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Home / Syllabus / Bachelor of Management Studies (B.M.S.) / TY BMS / Semester 6 / Operation Research

Bachelor of Management Studies (B.M.S.) Operation Research Syllabus - Mumbai University

This is the TY BMS syllabus under NEP 2020, in force from the academic year 2026-27, examined under form 2225161. The University still sets the earlier Choice Based papers alongside it — forms 2M00155 and 2M00156, whose documents are below — so check which scheme your exam form names before you revise.

Operation Research Syllabus.pdf
Major · Semester 6 · TY BMS · 4 credits · 100 marks

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Syllabus for Operation Research

Major · Semester 6 · TY BMS · 4 credits · 100 marks

MU heads this block “Operation Research”. Its own programme structure table in the same circular, and the University’s exam timetable, both call it Operations Research.

Module I: Introduction to Operations Research and Linear Programming

  • Introduction To Operations Research
  • Operations Research - Definition, Characteristics of OR, Models, OR Techniques, Areas of Application, Limitations of OR.
  • Linear Programming Problems: Introduction and Formulation
  • Introduction to Linear Programming
  • Applications of LP
  • Components of LP
  • Requirements for Formulation of LP Problem
  • Assumptions Underlying Linear Programming
  • Steps in Solving LP Problems
  • LPP Formulation (Decision Variables, Objective Function, Constraints, Non Negativity Constraints)
  • Linear Programming Problems: Graphical Method
  • Maximization & Minimization Type Problems. (Max. Z & Min. Z)
  • Two Decision Variables and Maximum Three Constraints Problem
  • Constraints can be “less than or equal to”, “greater than or equal to” or a combination of both the types i.e. mixed constraints.
  • Concepts: Feasible Region of Solution, Unbounded Solution, Redundant Constraint, Infeasible Solution, Alternative Optima.
  • Linear Programming Problems: Simplex Method • Only Maximization Type Problems. (Only Max. Z). No Minimization problems. (No Min. Z)
  • Two or Three Decision Variables and Maximum Three Constraints Problem. (Up to Maximum Two Iterations)
  • All Constraints to be “less than or equal to” Constraints. (“Greater than or Equal to” Constraints not included.)
  • Concepts : Slack Variables, Surplus Variables, Artificial Variables, Duality, Product Mix and Profit, Feasible and Infeasible Solution, Unique or Alternate Optimal Solution, Degeneracy, Non Degenerate, Shadow Prices of Resources, Scarce and Abundant Resources, Utilized and Unutilized Capacity of Resources, Percentage Utilization of Resources, Decision for Introduction of a New Product.
  • Note:
  • Surplus Variable, Artificial Variable and Duality to be covered only at Conceptual level for Theory Questions only and not included in Numerical.
  • Sensitivity Analysis including Profit Range and Capacity Range is not included.

Module II: Assignment and Transportation Models

  • Assignment Problem – Hungarian Method
  • Maximization & Minimization Type Problems.
  • Balanced and Unbalanced Problems.
  • Prohibited Assignment Problems, Unique or Multiple Optimal Solutions.
  • Simple Formulation of Assignment Problems.
  • Maximum 5 x 5 Matrix. Up to Maximum Two Iterations after Row and Column Minimization.
  • Note:
  • Travelling Salesman Assignment Problem is not included.
  • Transportation Problems
  • Maximization & Minimization Type Problems.
  • Balanced and Unbalanced problems.
  • Prohibited Transportation Problems, Unique or Multiple Optimal Solutions.
  • Simple Formulation of Transportation Problems.
  • Initial Feasible Solution (IFS) by: a. North West Corner Rule (NWCR) b. Least Cost Method (LCM) c. Vogel’s Approximation Method (VAM)
  • Maximum 5 x 5 Transportation Matrix.
  • Finding Optimal Solution by Modified Distribution (MODI) Method. (u, v and ∆)
  • Maximum Two Iterations (i.e. Maximum Two Loops) after IFS.
  • Note:
  • Production Scheduling Problem is not included.
  • Time Minimization Problem is not included.
  • Degeneracy Concept to be covered only at Conceptual Level. Not to be included in Numerical.

