AI-Powered Learning Platform

Subject Syllabus

CB-406 - Operations Research

CSBS · Semester 4

Course Modules

Learn topic-wise with Hyper AI and revise using mapped PYQs.

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 implementing solution

Linear programming – Examples from industrial cases, formulation & definitions, Matrix form Implicit assumptions of LPP Some basic concepts and results of linear algebra – Vectors, Matrices, Linear Independence/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-dual algorithms

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

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

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

Definitions – queue (waiting line), waiting costs, characteristics (arrival, queue, service discipline) of queuing 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; brief description about some special models Definition and steps of simulation, random number, random number generator Discrete Event System Simulation – clock, event list, Application in Scheduling, Queuing systems and Inventory systems