1. Punjab College of Technical Education Ludhiana
(Course Plan)
Course Objective:
This Course is helpful in building skills for solving various technical business problems by
application of scientific methods.
Name of Teacher: PD (pallavi@pcte.edu.in)
Subject Name: Operation Research
Break up of marks: First hourly :5 Marks
Second Hourly : 5 Marks
MSE : 15 marks
Presentation : 5 Marks
End Sem Class Test : 5 Marks
Practice Assignments: 5 Marks
Practice Assignments: 5 Practice assignments are attached with course breakup. These 5
assignments are based on 5 different topics from the syllabus and contain questions which are
typical in nature. Assignment will be given when that particular topic will be discussed in the
class. Submission of the assignment is subject to the viva.
Case studies:
• Assigning students to school (Simplex Method)
• Project Pickings (Assignment Problem)
• Case with Many Transportation Problems (Transportation Problem)
Date LECTURE Contents Assignments/Tests
1 Introduction to OR: Concept & Historical
development
Definition of OR
Usefulness of OR in decision making:
Decision, Alternatives, Constraints,
objectives
Management Applications & Limitations
of OR
OR Models: on basis of structure,
Purpose, Nature of environment, behavior,
method of solution, use of digital
computers
Principles of modeling
Main Phases of OR:
 Formulation of

2. problem
 Construction of
Math. Model
 Solutions from
models
 Testing of model
 Control of sol
 Implementation of
sol.
2 Linear Programming: Introduction
Problem Definition: Example Wyndor
Glass. Co.
Linear Programming Model&
Assumptions
3 Graphical Method to solve Linear
programming Problem
Hillier Book 4 Some typical cases of graphical Method.
Pg No. 34,
35,36
5 Simplex Method: Introduction,
Maximization Problem
6 Simplex Method : Minimization problem
7 Simplex Method : Mixed Constraints
8 Simplex Method : Mixed Constraints
9 Simplex Method : Typical Cases
10 Application of Simplex Method in
Organizations with the help of cases:
• Choosing the product mix at
Ponderosa Industrial
• Personnel Scheduling at United
Airlines
• Planning Supply, Distribution
and Marketing at Citgo
Petroleum Corporation
Case study: Assigning students to
school
11 Duality: Meaning & Construction of Dual
12 Practice of dual Problem
13 Assignment Model
• Meaning
• Purpose
• Formulation of assignment Model
Hungarian Method to solve the
Assignment problem
14 Solution of assignment model for square

3. matrix/ non square matrix/with
restrictions
15 Solution of assignment model with
maximization problem
16 Traveling sales man problem
17 Air crew assignment
18 Case Study: Project Pickings
19 Introduction to Transportation Model 1
 Feasible sol
 Basic feasible sol
 Optimal sol
 Balance & Unbalanced
transportation model
 Conversion of maximization
into minimization
20 Steps in sol of a balanced
transportation model :
Step I : Make a
transportation model
o Step II : To find a basic
feasible sol
 North West
Corner rule
 Least Cost
Method
21 Initial Basic Feasible Solution:
Vogel approximation Method (VAM)
22 Problem of Degeneracy
Optimality Test – MODI
23
Optimality Test – MODI
24 Stepping Stone Method
25 Transshipments problem

4. 26 Case study : Case with Many
Transportation Problem
27 Game Theory
Competitive Games : Properties
Terminology in Game Theory :
Participant, play strategy, pure strategy,
mixed strategy, two person zero sum
game , n person zero sum game
28 Sol. of game problem with pure strategy
Principle of dominance for rows and
columns
29 Sol of 2xn or mx2 games ( mixed
Strategy) : Method of Subgames
30 Sol of 2xn or mx2 games( mixed Strategy)
: Graphical Method
31 Network Analysis
PERT & CPM: Concept & History
Event, Activity
Predecessor event, successor event
Drawing a network
Numbering of events: Fulkerson’s
rule
32 Dummy, Looping, Dangling, Back ward
Pass
Forward Pass, Earliest expected time,
Latest occurrence time, Critical path,
Project Time
33 EST
EFT
LST
LFT
Slack
Float : Independent, free, total
34 PERT Computations: expected
time, optimistic time, pessimistic
time, most likely time
Probability of completing a project
35 Crashing
36 Applications of Network Analysis in
some companies