Module III: Network Analysis

  • Critical Path Method (CPM)
  • Concepts: Activity, Event, Network Diagram, Merge Event, Burst Event, Concurrent and Burst Activity,
  • Construction of a Network Diagram. Node Relationship and Precedence Relationship.
  • Principles of Constructing Network Diagram.
  • Use of Dummy Activity • Numerical Consisting of Maximum Ten ( 10) Activities.
  • Critical Path, Sub-critical Path, Critical and Non-critical Activities, Project Completion Time.
  • Forward Pass and Backward Pass Methods.
  • Calculation of EST, EFT, LST, LFT, Head Event Slack, Tail Event Slack, Total Float, Free Float, Independent Float and Interfering Float
  • Project Crashing
  • Meaning of Project Crashing.
  • Concepts: Normal Time, Normal Cost, Crash Time, Crash Cost of Activities. Cost Slope of an Activity.
  • Costs involved in Project Crashing: Direct, Indirect, Penalty and Total Costs.
  • Time – Cost Trade off in Project Crashing.
  • Optimal (Minimum) Project Cost and Optimal Project Completion Time.
  • Process of Project Crashing. • Numerical Consisting of Maximum Ten (10) Activities.
  • Numerical based on Maximum Four (04) Iterations of Crashing
  • Program Evaluation and Review Technique (PERT)
  • Three Time Estimates of PERT: Optimistic Time (a), Most Likely Time (m) and Pessimistic Time (b).
  • Expected Time (te) of an Activity Using Three Time Estimates.
  • Difference between CPM and PERT.
  • Numerical Consisting of Maximum Ten (10) Activities.
  • Construction of PERT Network using tevalues of all Activities.
  • Mean (Expected) Project Completion Time.
  • Standard Deviation and Variance of Activities.
  • Project Variance and Project Standard Deviation.
  • ‘Prob. Z’ Formula.
  • Standard Normal Probability Table. Calculation of Probability from the Probability Table using ‘Z’ Value and Simple Questions related to PERT Technique.
  • Meaning, Objectives, Importance, Scope, RORO/LASH

Module IV: Decision Theory, Sequencing and Theory of Games

  • Decision Theory • Decision Environments – Risk & Uncertainty. Payoff Table, Regret Table
  • Decision Making under Uncertainty Maximin & Maximax Criteria Minimax Regret Criterion Laplace Criterion Hurwicz Criterion Expected Monetary Value Criterion. Expected Value of Perfect Information (E.V.P.I) Expected Opportunity Loss (E.O.L).
  • Job Sequencing Problem
  • Processing Maximum 9 Jobs through Two Machines only.
  • Processing Maximum 6 Jobs through Three Machines only.
  • Calculations of Idle Time, Elapsed Time etc.
  • Theory of Games
  • Introduction
  • Terminology of Game Theory: Players, Strategies, Play, Payoff, Payoff matrix, Maximin, Maximax, Saddle Point.
  • Types of Games.
  • Numericals based on: Two Person Zero Sum Games - Pure Strategy Games (Saddle Point available)

Reference Books

  • 1 Taha H.A., Operations Research - An Introduction, 6th Edition , Hall of India
  • 2 Kapoor V.K., Operations Research Techniques for Management, 7th Edition, Sultan Chand & Sons
  • 3 Kantiswarup, Gupta P.K. & Manmohan, Operations Research 9th Edition, Sultan Chand & Sons
  • 4 Sharma S.D.,Operations Research, 8th Edition, Kedarnath, Ramnath & Company
  • 5 Bronson R, Operations Research, 2nd Edition, Shaum's Outline Series
  • 6 Vora N.D, Quantitative Techniques in Management, 3rd Edition, Tata McGraw Hill co.
  • 7 Shreenath L.S, Principles & Application 3rd Ed,., PERT & CPM, Affiliated East-West Press Pvt. Ltd.
  • 8 Wagener H.M.,Principles of Operations Research 2nd Edition, Prentice - Hall of India
  • 9 Sasieni M, Yaspan A & John Wiley & Sons Friedman L, Operations Research - Methods & Problems 1st Edition
  • 10 NatrajanBalasubramani, Tamilarasi, Operations Research, Pearson Education
  • 11 G. Hadley, Linear Programming, Narosa Book Distributors Private Ltd
  • 12 L.C. Jhamb, Quantitative Techniques (For Managerial Decisions VOL I), Everest Publishing House, Pune.
  • 13 Paul Loomba, Linear Programming, Tata McGraw Hill Publishing Co. Ltd.
  • 14 Aditham B. Rao , Operations Research Edition 2008, Jaico Publishing House, Mumbai

Reproduced from the University of Mumbai syllabus for Bachelor of Management Studies (B.M.S.) under NEP 2020, in force from the academic year 2026-27. Wording is as printed in that syllabus. Module numbering is as printed there too.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

PDF BMS Sem I & II 2024-25 NEP (Item 7.13 R) NEP 2020 syllabus, in force from 2024-25 Read full PDF Read
PDF BMS Sem III & IV 2025-26 NEP (Item 7.8 R) NEP 2020 syllabus, in force from 2025-26 Read full PDF Read
PDF BMS Sem V & VI 2026-27 NEP (Item 8.18 N) NEP 2020 syllabus, in force from 2026-27 Read full PDF Read
PDF BMS Minor Sem V & VI 2026-27 NEP (Item 8.4 N 13) NEP 2020 syllabus, in force from 2026-27 Read full PDF Read
PDF BMS V & VI 2018 2019 Earlier Choice Based syllabus, still set for ATKT candidates Read full PDF Read
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PDF BMS V & VI 2016 17 Earlier Choice Based syllabus, still set for ATKT candidates Read full PDF Read
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