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problems as linear programming problems (LPP) and solve them by different OR
techniques and tools
 Use of Simplex Method, Big-M Method, Dual Simplex method. Learn Duality Theory and
solution of LPP by duality theory.
 Formulate the Integer Programming, Assignment and Transportation problems models and
their solutions by different methods or algorithms.
 The basic concepts and derive results related to Queueing systems, Queueing problem, the
Poisson process, and its properties.
 The importance of the Revised Simplex Method, learn the basic concepts of the method to
solve the Linear Programming Problem and use the various Operations Research models
in solving various decision analysis problems modelled form the real-world domain using
different algorithms, OR tools and techniques.

LEARNING OUTCOMES:

After the completion of the course, students are able to
 Understand the history and applications and uses of OR techniques in decision making.
 Understand the convex set theory to find the optimal Basic feasible solution of LPP.
Modelled the real-world problems as linear programming problems (LPP) and solve them
by different OR techniques and tools
 Solve the LPP graphically, and use of Simplex Method, Big-M Method, Dual Simplex
method. Learn Duality theory and solution of LPP by duality theory.
 Formulate the Integer Programming, Assignment and Transportation problems models and
their solutions by different methods or algorithms.
 Understand the basic concepts and derive results related to Queueing systems, Queueing
problem, the Poisson process, and its properties.
 Understand the importance of the Revised Simplex Method, learn the basic concepts of the
method to solve the Linear Programming Problem and use the various Operations
Research models in solving various decision analysis problems modelled form the real-
world domain using different algorithms, OR tools and techniques.

THEORY (45 Hours)

UNIT I (15 Hours)

Brief Idea about: Introduction, origin and History of OR, Scientific Methods, Modelling in OR,
OR models, Methodology of OR, OR in Decision making, and Applications of OR. Convex sets
and their properties: convex sets, Hyperplane, and hyperspheres, Open and Close half-spaces,
Theorem on; Convex sets, Convex polyhedron, feasible, basic feasible and optimal solutions,
extreme points. Linear Programming Problem (LPP): Mathematical formulation of LPP,
Graphical solution of LPP, Simplex Method, Charnes Big M Method, Two-phase Method,
Degeneracy, Unrestricted variables, unbounded solutions, Revised Simples Method (Standard for-
I). Duality theory: Concept of duality in LPP, Dual LPP, fundamental properties of Dual
problems, Duality theorems, Complementary slackness, Advantages of Duality.
UNIT II (15 Hours)

Dual Simplex Method: computational procedure of dual Simplex Method. Integer programming
(IPP): Pure and Mixed IPP, Gomory‘s Method, Geometrical Interpretation of Cutting plane
method, Branch, and Bound Method. Transportation Problem (TP): Mathematical formulation,
Basic feasible solutions of TPs by North–West corner method, Least cost-Method, Vogel‘s
approximation method. Unbalanced TP, Optimality test of Basic Feasible Solution (BFS) by U-V
method, Degeneracy in TP. Assignment Problem (AP): Mathematical formulation, assignment

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