Module 1 (8 hours)
Linear Programming: Graphical method for solving LP problems in two variables. Feasible region and optimal solution.
Canonical and standard forms of linear programming problems. Simplex method, special cases: Unbounded solutions, infeasibility, degeneracy.
Duality in linear programming: Dual problems and their properties. Economic interpretation of the dual variables.

Module 2 (8 Hours)
Sensitivity Analysis and Duality Theory: Sensitivity Analysis: Changes in Objective Function Coefficients and Constraint Coefficients.
The role of shadow prices in resource allocation. Duality theory: Relationship between primal and dual solutions. Theorems and economic implications of duality. Practical applications of sensitivity analysis in business decisions.

Module 3: (8 Hours)
Network Optimization Models Introduction to network models: Nodes, arcs, and flows. Shortest path problems: Dijkstra’s and Bellman-Ford algorithms. Maximum flow problems: Ford-Fulkerson algorithm and applications. Minimum cost network flow problems: Simplex-based methods for network problems. Applications in transportation, telecommunications, and logistics.

Module 4 (6 Hours)
Decision Analysis and Decision Trees: Decision-making under uncertainty: Types of decisions (e.g., risk, uncertainty, certainty).
Decision tree analysis: Constructing and solving decision trees. Expected value, expected utility, and risk analysis.
Real-world applications in project management, investments, and market research. Sensitivity analysis in decision trees.

Module 5 (6 Hours)
Inventory Management Models: Introduction to inventory management in operations research. Economic Order Quantity (EOQ) model: Basic assumptions and solution. Reorder point, safety stock, and service levels. Multi-item inventory models and applications. Models with stochastic demand: the newsvendor model and continuous review and periodic review policies.

Understand key operations research methods and their applications.

Solve linear programming problems and interpret their solutions.

Apply decision analysis and network optimization techniques.

Understand and apply concepts related to inventory management, queuing, and project scheduling.

CO1: Students will be able to analyze and translate complex real-world problems in areas such as manufacturing, transportation, finance, and healthcare into mathematical models.
CO2: Identifying key decision variables, constraints, and objective functions.
CO3: Applying optimization and decision analysis in financial portfolio management, risk assessment, and strategic investments.
CO4: Optimizing production processes, supply chains, and inventories.
CO5: Students will be able to apply network optimization techniques to solve problems related to transportation, flow, and logistics.

H. A. Taha, Operations Research: An Introduction, Pearson Education Limited, 2011

Wolsey, L.A., introduction to Mathematical Programming, Pearson

W. L.Winston, Operation Research, Thomson Learning EMEA, Limited, 1998

S. Hillier and G. J. Lieberman,, Introduction to Operation Research, Tsinghua University Press, 2006.