The document provides information about operations research (OR) including: (1) OR uses mathematical models and statistics to aid decision-making, typically to optimize performance of complex systems. (2) The basic OR process involves recognizing a problem, formulating it, constructing a model, finding a solution, defining the process, implementing it, and refining it. (3) Linear programming applications discussed include marketing, finance, operations management, and blending problems. Graphical and algebraic methods are used to solve transportation problems.

1. MBA 205 OPERATIONS RESEARCH Page 1
SPRING 2017
MBA
SEMESTER - II
SUBJECT CODE & NAME - MBA205 & OPERATIONS RESEARCH
SET- 1
Q.1 Explain the process of OR.
Answer:
OperationsResearchis“the use of mathematical models,statisticsandalgorithmstoaidindecision-
making. It is most often used to analyze complex real-world systems, typically with the goal of
improving or optimizing performance. It is one form of applied mathematics.” (Wikipedia)
The questfor improvement has been a continual one and operations research has been one of the
areas thathas beentraditionallyfocused on improving operations across the company, particularly
in production, operation, scheduling and physical systems. As such, there is a wide body of
knowledge upon which can draw to improve procurement and sourcing operations when properly
applied and modified. Even Six Sigma’s (Strategic Sourcing) toolbox makes extensive use of
techniques and processes that have their foundations in operations research.
Basic Operations ResearchProcess, which,simplyput, is:
(1) Recognize the Problem
(2) Formulate the Problem
(3) Construct a Model
(4) Finda Solution
(5) Define the Process
(6) Implementthe Solution
(7) Repeatand Refine
Essentially, the operations research process is your basic problem solving process, like the
introductory problem solving process you might encounter if you were studying (cognitive)
psychology,the art of mathematics, or (classical) engineering. Furthermore, it neatly captures the

2. MBA 205 OPERATIONS RESEARCH Page 2
keystepsyou will have to work through as you attempt to improve and evolutionize your sourcing
process.
(1) You first have to define what your primary problem is and what your key goals are. Are you
spending too much money? If so, where. Are you spending too much time on the process? If so,
why? Etc.
(2) Then you have to formulate and frame the key problem. For example, you believe you’re
spendingtoomuchon yourhighvolume directmaterialsoryouare spending too much time in your
data collection process.
(3) Once youhave preciselyformulatedthe problem to solve, you need to model what you believe
the solutionshouldlooklike. Manyindividualsandorganizationsskipthisstepandgostraightto the
solutionidentificationstep. However,if youdon’tknow whatthe solutionshould look like, you risk
selecting the wrong solution.
(4) Often this step will be accomplished in practice by selecting a readily available technology,
methodology, process, or model from the public domain or commercial marketplace. Don’t try to
reinventthe wheel,chancesare yourproblemisnotunique andsomeone else has already solved it
for you. For example, the inventor and followers of TRIZ (an innovative problem solving
methodologythatwe will discuss at a later time) have collectively reviewed over 2 million patents
and discovered that less then 4% contained a new concept and only 1% contained a revolutionary
discovery. The restwere merelyimprovementsonexistingsolutionsandprocesses. In other words,
there is at least a 95% chance that a solution to your problem already exists, and at least a 99%
chance that a solution to a similar problem exists that can be adapted to your problem.
(5) Once you have a selected a solution – be it a technology or a new methodology, you need to
define howitisgoingto be integrated into your current operational processes. This step is easy to
overlook,butif the introductionof anew process or technology disrupts your daily operations, you
will not realize the full benefits.
Q.2 a. Discuss any four applications of linear programming.
Ans.2a.
Four applications of linear programming are as follows:

