Syllabus - Operations Research (CB-406)

Computer Science and Business System (CSBS)

Operations Research (CB-406)

IV

Unit 1

Introduction to OR

Origin of OR and its definition. Concept of optimizing performance measure, Types of OR problems,Deterministic vs. Stochastic optimization, Phases of OR problem approach – problem formulation,building mathematical model, deriving solutions, validating model, controlling and implementingsolution.

Unit 2

Linear Programming

Linear programming – Examples from industrial cases, formulation & definitions, Matrix form. Implicit assumptions of LPP. Some concepts of linear algebra – Vectors, Matrices, LinearIndependence/Dependence of vectors, Rank, Basis, System of linear eqns., Hyperplane, Convex set,Convex polyhedron, Extreme points, Basic feasible solutions. Geometric method: 2-variable case, Special cases – infeasibility, unboundedness, redundancy &degeneracy, Sensitivity analysis. Simplex Algorithm – slack, surplus & artificial variables, computational details, big-M method,identification and resolution of special cases through simplex iterations. Duality – formulation, results, fundamental theorem of duality, dual-simplex and primal-dualalgorithms.

Unit 3

Transportation and Assignment problems

TP - Examples, Definitions – decision variables, supply & demand constraints, formulation, Balanced & unbalanced situations, Solution methods – NWCR, minimum cost and VAM, test for optimality(MODI method), degeneracy and its resolution. AP - Examples, Definitions – decision variables, constraints, formulation, Balanced &unbalanced situations, Solution method – Hungarian, test for optimality (MODI method), degeneracy & its resolution.

Unit 4

PERT – CPM

Project definition, Project scheduling techniques – Gantt chart, PERT & CPM, Determination ofcritical paths, Estimation of Project time and its variance in PERT using statistical principles, Conceptof project crashing/time-cost trade-off.

Unit 5

Inventory Control

Functions of inventory and its disadvantages, ABC analysis, Concept of inventory costs, Basics ofinventory policy (order, lead time, types), Fixed order-quantity models – EOQ, POQ &Quantitydiscount models. EOQ models for discrete units, sensitivity analysis and Robustness, Special cases ofEOQ models for safety stock with known/unknown stock out situations, models under prescribedpolicy, Probabilistic situations.

Unit 6

Queuing Theory

Definitions – queue (waiting line), waiting costs, characteristics (arrival, queue, servicediscipline) ofqueuing system, queue types (channel vs. phase). Kendall’s notation, Little’s law, steady state behaviour, Poisson’s Process & queue, Models with examples - M/M/1 and its performance measures; M/M/m and its performance measures; briefdescription aboutsome special models.

Unit 7

Simulation Methodology

Definition and steps of simulation, random number, random number generator, DiscreteEventSystem Simulation – clock, event list, Application in Scheduling, Queuing systems andInventory systems.

Course Objective

None

Course Outcome

None

Practicals

  • Formulation of linear programming problems.

    None

  • Solution of linear programming problem using graphical method with: i. Multiple constraints ii. Unbounded solution iii. Alternative or multiple solution Infeasible solution

    None

  • Enumeration of all basic solutions for linear programming problem.

    None

  • Solution of linear programming problem with simplex method.

    None

  • Problem solving using Big M method.

    None

  • Problem solving using two phase method.

    None

  • Solution on primal problem as well as dual problem.

    None

  • Solution based on dual simplex method.

    None

  • Verification of weak duality, strong duality and complementary slackness property.

    None

  • Solution of transportation problem.

    None

  • Solution of assignment problem.

    None

  • Solution of integer programming problem using Branch and Bound method.

    None

  • Solution of integer programming problem using Gomory’s cutting plane method.

    None

  • Simulation: Random number generation.

    None

  • Monte Carlo method.

    None

  • Performance measures for M/M/1 queuing model.

    None

  • ABC analysis.

    None

  • Inventory model.

    None

Reference Books

  • Operations Research: An Introduction.H.A. Taha.

  • Linear Programming. K.G. Murthy.

  • Linear Programming. G. Hadley.

  • Principles of OR with Application to Managerial Decisions. H.M. Wagner.

  • Introduction to Operations Research. F.S. Hiller and G.J. Lieberman.

  • Elements of Queuing Theory. Thomas L. Saaty.

  • Operations Research and Management Science, Hand Book: Edited By A. Ravi Ravindran.

  • Management Guide to PERT/CPM. Wiest& Levy.

  • Modern Inventory Management. J.W. Prichard and R.H. Eagle.