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QUESTION BANK ON OPERATIONS RESEARCH UNIT-1: Basics of operations research

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• Operations Research

A Model-Based Approach

• © 2010
• H. A. Eiselt 0 ,
• Carl-Louis Sandblom 1

Faculty of Business Administration, University of New Brunswick, Fredericton, Canada

You can also search for this author in PubMed   Google Scholar

Dept. Industrial Engineering, Dalhousie University, Halifax, Canada

• Covers the standard operations research techniques
• Presents an approach to operations research that is heavily based on modeling and makes extensive use of sensitivity analyses
• Emphasis is on getting insight into problems, rather than computing solutions

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Table of contents (13 chapters)

Front matter, introduction to operations research.

• H. A. Eiselt, C. -L. Sandblom

Linear Programming

Multiobjective programming, integer programming, network models, location models, project networks, machine scheduling, decision analysis, inventory models, stochastic processes and markov chains, waiting line models, back matter.

• Industrial Engineering
• Management Science
• Optimization
• Quantitative Methods
• organization
• Engineering Economics

About this book

From the reviews:

“This course resource by Eiselt … is an introduction to operations research at the undergraduate level. The book introduces a wide variety of deterministic and stochastic operations research models, including linear and integer programming, network flows, facility location problems, machine scheduling problems, inventory models, queuing models, and discrete event simulation models. … Summing Up: Recommended. Business and industrial engineering collections serving upper-division undergraduates.” (B. Borchers, Choice, Vol. 48 (3), November, 2010)

“The book gives an overview of the operations research models applied in many practical problems. … The book is a great contribution to the OR models’ application and can be a significant help to the decision makers.”­­­ (Kristina Šorić, Zentralblatt MATH, Vol. 1198, 2010)

Authors and Affiliations

H. A. Eiselt

Carl-Louis Sandblom

Bibliographic Information

Book Title : Operations Research

Book Subtitle : A Model-Based Approach

Authors : H. A. Eiselt, Carl-Louis Sandblom

DOI : https://doi.org/10.1007/978-3-642-10326-1

Publisher : Springer Berlin, Heidelberg

eBook Packages : Business and Economics , Business and Management (R0)

Copyright Information : Springer-Verlag Berlin Heidelberg 2010

eBook ISBN : 978-3-642-10326-1 Published: 17 May 2010

Edition Number : 1

Number of Pages : XII, 448

Number of Illustrations : 162 b/w illustrations

Topics : Operations Research/Decision Theory , Optimization , Engineering, general , Operations Research, Management Science , Engineering Economics, Organization, Logistics, Marketing

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TYBMS Semester 6 Operation Research (Q.P. April 2019 with Solution)

 paper/ subject code 86001/ operation research, tybms semester 6 operation research , (q.p. april 2019 with solution), 1) april 2019 q.p. with   solution (pdf) , 2) november 2019 q.p. with  solution (pdf), 4 ) april 2023 q.p. with  solution (pdf).

Please check whether you have got the right question paper.

1. All questions are compulsory. (Subject to Internal Choice)

2. Figures to the right indicate full marks

3. Use of non-programmable calculator is allowed and mobile phones are not allowed.

4. Normal distribution table is printed on the last page for reference. Support your answers with diagrams / illustrations, wherever necessary

6. Graph papers will be supplied on request.

___________________________________________________________________________

Q1.A) Multiple choice questions (Attempt Any 8)                                                  (8)

I) ln linear programming, unbounded solution means ____________. .

a) infeasible solution   b) Degenerate solution

c) Infinite solutions     d) Unique solution

  Ans:  c) Infinite solutions

Ii) if m + n-1 = number of allocations in transportation, it means _________..

(Where 'M' is number of rows and N' is number of columns)

a) There is no degeneracy       b) Problem is unbalanced

c) Problem is degenerate        d) Solution is optimal

 Ans:  a) There is no degeneracy   

Ijü) floats for critical activities will be always _________________..

a) One             b) Zero

c) Highest        d) Same ás duration of the activity

 Ans:  b) Zero

Iv) the total time required to complete all the jobs-in a job sequencing problem is known as __________,.

a) Idle time                                 b) Processing time

c)Elapsed time                        d) Processing order

 Ans:  c)Elapsed time

V) in linear programming, _____________ represents mathematical equation of the limitations imposed by the problem..

a) Objective function              b) Decision variable

c)Redundancy                         d) Constraints

Ans:    d) Constraints

Vi) if in an assignment problem, number of rows is not equal to number of columns then ____________..

