Topic

No. of hours

Lecture

Tutorial/Practical

OR Review :-

What Is Operations Research?

Operations Research Models.

Solving the OR Model.

Queuing and Simulation Models.

Art of Modeling.

Phases of an OR Study.

3

3

-

Modeling with Linear Programming :-

Two-Variable LP Model.

GraphicallP Solution.

Solution of a Maximization Model.

Solution of a Minimization Model.

Selected lP Applications.

Urban Planning.

Currency Arbitrage.

Investment.

Production Planning and Inventory Control.

Blending and Refining.

Manpower Planning.

Additional Applications.

Computer Solution with Excel Solver and AMPL.

LP Solution with Excel Solver.

LP Solution with AMPL.

3

3

-

The Simplex Method and Sensitivity Analysis :-

LP Model in Equation Form.

Converting Inequalities into Equations.

with Nonnegative Right-Hand Side.

Dealing with Unrestricted Variables Transition from Graphical to Algebraic Solution.

The Simplex Method.

Iterative Nature of the Simplex Method.

Computational Details of the Simplex Algorithm.

Summary of the Simplex Method.

Artificial Starting Solution.

M-Method.

Two-Phase Method.

Special Cases in the Simplex Method.

Degeneracy.

Alternative Optima.

Unbounded Solution.

Infeasible Solution.

Sensitivity Analysis.

Graphical Sensitivity Analysis.

Algebraic Sensitivity Analysis-Changes in the Right-Hand Side.

Algebraic Sensitivity Analysis-Objective Function.

Sensitivity Analysis with TORA, Solver, and AMPL.

3

3

-

Duality and Post-Optimal Analysis :-

Definition of the Dual Problem.

Primal-Dual Relationships.

Review of Simple Matrix Operations.

Simplex Tableau Layout.

Optimal Dual Solution.

Simplex Tableau Computations.

Economic Interpretation of Duality.

Economic Interpretation of Dual Variables.

Economic Interpretation of Dual Constraints.

Additional Simplex Algorithms.

Dual Simplex Method.

Generalized Simplex Algorithm.

Post-Optimal Analysis.

Changes Affecting Feasibility.

Changes Affecting Optimality.

3

3

-

Transportation Model and Its Variants.

Definition of the Transportation Model.

Nontraditional Transportation Models.

The Transportation Algorithm.

Determination of the Starting Solution.

Iterative Computations of the Transportation.

Algorithm.

Simplex Method Explanation of the Method of Multipliers.

The Assignment Model.

The Hungarian Method.

Simplex Explanation of the Hungarian Method.

The Transshipment Model.

3

3

-

Advanced Linear Programming :-

Simplex Method Fundamentals.

From Extreme Points to Basic Solutions.

Generalized Simplex Tableau in Matrix Form.

Revised Simplex Method.

Development of the Optimality and Feasibility.

Conditions.

Revised Simplex Algorithm.

Bounded-Variables Algorithm.

Duality.

Matrix Definition of the Dual Problem.

Optimal Dual Solution.

Parametric linear Programming.

Parametric Changes in C.

Parametric Changes in b.

3

3

-

Integer Linear Programming :-

Illustrative Applications.

Capital Budgeting.

Set-Covering Problem.

Fixed-Charge Problem.

Either-Or and If-Then Constraints.

Computational Considerations in ILP.

Traveling Salesperson Problem (TSP).

Heuristic Algorithms.

B&B Solution Algorithm.

Cutting-Plane Algorithm.

3

3

-

Deterministic Dynamic Programming :-

Recursive Nature of Computations in DP.

Forward and Backward Recursion.

Selected DP Applications.

Knapsack/Fly-Away/Cargo-Loading Model.

Work-Force Size Model.

Equipment Replacement Model.

Investment Model..

Inventory Models.

Problem of Dimensionality.

3

3

-

Deterministic Inventory Models :-

General Inventory Model.

Role of Demand in the Development of Inventory Models.

Static Economic-Order-Quantity (EOQ) Models.

Classic EOQ model.

EOQ with Price Breaks.

Multi-Item EOQ with Storage Limitation.

Dynamic EOQ Models.

No-Setup Model.

Setup Model.

3

3

-

Review of Basic: Probability :-

laws of Probability.

Addition law of Probability.

Conditional law of Probability.

Random Variables and Probability Distributions.

Expectation of a Random Variable.

Mean and Variance (Standard Deviation) of a Random Variable.

Mean and Variance of Joint Random Variables.

Four Common Probability Distributions.

Binomial Distribution.

Poisson Distribution.

Negative Exponential Distribution.

Normal Distribution.

Empirical Distributions.

3

3

-

Decision Analysis and Games :-

Decision Making under Certainty-Analytic Hierarchy Process (AHP).

Decision Making under Risk.

3

3

-

Probabilistic: Inventory Models.

Continuous Review Models.

"Probabilitized" EOQ Model.

Probabilistic EOQ Model.

Single-Period Models.

No-Setup Model {Newsvendor Model).

Setup Model (s-5 Policy).

Multiperiod Model.

3

3

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