCH 2024
PROGRAM MASTER OF BUSINESS ADMINISTRATION
(MBA)
SEMESTER II
COURSE CODE & NAME DMBA205-OPERATIONS RESEARCH
Assignment Set – 1
1. What is Operations Research? Explain the Methodology used to
solveOperationsResearch Problems in brief.
Ans 1.
Operations Research
Operations Research (OR) is a discipline that utilizes mathematical models, statistical
analysis, and optimization techniques to aid in decision-making and problem-solving. It
involves applying scientific methods to complex problems in order to help organizations
make better decisions and improve their operations. OR is used in various industries and
sectors, including manufacturing, logistics, finance, healthcare, and telecommunications,
among others.
Methodology Used to Solve Operations Research Problems
Problem Formulation The first step in solving an Operations Research problem is to clearly
Its Half solved only
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2. Solve the following linear programming problem using its Dual form:
Minimize Z = 3×1 + 4×2
Subject to: 4×1 + x2 ≥ 30
-x1 – x2 ≤ -18
x1 +3×2 ≥ 28
where x1, x2 ≥ 0

3. A firm marketing a product has four salesman S1, S2, S3 and S4. There are three
customers to whom a sale of each unit to be made. The chance of making a sale to a
customer depend on the salesman customer support. The data depicts the probability
with which each of the salesman can sell to each of the customers.
Salesman
Customer S1 S2 S3 S4
C1 0.7 0.4 0.5 0.8
C2 0.5 0.8 0.6 0.7
C3 0.3 0.9 0.6 0.2
If only one salesman is to be assigned to each of the customers, what combination of
salesman and customers shall be optimal. Give further that the profit obtained by
selling one unit of C1 is Rs. 500, whereas it is respectively Rs 450 and Rs. 540 for sale to
C2 and C3. What is the expected profit?
Ans 3a.
Multiply each customers profit value with the probability of each salesman and customer
Customer Salesmen
S1 S2 S3 S4
C1 0.7*500 0.4*500 0.5*500 0.8*500
C2 0.5*450 0.8*450 0.6*450 0.7*450
C3 0.3*540 0.9*540 0.6*540 0.2*540
Assignment Set – 2
1. What is Monte Carlo simulation? Explain Monte Carlo Simulation Procedure in
brief.
Ans 1.
Monte Carlo Simulation: A Powerful Tool for Decision Making
Monte Carlo simulation is a computational technique used to assess the impact of risk and
uncertainty in decision-making processes. Named after the famous Monte Carlo Casino in
Monaco, known for its games of chance, this method involves using random sampling and
probability distributions to model different possible outcomes in a problem. It provides a
range of possible outcomes and the probabilities they will occur for any choice of action,
2. Asmallprojectiscomposedofsevenactivities,whosetimeestimatesarelistedin the table
below:
Estimated Duration (Weeks)
Activity (i – j) Optimistic Most LikelyPessimistic
1 – 2 1 1 7
1 – 3 1 4 7
1 – 4 2 2 8
2 – 5 1 1 1
3 – 5 2 5 14
4 – 6 2 5 8
5 – 6 3 6 15
Draw the network diagram of activities in the project.
Find the expected duration and variance for each activity. What is the expected project
length?
Calculate the variance and standard deviation of the project length. What is the
probability that the project will be completed atleast 4 weeks earlier than expected time.
Z 0.67 1.00 1.33 2.00
Prob. 0.2514 0.1587 0.0918 0.0228
Ans 2.
Making use of time estimates t0,tm and tp, the calculations for expected time te and variance
σ2 for activities are shown in table below:
Activity Time Duration (Weeks)
Sequence 𝐭𝐨 𝐭𝐦
𝐭𝐨 + 𝟒𝐭𝐦 + 𝐭𝐩 𝛔𝟐 = (𝐭𝐩 ― 𝐭𝐨
𝟔 )𝟐
1 ― 2 1 1 7 2 1
1 ― 3 1 4 7 4 1
3. There is a game between the two players A and B where A is maximizing player and
B is minimizing player. Player A wins B’s coin if the two coins total are equal to odd
number and losses his coin if total to two coins is even. It is game of 1, 2, 5, 10 and 50
rupees coins. Determine the payoff matrix, the optimal strategies for each player and
the value of the game to A.
Ans 3.
To solve this, let’s first construct the payoff matrix:
Let’s represent the coins as 1, 2, 5, 10, and 50 rupees, respectively. Player A is the
maximizing player and Player B is the minimizing player. The possible totals can be odd (win
for A) or even (loss for A). The matrix will have rows for Player A’s choices and columns for
Player B’s choices, and the entries will represent the payoff to A.