a) Problem is degenerate                                    b) Problem is ‘unbalanced

c) It is a maximization problem                      d) Optimal solution is not possible

Ans:    b ) Problem is ‘unbalanced

 vii) the maximum time in which an activity will be completed assuming all possible delays and postponements is termed as __________..

a) Optimistic time                   b) Most likely time

c) Pessimistic time                  d) Expected time

Ans:  c) Pessimistic time

Viii) the various alternatives or courses of actions available to each player in a game are called as __________..

a) Saddle points                      b) Strategies

c) Pay off                                d) 'n' player game

Ans:  b) Strategies

Ix) in simplex, a maximization problem is optimal when all delta j, i.e., cj-zj values are.

a) Either zero or positive                       b) Either zero or negative

c) Only positive                                  d) Only negative

Ans:     b) Either zero or negative

X) which of the following considers difference between two least costs for each row and column while finding initial basic feasible solution in transportation.

a) North west corner rule                    b) Least cost method

c) Vogel's Approximation method       d) Row minima method

Ans:    b) Least cost method

Q1.B) True or false (Attempt Any 7)                                               (7)

i) Probability of a project completing in its expected time (Te) will be always 100%

Ii) lf saddle point is available in a game, it is called as pure strategy game., iii) slack represents unutilized resources., iv) if in a transportation problem, number of rows is not equal to number of columns, then the problem is unbalanced., v) lf we introduce an unnecessary dummy activity, the error is termed as redundancy., vi) job sequencing problems are solved to ensure that, both, the total time to complete all jobs and idle time of each machine are maximum., vii) when more than one optimal solution is possible in a linear programming problem, it is termed as 'unique solution'., viii) regret matrix is made to convert a maximization problem into minimization problem in assignment., ix) critical path method (cpm) considers the three-time estimates: most likely, optimistic and pessimistic time estimates., x) in solving a job sequencing problem, it is assumed that all jobs require the same sequence of operations., q.2 a) a company produces 2 products a and b: x 1 and x 2 , are the quantities manufactured of products a and b respectively. the following objective function along with constraints is given to you: .

Max Z = 8x 1 + 16x 2 ,

Subject to constraints:

x 1 + x 2 < 200

x 2 < 125

x 1 + 2x 2 < 300

x 1 , x 2 > 0

Find how many units of Product A and Product B should be produced by the company so that the profit is maximized. Ls it a case of multiple optimal solutions? Use graphical method to solve the LPP.

Video solution.

x 1 + x 2 < 200   ---- (i)

x 2 < 125           ---- (ii)

x 1 + 2x 2 < 300 ---- (iii)

x 1 , x 2 > 0  

x 1 + x 2 = 200

Let X 1 = 0

0 + x 2 = 200

Therefore x 2 = 200                  (x 1 , x 2 ) = (0, 200)

Let X 2 = 0

 x 1 + 0 = 200

Therefore x 1 = 200                      (x 1 , x 2 ) = (200, 0)

  x 2 < 125    ---- (ii)

Let x 2 = 0

x 2 = 125                 (x 1 , x 2 ) = (0, 125)

x 1 + 2x 2 < 300     ---- (iii)

x 1 + 2x 2 = 300

Let x 1 = 0

 0 + 2x 2 = 300

            x 2 = 300 / 2                             Therefore x 2 = 150             (x 1 , x 2 ) = (0, 150)

x 1 + 2x 2 = 300 Let x 2 = 0 x 1 + 2(0) = 300 x 1 = 300                     (x 1 , x 2 ) = (300, 0)

Corner Point Method:

Optimal Profit Maximization is Rs. 2,400

Q2.b) you are given the per unit cost of transporting goods from 3 factories to 4 customers. the 3 factories a b and c have capacity to supply 500,300 and 200 units respectively. the 4 customers p, q, r and s require 180,150,350 and 320 units respectively., i) you are required to find the initial basic feasible solution using vogel's approximation method                                                                                                                 (5) ii) find the total cost of transportation schedule obtained using vam          (2).

Total Demand = 1000

Total Supply = 1000

Total Demand = Total Supply

Cost data is given

Minimization Problem

RIM Condition:

M + N – 1 = No. of Allocation

3 + 4 – 1 = 6

Therefore, RIM Condition is satisfied.