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1. Marketing applications:
 Main application of linear programming in marketing is “media selection”.
 Linear programming can be used to help marketing managers allocate a fixed
budget to various advertising media.
 The main objective is to maximize frequency and quality of exposure.
 Restrictions on the allowable allocation usually arise during consideration of
company policy, contract requirements, and media availability.
2. Financial applications:
 Linear programming can be used in financial decision-making that involves
capital budgeting, make-or-buy, asset allocation, portfolio selection, financial
planning, and more.
 Portfolio selection problems involve choosing specific investments – for
example, stocks and bonds – from a variety of investment alternatives.
 This type of problem is faced by managers of banks, mutual funds, and
insurance companies.
 The objective function usually is maximization of expected return or
minimization of risk.
3. Operations Management applications:
 Linear programming can be used in operations management to aid in
decision-making about product mix, production scheduling, staffing,
inventory control, capacity planning and other issues.
 An important application of linear programming is multi-period planning
such as production scheduling.
 Usually the objective is to establish an efficient, low-cost production
schedule for one or more products over several time periods.
 Typical constraints include limitations on production capacity, labour
capacity, storage space, and more.
4. Blending problem:

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 Linear programming technique is also applicable to blending problem when a
financial product is produced by mixing a variety of raw materials. The
blending problem arises in animal feed, diet problems, petroleum products,
chemical products, etc.
 In all such cases, with raw materials and other inputs as constraints, the
objective function is to minimise the cost of final product.
b. An organisation produces X1 and X2 units of products R and S,
respectively. In this case, the objective function and constraints are
expressed as follows:
Maximise Z = 60X1 + 120X2
Subject to, 3X1 + 6X2 ≤ 240 Raw material constraint
2X1 + 4X2 ≤ 800 Labour hours constraint
X1, X2 ≥ 0 Non-negativity condition
Use graphical method to determine how many units of products R and S the
organisation should produce to maximise its profits.
Answer 2(b) - Here,
We have to maximise Z = 60X1 + 120X2
Subject to,
3X1 + 6X2 ≤ 240
2X1 + 4X2 ≤ 800
X1, X2 ≥ 0
First constraint 3X1 + 6X2 ≤ 240 in the form of equation,
3X1 + 6X2 = 240
X1 + 2X2 = 80
When X1 = 0, then X2 = 40

5. MBA 205 OPERATIONS RESEARCH Page 5
When X2 = 0, then X1 = 80
The coordinates will be (0, 40) and (80, 0)
Second constraint 2X1 + 4X2 ≤ 800 in the form of equation,
2X1 + 4X2 = 800
X1 + 2X2 = 400
When X1 = 0, then X2 = 200
When X2 = 0, then X1 = 400
The coordinates will be (0, 200) and (400, 0)
There is
no common feasible region generated by two constraints together so that we cannot identify a
single point satisfying the constraints. Hence there is no optimal solution.
Q.3a. Explain the concept of Trans-shipment.
b. Solve the following transportation problem using North-west corner
method & Matrix minimum method.
Ans.
3(a). Transhipment is the act of off-loading a container from one ship and loading it onto another
ship.Inany service operatedbyanyline there are practical restrictionsintermsof coverage of ports.

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There isno shippingline thatcancover all ports around the world on a single service and therefore
the services are segregated into trade lanes.
Let’s say there is a liner service that connects Durban to Far East with Singapore, Hong Kong, and
Port Kelangbeingthe portsof call on the voyage fromSouthAfricato Far East. Let’scall thisvessel A.
Let’s say that there is a shipment from Durban in South Africa to Manila in Philippines. Since this
vessel adoesnotcall Manilaas part of itsrotation/service,the container(s) will need to be taken off
at one of the ports that vessel A calls.Let’s assume thatthisportisSingapore. These container(s)will
be off-loaded at Singapore and then loaded onto another vessel that operates on a route that
connects Singapore to Manila. Let’s call this vessel B.
So the container that left Durban on vessel A will reach Manila on vessel B via transhipment at
Singapore. The bill of lading that the customer has been issued will show Vessel A, but the arrival
notification that the consignee in Manila receives will show Vessel B.
Most of the big lines like MSC, Maersk etc. have services covering virtually all corners of the globe
via transhipment connections from one port or the other.. These lines also have what is known as
TranshipmentHubswhich are the ports on their service routes that have transhipment connection
optionstootherparts of the world.Example:MSC’stranshipmenthubfortheirservice toAustraliais
Port Louis; Maersk’s transhipment hub for their service to Middle East is Shalala.
This transhipment concept truly connects the world and one is able to ship a container from
anywhere to anywhere in the world.
3(b).
The transportation problem given is :
C1 C2 C3 C4 S
F1 3 2 7 6 50
F2 7 5 2 3 60
F3 2 5 4 5 25
R 60 40 20 15