5. 37 Sensitivity Analysis: Meaning, Basic
Practicals
38 Replacement Model
39 Replacement Model Considering Time
value Of Money
41 Inventory Models: Introduction , Terms
Used, Calculation Of EOQ
42 Explanation of all formulas: Max. Level,
Min Level, Reorder Level.
43 Queuing Theory: Introduction ,
Terminology, Model 1
44 Model 2 ( along with numerical)
45 Dynamic Programming
Punjab College of Technical Education, Ludhiana (Baddowal)
Class: M.B.A 3rd Semester
Assignment:1
Assignment LPP
1. Obtain the Optimal solution to the following linear programming problem.
Minimize Z = X1 + X2 + X3
S. T. C. X1 - 3X2 + 4X3 = 5,
X1 - 2X2 < 3
2X2 - X3 > 4
Where, X1, X2 >0, X3 unrestricted in sign
2. A small company has 5 skilled and 10 semiskilled men and produces two products with the
following information:
Products P1 P2 Hours Available
Man Hours Skilled 2 1 40
Man Hours Unskilled 2 3 80
Profit/Unit (Rs.) 10 8
By union rules no man work more than 8 hours. Formulate this as a linear programming and solve
graphically.
3. A Co. that produces soft drinks has a contract that requires that a minimum of 80 units of the chemical
A and 60 units of the chemical B into each bottle of the drink. The chemicals are available in a
prepared mix from two different suppliers. Supplier X1 has a mix of 4 units of A and 2 units of B that
costs Rs. 10, and Supplier X2 has a mix of 1 unit of A and 1 unit of B that Costs Rs. 4. How many
mixes from company X1 and Company X2 should the company purchase to honor contract requirement
and yet minimize cost? Solve it graphically.
4. A company has two grades of inspectors, 1 and 2 to undertake quality control inspection. At least 1500
pieces must be inspected in an 8- hour’s day. Grade 1 inspectors can check 20 pieces in an hour with
an accuracy of 96%. Grade 2 inspectors check 14 pieces an hours with an accuracy of 92%.

6. The daily wages of grade 1 inspectors are Rs. 5 per hour while those of grade 2 inspector
are Rs. 4 per hour. Any error made by an inspector costs Rs. 3 to the company. If there
are, in all, 10 grade 1 inspector and 15 grade 2 inspectors in the company, find the
optimal assignment of inspectors that minimize the daily inspection cost. Formulate the
problem and solve it graphically.
6. Solve by simplex method:
Maximize Z=10x + 15y
Subject to: 2x + y < 26
2x + 4y < 56
x – y > -5 x,y > 0
7. Solve graphically:
Minimize Z = 2y – x
Subject to: 0.5x + 0.5y < 3
2x – 2y > 4 x,y > 0
8. A company produces two types of pens, say A & B. Pen A is of superior quality and Pen B is of
inferior quality. Profit on pens A & B is Rs 5 & Rs 3 per pen respectively. Raw material required for
each pen A is twice as that for pen B. The supply of raw materials is sufficient only for 1000 pens. Pen
A requires a special clip and only 400 such clips are available per day. For pen B, only 700 clips are
available per day. Find graphically the product mix so that the company can make maximum profit.
8. A company produces two types of container K & L. Each product has resources requirement and
profit contribution as follows:
Resources K L Total resources available
Material (kg/unit) 1 2 10 kgs
Labour (hr/unit) 6 6 36 hours
Profit 4 5
In addition, because of demand, a maximum of 4 units of container K will be produced. By Simplex
method obtain the optimal plan that maximizes the profit.
7. A farmer has 2000 acres of land on which he can grow corn wheat soybean. Each acre of corn
costs Rs. 200 for preparation, requires 14 man days and yields a profit of Rs. 60. An acre of
wheat cost Rs. 240 to prepare, Requires 20 man days and yields a profit of Rs. 80. An acre of
soybean costs Rs. 140 to prepare requires 16 man days of work and yields a profit of Rs. 40. If
farmer has Rs. 2 Lakh for preparation and can count on 16000 man days of work, how many
acres should be allocated to each crop to maximize profits.
8. A company is engaged in producing three products A, B, C. The following data is available
Products A B C
Net Sale Price (Rs. Per Unit) 10 12 15
Cost (Per Unit) 6 9 10
The wholesaler who is responsible for selling to the customer is to be paid Rs. 150 per day
irrespective of the quantities sold in each of the products. The products are processed in three different
operations. The time (hrs) required to produce one product in each of the operations and the daily
capacity (hrs) available for each operation Centre are given as
Products