Optimal Solution is Non-Degeneracy

(ii) Total Cost of Transportation :

            = (150 x 10) + (230 x 12) + (120 x 13) + (180 x 7) + (120 x 8) + (200 x 7)

            = Rs. 9, 440

Q.2 C) You are given the following details for a project consisting of 8 activities:

(i) Draw the network diagram and identify the critical path.                    (3) (ii) Find earliest start time, earliest finish time, latest start time and latest finish time for each activity.                                                                                                      (4) (iii) Find free float for activity B.                                                              (1)

  Solution:    [Video Explanation ]

(i)                  Network Diagram

Paths in Network:

(1) A-E-F = 4 + 20 + 10 = 34 days

(2) A-D-G = 4 + 5 + 6 = 15 days

(3) B-G = 6 + 6 = 12 days

(4) C- H = 13 + 16 = 29

Projection Completion Time : 34 days

(ii)               Free Float for Activity B:

= Ej – Ei – t

= 9 – 0 – 6

= 15  

Q.2 D) There are 6 jobs to be performed in a factory and each would go through 2 machines A and B in the order AB. The processing time (in hours) is given for each job in each machine.

(i) determine the sequence of performing the jobs that would minimize the total time of completing all the jobs:                                                                                 (2) (ii) find the elapsed time.                                                                               (3) (iii) find idle time for both the machines.                                                    (2).

Solution :    [Video Explanation ]

(i)                  Optimal Sequence

A                                                                                                                           B

(ii)                 Elapsed Time Calculation :

  Total Min. Elapsed Time = 36 Hrs.

(iii)            Idle time for Machinery A    = 36 – 35 = 1 Hrs

Idle time for Machinery A    = 36 – 28 = 8 Hrs

Q.3. B) You are given the following details for a project with 8 activities.

(i) Draw the network diagram.                                                                                     (3)

(ii) Find the expected time of project completion along with standard deviation.       (2)

(iii) What is the probability of the project completing in 55 days?                               (2)

Ans:    [Video Explanation]

Network Diagram:

Paths in the Network:

1)       1-2-3-5-7-8  = 47 days

2)       1-2-4-6-7-8 = 33 days

Expected Project Completion Time : 47 days

Variance of critical path = 16/36 + 100/36 + 256/36 + 64/36 + 4/36 = 440/36 =12.22

SD of critical path = √variance

SD = √ 12.22   = 3.495                        = 3.5 days

Time = 55 days = te

Z = t – CP / SD

= 55 – 47 / 3.5 = 2.29 

Table value = 0.4890

P(55 days) = 0.5 + 0.4890      = 0.9890                      = 98.90% 

Q.3. C) You are given information about the cost (in Rs. Thousands) of performing different jobs by different persons. PI cannot perform J3. P3 cannot perform J4

(i)Obtain optimal assignmnt and find cost of such assignment.

(i)Is it a case of alternative optimal solution?

Ans:      [Video Explanation]

Prohibited Assignment = X (infinity)

The problem is unbalanced.

Taking P5 as Dummy

Cost is given.

Hence Minimization Problem.

Row Minimization

Column Minimization Not Required.

Min. No. of Lines = 4

Size of Matrix = 5 x 5

Therefore Not optimal

Change = Min. open Value = 4

Optimal Cost = 66,000

Q3.D) Two firms, Lacko textiles and Rayon textiles have 3 strategies each to select from. The 3 strategies are no advertisement, using moderate advertising and using heavy advertising. You are given the pay off matrix from view point of Lacko textiles, showing its market share under several combinations of strategies:

(    (i) Find the saddle point and value of game.      (ii) Comment on the strategy to be selected by both the companies.

Value of the Game = 50 x 10000 =     5,00,000

Q. 4 a) you are given a solution for a transportation cost problem. figures in each cell represent per unit transportation cost. figures in circle within each cell represent number of units allocated for transportation. x, y and z. are the 3 factories and a, b, c and d are the 4 customers..

(i) You are required to check the above solution for optimality.

(ii) If it is not optimal, use modified distribution method to obtain optimal solution.

(iii) Find optimal transportation cost.

Ans:  [Video Explanation]

No negative ∆, Hence Optimal Solution.

(iii) Optimal transportation Cost:

= (200 x 7) + (120 x 18) + (100 x 15) + (280 x 7) + (180 x 11) + (12 x 5)

= RS. 9,600

B) You are given the following information, for a project with 8 activities:

The cost of completing the eight activities in normal time is Rs.6,500.

Indirect cost is Rs 160 per day. The contract includes a penalty of Rs. 100 per day for every day of delay more than 17 days.

  (i)   Draw the network diagram and find critical path.