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The north-west corner method generates an initial allocation according to the following
Procedure:
1. Allocate the maximum amount allowable by the supply and requirement constraints to the
variable (i.e. the cell in the top left corner of the transportation table).
2. If a column (or row) is satisfied, cross it out. The remaining decision variables in that column (or
row) are non-basicandare set equal tozero.If a row andcolumnare satisfiedsimultaneously, cross
only one out (it does not matter which).
3. Adjust supply and demand for the non-crossed out rows and columns.
4. Allocate the maximumfeasible amounttothe firstavailablenon-crossed out element in the next
column (or row).
5. When exactlyone rowor columnisleft,all the remainingvariables are basic and are assigned the
only feasible allocation.
Using North West corner method
C1 C2 C3 C4 S
F1 3 2 7 6 0
F2 7 5 2 3 0
F3 2 5 4 5 0
R 0 0 0 0
Minimum transportation cost = 50*3 + 10*7 + 40*5 + 10*2 + 10*4 + 5*15
= 150 + 70 + 200 + 20 + 40 + 75
50
10 40 10
10

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= 555
MATRIX MINIMUM METHOD:
1. Assignas muchas possible tothe cell withthe smallestunitcostinthe entire table.If there isa tie
then choose arbitrarily.
2. Cross out the row or columnwhich has satisfied supply or demand. If a row and column are both
satisfied then cross out only one of them.
3. Adjust the supply and requirement for those rows and columns which are not crossed out.
4. When exactlyone rowor columnisleft,all the remainingvariables are basic and are assigned the
only feasible allocation.
Using matrix minimum method
C1 C2 C3 C4 S
F1 3 2 7 6 0
F2 7 5 2 3 0
F3 2 5 4 5 0
R 0 0 0 0
Minimum transportation cost = 10*3 + 25*7 + 25*2 + 40*2 + 20*2 + 3*15
= 30 + 175 + 50 + 80 + 40 + 45
= 420
10
25
40
20
25
15

9. MBA 205 OPERATIONS RESEARCH Page 9
SET - 2
Q.1 The processing time of four jobs and five machines (in hours, when
passing is not allowed) is given in following table
a. Find an optimal sequence for the above sequencing problem.
b. Calculate minimum elapsed time & idle time for machines A, B, C, D & E.
Answer1.
The Processing time for the new problem is given below:
The optimal sequence is
2 1 4 3

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Total elapsed time = 61
Idle time for machine A = 61 – 34 = 27 hours
Idle time for machine B = 7 + (15-13) + (25-19) + (34-30) + (61-41) = 39 hours
Idle time for machine C = 13 + (19-20) + (30-27) + (41-39) + (61-50) = 27 hours
Idle time for machine D = 20 + (27-24) + (39-30) + (50-46) + (61-56) = 41 hours
Idle time for machine E = 24 + (30-28) + (46-38) + (56-53) + (61-61) = 37 hours
Q.2 Define following criteria’s used for decision making under Uncertainty
a. Optimism (maximax or minimin) criterion
Ans.2(a)
Maximax (Optimist)
The maximax looks at the best that could happen under each action and then chooses the action
with the largest value. They assume that they will get the most possible and then they take the
actionwiththe bestcase scenario.The maximum of the maximums or the "best of the best". This is
the lotto player; they see large payoffs and ignore the probabilities.
b. Pessimism (maximin or minimax) criterion
Ans.2(b)
Maximin (Pessimist)
The maximin person looks at the worst that could happen under each action and then choose the
actionwiththe largestpayoff.Theyassume that the worst that can happen will, and then they take
the action with the best worst case scenario. The maximum of the minimums or the "best of the
worst". This is the person who puts their money into a savings account because they could lose
money at the stock market.
c. Equal probabilities (Laplace) criterion
Ans.2(c)