7. Operations A B C Daily Capacity
(hrs)
1 2 3 2 400
2 3 2 2 350
3 1 4 2 300
What product mix would yield maximum profits and how much.
Punjab College of Technical Education, Ludhiana (Baddowal)
Class: M.B.A 3rd Semester
Assignment:2 (Assignment Model)
1 A firm produces four products. There are four operators who are capable of producing any of these
four products. The processing time varies from operator to operator. The firm records 8 hours a day
and allows 30 minutes for lunch. The processing time in minutes and profit for each of products are
given below:
Operators Products
A B C D
1 15 9 10 6
2 10 6 9 6
3 25 15 15 9
4 15 9 10 10
Profits (Rs.) per unit 8 6 5 4
Find the optimal assignment of products to operators.
2. An airline operating for seven days a week has time table shown below. Crew must have a
minimum layover (rest time) of 5 hrs between flights. Obtain the pair of flights that minimizes lay
over time away from home. For any given pair the crew will be based at the city that results in the
smaller layover. For each pair , mention the town where the crews should be based.
Delhi Jaipur Jaipur Delhi
Flight No. Departure Arrive Flight No. Departure Arrive
1 7:00 A.M 8: 00 A.M 101 8:00 A.M 9:15 A.M
2 8:00 A.M 9:00 A.M 102 8:30 A.M 9:45 A.M
3 1:30 P.M 2:30 P.M 103 12:00 noon 1:15 A.M
4 6:30 A.M 7:30 P.M 104 5:30 P.M 6:45 P.M

8. 3. In a textile sales emporium 4 salesmen are available to 4 counters. Each salesman can handle any
counter. The service (in hours) of each counter which is managed by each salesman is given below:
Salesman A B C D
W 41 72 39 52
Counter X 22 29 49 65
Y 27 39 60 51
Z 45 50 48 52
How should the salesman be allocated to appropriate counters so as to minimize the service time. Each
salesman must handle only one counter. Also indicate the total service time.
4. A company has 5 jobs to be done. The following matrix shows the return in rupees on assignment
ith (i= 1,2,3,4,5) machine to jth job (J= a,b,c,d,e). Assign the five jobs to the five machines so as to
maximize the total expected profit.
Jobs
A B C D E
1 5 11 10 12 4
Machines 2 2 4 9 3 5
3 3 12 5 14 6
4 6 14 4 11 7
5 7 9 8 12 5
5. Solve the following ‘Traveling Salesman Problem” given by the following data:
C12 = 4, C13 = 7, C14 = 3, C23 = 6, C24 = 3, and C34 = 7, where Cij = Cji
6..Find the minimum cost solution for the 5x5 assignment problem whose cost coefficients are as
given below:
A B C D E
A -2 -4 -8 -6 -1
B 0 -9 -5 -5 -4
C -3 -8 -9 -2 -6
D -4 -3 -1 0 -3
E -9 -5 -8 -9 -5
9. Five mechanics are available to work on five machines and their respective cost in Rs for each
mechanic machine combination is given in the matrix below. A sixth machine is available to
replace one of the existing machines and the associated cost is given in the table. Determine
1) Whether the new machine can be accepted. ii) Optimal assignment and the associated
cost.
1 2 3 4 5 6
A 19 15 -- 16 13 22
B 13 -- 15 -- 21 14
C 15 17 19 20 12 18
D 20 22 16 18 17 --
E -- 16 14 19 18 15
Dummy 0 0 0 0 0 0