(i     (ii)  Crash the projèct duration to find the total 'cost of completing the project in 17 days (4)

  Ans:  [Video Explanation]

Q.4. C) A company produces 2 products x and xX) using three resources S1, S2 and S. Product x1 gives profit of Rs.30 per unit and product x2 gives profít of Rs.40 per unit. The 3 resources Si. S and S; are available to the extent of 200 units, 600 units and 500 units respectiveiy The following objective function and constraints are given to you:

Max Z = 30x1 + 40x2

Subject to constraints;

x 1 + 2x 2 < 200

8x 1 + 5x 2 < 600

3x 1 + 4x 2 < 500

X1 >0; x2 >0

You are given the following simplex solution to the above problem:

  A) With reference to the above table answer the following:

i) Check if the above solution is optimal or not.

ii) lf it is not optimal, find optimal solution.

B) With reference to the optimal simplex table in the above problem obtained by you, answer the following:

iii) Find the optimal product mix and optimal profit

iv) Which resources are scarce and which are, unutilized?

v) Is it a case of alternative solution? Justify your answer

vi) What are the shadow prices of the resources? Justify

Ans:       [Video Explanation]

Testing the given solution for optimality ;

Positive ∆

Hence, solution not optimal.

(ii) Revising the Solution for Optimality:

No positive ∆

Therefore, Optimal Solution

(iii) Optimal Product Mix;

No. of units of X1 = 200/11        = 18.18

No. of units of X1 = 1000/11      = 90.90

Optimal Profit:

Max Z = [30 x 200/11] + [40 x 1000/11]

          = Rs. 46,000 /11

          = Rs. 4,181.81

(iv) Abundant Resource:

S3 = 900/11 ----- in optimal solution

Therefore Unutilized Capacity of S3 = 900 / 11

S3 is Abundant resource.

S1 and S2 are non-basis variable in optimal solution.

 Unutilized Capacity of S1 and S2 are 0

(i)                 ∆ of non basis variable :

∆ of S1 = - 170 / 11

∆ of S2 = -20/11

No zero ∆ value.

Hence, this is a case of Unique Solution.

There is no alternate optimal solution.

(ii)              Zj value of slack variables:

Q.5 A) Explain the concepts : Total float, free float, Independent float and Interfering float.           (8) 

(a) Total float:

lt is the amount of time by which the completion of an activity can be delayed beyond the earliest possible finishing time without affecting total project completion time.

 Total Float = (LST - EST) or (LFT - EFT)

.:: Total float = LST - EST -[;-t]-E Total Float = [Lj- E -t

(b) Free float:  It is the amount of time by which the completion of an activity can be delayed beyond the earliest finishing time without affecting the earliest possible start of a subsequent activity.

Free float = Earliest starting time of subsequent activity - Earliest finishing time of activity ij = Ej- [E, + t;] . Free Float = Ej- E-tj

(c) Independent float:  It is the amount of time by which the start of an activity can be delayed without affecting the earliest start of a subsequent activity, assuming that the preceding activity has finished at its latest finishing time. .

:. Independent float = Earliest starting time of subsequent activity - Latest finishing time of preceding activity - ij

:. Independent Float = [Ej-Li]-tij;

(d) Interfering float:  It is that part of total float which reduces the float of a subsequent activity. It is the amount of time by which the earliest possible start of a subsequent activity will be delayed if activity ÷ finishes on latest finishing time.

:. Interfering float = Latest finishing time of activity ij - Earliest starting time of subsequent activity. :. Interfering Float= Lj-Ej

B) Discuss any 5 areas where techniques of operation Research can be applied.    (7) 

OR techniques are applied to a variety of business problems. Some examples are:

(A) Production management:

(1) To calculate loss of time due to waiting time, queuing time etc.

(2) To decide optimum allocation of jobs and optimum sequence in which jobs should be sequenced.

(B) Personnel management:

(1) To study labour turnover. (2) To do human resource planning. (3) To decide number of personnel required to be kept on standby in case of demand for higher manpower.

(C) Inventory management: (1) To study economic lot size to be ordered.

(D) Marketing management: (1) To decide optimal product mix for maximum profit. (2) Media selection for advertising for maximum reach. (3) Sales forecasting.

(E) Transportation management: (1) To determine transportation schedule for minimum cost or minimum time.

(F) Project management (1) To identify critical and non-critical activities of a project (2) To determine minimum project completion time. (3) To determine optimal project cost.