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Laplace criterionisalsocalledaslawof equal probabilities criterion or criterion of rationality, since
probabilityof statesof nature are not knownitisassumedthatall statesof nature will occurin equal
probability. I.e. assign an equal probability. The Laplace criterion uses all the information by
assigning equal probabilities to the possible pay offs for each acton and then selecting that
alternative whichcorrespondstothe maximumexpectedpayoff.This is one of the decision making
technique under the conditions of uncertainty.
d. Coefficient of optimism (Hurwicz) criterion
Ans.2(d)
A compromise between the maximax and maximin criteria. The decision maker is neither totally
optimistic (as the maximax criterion assumes) nor totally pessimistic (as the maximin criterion
assumes).Withthe Hurwiczcriterion,the decisionpayoffsare weightedbyacoefficientof optimism,
a measure of the decisionmaker'soptimism.The coefficientof optimism, defined as a, is between 0
and 1 (i.e., 0 < a < 1.0). If a = 1.0, then the decision maker is completely optimistic, and if a = 0, the
decisionmakeriscompletelypessimistic.(Giventhisdefinition,1 - a is the coefficientof pessimism.)
For each decision alternative, the maximum payoff is multiplied by a and the minimum payoff is
multiplied by 1 - a. For our investment example, if a equals 0.3 (i.e., the company is slightly
optimistic) and 1 - a = 0.7.
e. Regret (salvage) criterion
Ans.2(e)
The minimizationof regretthatishighestwhenone decisionhasbeenmade insteadof another. In a
situationinwhichadecisionhas been made that causes the expected payoff of an event to be less
than expected, this criterion encourages the avoidance of regret. also called opportunity loss.
Q.3 Explain the following:
a. Economic Order Quantity (EOQ)
Answer 3(a).
Economicorderquantity(EOQ) isan equationforinventorythatdeterminesthe ideal orderquantity
a companyshouldpurchase for its inventory given a set cost of production, demand rate and other
variables. This is done to minimize variable inventory costs, and the formula takes into account
storage, or holding, costs, ordering costs and shortage costs. The full equation is as follows:
Economic Order Quantity (EOQ)
where :
S = Setup costs
D = Demand rate

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P = Production cost
I = Interest rate (considered an opportunity cost, so the risk-free rate can be used)
b. PERT and CPM
Answer 3(b).
PERT standsfor Program EvaluationReview Technique,amethodology developed by the U.S. Navy
in the 1950s to manage the Polaris submarine missile program. A similar methodology, the Critical
Path Method(CPM) was developedforprojectmanagementinthe private sector at about the same
time.
CPM and PERT (Program Evaluation and Review Technique) are most commonly used methods for
projectmanagement.There are some similaritiesanddifferences between PERT and CPM. PERT can
be applied to any field requiring planned, controlled and integrated work efforts to accomplish
definedobjectives.Onthe otherhand,CPM(Critical PathMethod) isthe methodof projectplanning
consisting of a number of well-defined and clearly recognizable activities.
c. Applications of queuing models
Ans. 3(c)
QueuingTheoryhasa wide range of applications,andthis section is designed to give an illustration
of some of these. It has been divided into 3 main sections, Traffic Flow, Scheduling and Facility
DesignandEmployee Allocation. The givenexamples are certainly not the only applications where
queuing theory can be put to good use, some other examples of areas that queuing theory is used
are also given.
Traffic Flow
This is concerned with the flow of objects around a network, avoiding congestion and trying to
maintain a steady flow, in all directions.
Queueing on roads Queues at a motorway junction, and queuing in the rush hour
Scheduling
Computer scheduling
Facility Design and Employee Management
Queues in a bank
A Mail Sorting Office
Some Other Examples
Design of a garage forecourt
Airports - runway layout, luggage collection, shops, passport control etc.
Hair dressers
Supermarkets
Restaurants
Manufacturing processes