9. 10. WELLDONE Company has taken the third floor of a multistoreyed building for rent with a
view to locate one of their zonal offices. There are five main rooms in this floor to be assigned
to five managers. Each room has its own advantages and disadvantages. Some have windows;
some are closer to the washrooms or to the canteen or secretarial pool. The rooms are of all
different sizes and shapes. Each of the five managers were asked to rank their room
preferences amongst the rooms 301, 302, 303, 304, 305. Their preferences were recorded in a
table as indicated next:
Manager
M1 M2 M3 M4 M5
302 302 303 302 301
303 304 301 305 302
Rooms 304 305 304 304 304
-- 301 305 303 --
-- -- 302 -- --
Most of the managers did not list all the five rooms since they were not satisfied with some of these
rooms and they have left off these from the list. Assuming that there preferences can be quantified by
numbers, find out as to which manager should be assigned to which rooms so that their total
preference ranking is a minimum.
9. Imagine yourself to be the Executive Director of a 5 star hotel. Hotel has four banquet halls. During
a heavy marriage season, 4 parties approached you to reserve a hall on the same day. These parties
were told that the first choice among these halls will cost Rs 10000. they were also told to list the
preferences for second, third and fourth. Party A & D are not interested in 3 & 4. other particulars are:
Revenue/ Hall
Hall
Marriage 1 2 3 4
Party
A 10000 9000 -- --
B 8000 10000 8000 5000
C 7000 10000 6000 8000
D 10000 8000 -- --
Decide on an allocation that will maximize the revenue to your hotel.
Punjab College of Technical Education, Ludhiana (Baddowal)
Class: M.B.A 3rd Semester
Assignment: 3 (Transportation Model)
Qno.1 P Iron & steel company has three open furnaces and five rolling mills. Transportation costs
(Rs. Per quintal) for transporting steel for furnaces to rolling mills are shown in the following table.
Mills
Furnaces M1 M2 M3 M4 M5 Capacity

10. F1 4 2 3 2 6 8
F2 5 4 5 2 1 12
F3 6 5 4 7 3 14
Requirement 4 4 6 8 8
What is the optimal schedule?
Qno. 2 Company has four factories F1, F2, F3 and F4 manufacturing the same product. Production and
the raw material costs differ from factory to factory and are given in the following table in the first two
rows. The transportation cost from the factories to sales depot S1, S2, S3, is also given. The last two
columns in the table give the sales price and the total requirement at each depot. The production
capacity of each factory is given in the last row.
F1 F2 F3 F4 Sales Price Requirement
(per Unit)
Production cost per unit 15 18 14 13
Raw Material costs per unit 10 9 12 9
Transportation cost (per unit) 3 9 5 4 34 80
S1
1 7 4 5 32 120
S2
5 8 3 6 31 150
S3
Production capacity 10 150 50 100
Determine the most profitable production and distribution schedule and the corresponding profit.
Qno.3 Solve the Transportation problem to maximize profits & give criterion for optimality.
1 2 3 4 capacity
A 40 25 22 33 100
B 44 35 30 30 30
C 38 38 28 30 70
requirement 40 20 60 30

11. Qno. 4 The Bombay transport company has trucks available at four different sites in the following
number:
Site A-5 trucks, site B -10 trucks, Site C -7 Trucks, site D -3 Trucks.
Customer W ,X and y require trucks as shown below.
Customer W-5 trucks, Customer X -8 trucks, Customer Y -10 trucks.
Variable costs getting trucks to the customer are:
From A to W Rs. 7 to X Rs. 3 to Y Rs. 6
From B to W Rs. 4 to X Rs. 6 to Y Rs. 8
From C to W Rs. 5 to X Rs. 8 to Y Rs. 4
From D to W Rs. 8 to X Rs. 4 to Y Rs. 3
Solve the above transportation problem.
Punjab College of Technical Education, Ludhiana (Baddowal)
Class: M.B.A 3rd Semester
Assignment 4 (Game theory)
QNo.1 State the four properties which a competitive situation should have, if it is to be called a
competitive game.
QNo.2 what are the assumptions made in game theory.
QNo3 Solve the game whose payoff matrix is given:
Optimum strategy for player B
1 2 3 4 5
-2 0 0 5 3 Optimum Strategy 1
3 2 1 2 2 For player A 2
-4 -3 0 -2 6 3
5 3 -4 2 -6
4
Qno.4 Two players A & B without showing each other , put on a table a coin with head or tail up. A
wins Rs. 8 when both the coins show head and Re. 1 if both the coins show tails. B wins Rs. 3 when the
coins do not match. Given the choice of being matching player (A) or non matching player (b) which
one would you choose and what would be your strategy.
Qno.5 Solve the following game graphically:
Player B
Player A 1 3 11
8 5 2
Qno.6 Explain the
term “saddle Point” and “Dominance” used in game theory.
Qno.7 Our forces are going to bomb a major enemy position. The bombers can either attack high or
low, the low run resulting in more accurate hit. The enemy will try to intercept with fighters that can
look either high or low but not both. If the bombers avoid fighters, they destroy three targets. But if
fighters find them, none of the targets are destroyed. If the bombers fly low they destroy three extra