(G) Financial management: project. (1) To decide investment portfolio to maximize return on investment. of such nature that it is impossible to find a feasible solution that can satis1y a the constraints. 

c) Answer any 3 of the following :            (15) 

I) explain the terms: redundant constraints and infeasible solution in linear programming. .

Ans:  A redundant constraint is the one which does not affect the optimal solution. Even if that constraint is not considered, we can still obtain the solution to the problem. Since the constraint is not required for obtaining the optimal solution, it is called redundant constraint cost.

Following sketch explains redundancy (redundant constraint):

There is no common feasible region for line AB and line CD

Hence, solution is infeasible.

A redundarnt constraint is the one which does not affect the optimal solution. Even if that constraint is not considered, we can still obtain the solution to the problem. Since the constraint is not required for obtaining the optimal solution, it is called redundant constraint. cost.

The feasible region for the above problem is OABC. The 3rd constraint does not affect the feasible region. Hence, the constraint [X1 S 16] is redundant constraint.

ii) what do you means by alternative optimal solution in transportation? How do you find that alternative solution? 

Alternate optimal solution or multiple optimal solutions mean there are two sets of solutions which provide the same optimal cost or optimal profit:

(a) In the optimal solution to a transportation problem, if there is an empty cell with zero A value, it means there is alternate optimal solution.

(b) To find alternate optimal solution, we should construct a closed loop from the empty cell with zero A. The new table we obtain after looping is the alternate optimal solution.

iii) Explain the time coat trade off in project crashing. 

The execution of a project involves two types of costs, direct cost and indirect cost.

(a) Direct costs: These include costs of materials, machinery, tools, manhours etc. When we estimate the duration of various activities in the project, it is assumed that normal amount of labour (manhours) & machines will be required to complete these activities. The estimation of direct costs is done based on the normal amount of resource required. This estimation gives us minimum possible direct cost required to complete the project. When we want to complete the project in a shorter period than critical path, we will need to employ more resources. Hence, direct cost will increase.

(b) Indirect costs: These include rent, overheads, administrative costs etc. Indirect costs vary with time. They are expressed on per day (or per week etc.) basis. Hence, when we shorten the project completion time, total indirect cost reduces.

Total P'roject Cost = Direct Cost + Indirect Cost

iV) Discuss the signification of theory of game. Briefly discuss the terms. Player and pay off.

Ans: Every one business party. The situation (also called competitive situation) involves more parties involved could be corporate. individuals, small firms or A number of outcome alternatives are available to each party for decision making. The (i.e. profit or loss) of the business decision does not depend on the alternative selected by one party alone, but on the interaction between the decisions of all the parties involved in the situation. Each party will try to select the alternative which maximizes gains for it, at the cost of its competitors. "Games Theory" deals with such business situations or problems where multiple parties are involved in the conflict through interaction of their alternatives or decisions.

Players: The various participants or decision markers in the game are called "Players". A game must have minimum two players (or competitors). A game having two competitors opposing each other is called 'two person game' and a game having more than 2 players is called 'n-person game'.

Payoff: Payoff is the outcome of the interaction of selected strategies of opponents in the game. Positive payoff is gain and negative payoff is loss. In a 'two person game', when one party gains, the other party loses.

v) Distinguished between PERT and CPM. 

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Operation Research Notes | PDF, Syllabus | MBA, B Tech 2024

• Post last modified: 5 April 2022
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Download Operation Research Notes , books, syllabus PDF for MBA, BBA, B.COM 2024. We provide complete operation research pdf . Business law lecture notes include operation research notes , operation research book, courses, case study, syllabus , question paper, MCQ, questions and answers and available in operation research pdf form.

Operation Research subject is included in MBA 1st semester subjects, business legislation MBA notes, Operation Research B Tech Notes, BBCOM 1st sem subjects and operation research BBA notes. So students can able to download operation research notes for MBA 1st sem pdf

Table of Content

• 1 Operation Research Syllabus
• 2 Operating Systems PDF
• 3 Operation Research Note
• 4 Operation Research Questions and Answers
• 5 Operation Research Question Paper
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Operation research Notes can be downloaded in operation research pdf from the below article.

Operation Research Syllabus

A detailed Operation Research Syllabus as prescribed by various Universities and colleges in India are as under. You can download the syllabus in operation research pdf form.

Unit 1 – Introduction to Operations Research: Introduction, Historical Background, Scope of Operations Research, Features of Operations Research, Phases of Operations Research, Types of Operations Research Models, Operations Research Methodology, Operations Research Techniques and Tools, Structure of the Mathematical Model, Limitations of Operations Research

Unit 2 – Linear Programming: Introduction, Linear Programming Problem, Requirements of LPP, Mathematical Formulation of LPP,    Case Studies of LPP, Graphical Methods to Solve Linear Programming Problems, Applications, Advantages, Limitations

Unit 3 – Graphical Analysis of Linear Programming Problems: Introduction, Graphical Analysis, Some Basic Definitions, Graphical Methods to Solve LPP, Some Exceptional Cases, Important Geometric Properties of LPP

Unit 4 – Simplex Method: Introduction, Standard Form of LPP, Fundamental theorem of LPP, Solution of LPP – Simplex Method, The Simplex Algorithm, Penalty Cost Method or Big M-method, Two-Phase Method, Solved Problems on Minimisation

Unit 5   -Duality in Linear Programming Problem: Introduction, Importance of Duality Concepts, Formulation of Dual Problem, Economic Interpretation of Duality, Sensitivity Analysis

Unit 6   -Transportation Problem: Introduction, Formulation of Transportation Problem (TP), Transportation Algorithm (MODI Method), the Initial Basic Feasible Solution, Moving Towards Optimality

Unit 7 – Assignment Problem: Introduction, Mathematical Formulation of the Problem, Hungarian Method Algorithm, Routing Problem, Travelling Salesman Problem

Unit 8 – Integer Programming Problem: Introduction, Types of Integer Programming Problems, Gomory’s All-IPP Method, All IPP Algorithm, Branch and Bound Technique

Unit 9   -Infinite Queuing Models: Introduction, Queuing Theory, Operating Characteristics of a Queuing System, Constituents of a Queuing System, Service Facility, Queue Discipline

Unit 10 -Mathematical Analysis of Queuing Theory: Introduction, Mathematical Analysis of Queuing Process, Properties of Queuing System, Notations, Service System, Single Channel Models, Multiple Service Channels, Erlang Family of Distribution of Service Times, Applications of Queuing Theory, Limitations of Queuing Theory

Unit 11 – Finite Queuing Models: Introduction, Finite Queuing Models

Unit 12 – Simulation: Introduction, Methodology of Simulation, Basic Concepts, Simulation Procedure, Application of Simulation

Unit 13 – Simulation Monte-Carlo Method: Introduction, Monte-Carlo Simulation, Applications of Simulation, Advantages of Simulation, Limitations of Simulation

Unit 14 – Project Scheduling and PERT-CPM: Introduction, Basic Difference between PERT and CPM, PERT/CPM Network Components and Precedence Relationship, Project Management – PERT

Unit 15 – Game Theory: Introduction, Competitive Situations, Characteristics of Competitive Games, Maximin – Minimax Principle, Dominance

Operating Systems PDF

Operation research note.

What is Operation Research?

Operations research (British English: operational research) (OR) is a discipline that deals with the application of advanced analytical methods to help make better decisions.

Further, the term operational analysis is used in the British (and some British Commonwealth) military as an intrinsic part of capability development, management and assurance. In particular, operational analysis forms part of the Combined Operational Effectiveness and Investment Appraisals, which support British defence capability acquisition decision-making.

Operation Research Questions and Answers

Some of the operation research questions and answers are mentioned below. You can download the QnA in operation research pdf form.

• Define Operations Research.
• What are the assumptions of LPP?
• What is Degeneracy in Transportation?
• Define prohibited assignment problems.
• Illustrate Saddle point.
• What is sequencing problem?
• Define the concept of EOQ.
• Differentiate between PERT and CPM.
• How to compute Re-order level of inventory?
• What is Duality?

Operation Research Question Paper

If you have already studied the operation research notes, then its time to move ahead and go through previous year operation research question paper.

It will help you to understand question paper pattern and type of operation research questions and answers asked in MBA, BBA, BCom operation research exam. You can download the syllabus in operation research pdf form.

Operation Research Book

Below is the list of operation Research Book recommended by the top university in India.

• Hamdy A Taha, 1999. Introduction to Operations Research, PHI Limited, New Delhi.
• Sharma, J.K., 1989. Mathematical Models in Operations Research, TMH
• Beer, Stafford, 1966. Decision and Control, John Wiley & Sons, New York.
• Levin, Rubin, Stinson, Gardner, 1992. Quantitative Approaches to Management, TMH
• Wagner, Harvery M., 1975. Principles of Operations Research, PHI, Egnlewood Cliffs, N.J.

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