12. targets (because of grater accuracy), before they meet enemy fighters i.e. in addition to other targets
they may destroy.
Set up a game matrix. What advice you give to our commander and why.
Qno.7 It is game between the two players where A is maximizing player and B is minimizing Player.
Player A wins B’s coin if the two coins total is equal to odd number and losses his coin if the total of
the two coins is even. It is game of 1, 2, 5, 10, 50 Rs. Coin. Determine the payoff matrix, the best
strategies for each player and the value of game to A.
Qno.8 Solve the following game by Equal gains method.
Two countries, A and B are at war with each other. A has two ammunition dumps. The first dump is
twice as valuable as second one. B intends to attack and destroy these dumps but can attack only one
of the two. A has definite information that B will attack one of the two dumps, but which one, is not
known. A can successfully defend only one dump at a time what should be the strategy of A and B?
what is the value of game.
Punjab College of Technical Education, Ludhiana (Baddowal)
Class: M.B.A 3rd Semester
Assignment: 5
Qno.1 what is inventory Management? Briefly explain the major decision concerning
inventory.
Qno.2 you have to supply your customer 100 units of a certain product every Monday. You obtain
the product from your supplier at Rs. 60 per unit. The cost of ordering and transportation from the
supplier are Rs. 150 per order. The cost of carrying inventory is estimated at 15% per year of the cost
of product carried. Find the lot size which will minimize the cost of the system. Determine the optimal
cost.
Qno.3 A manufacturing company purchases 9000 parts of a machine for its annual requirements,
ordering one month usage at a time. Each part costs Rs. 20. The ordering cost per order is Rs. 15 and
the carrying charges are 15% of the average inventory per year. You have been asked to suggest a
more economical purchasing policy for the company. What advice would you offer and how much it
save the company per year.
Qno.4 Given the following data for an item of uniform demand, Instantaneous delivery time and
back order facility: Annual demand = 800 units, Cost of an item =Rs. 40 Ordering Cost = Rs. 800
Inventory cost is = 40% Back order cost = Rs. 10.
• Find Minimum cost order quantity
• Maximum Inventory level
• Maximum No. of back orders
• Time between the orders
• Total annual Cost.
Qno. 5 The cost of a machine is Rs. 6100 and its scrap value is only Rs. 100. The maintenance costs
are found from experience to be:
Year Maintenance
Cost
1 100
2 250

13. 3 400
4 600
5 900
6 1250
7 1600
8 2000
When should machine be replaced?
Qno.6. a) Machine A costs Rs. 9000. Annual operating cost is Rs. 200 for the first year, and then
increase by Rs. 2000 every year i.e in the fourth year operating cost becomes rs. 62000. Determine the
best age at which to replace the machine. If the optimum replacement policy is followed, what will be
the average yearly cost of owning and operating the machine? (Assume that machine has no scrap
value.
b) Machine b costs Rs. 10000. Annual operating cost is Rs. 400for the first year and then increased by
Rs. 800 every year. You have own a machine of A type which is one year old. Should have replace
with B and if so when?
Presentation Topics:
• BSNL: Past Perfect, Future Tense
• The Euro: In danger of collapse
• Food Price Inflation: Threat to India
• Commodities ETFs and Emerging Markets
• India’s Fiscal deficit: A cause of concern
• Indian political history
Other topics will be based on latest business news.