Unit 2081 - Operations Research and Optimization Techniques

1. Introduction to Operations Research

• History and evolution of operations research
• Scope and interdisciplinary nature
• Applications across industries: manufacturing, logistics, healthcare, finance, etc.
• Key concepts: optimization, decision-making, modeling
• Techniques and methodologies overview

2. Linear Programming (LP)

2.1 Fundamentals

• Definition and assumptions
• Components of LP models: decision variables, objective function, constraints

2.2 Model Formulation

• Translating real-world problems into LP models

2.3 Solution Methods

• Graphical solution method (for two-variable problems)
• Simplex method: algorithm and implementation

2.4 Advanced Concepts

• Duality theory and economic interpretation
• Sensitivity analysis: changes in coefficients and constraints

2.5 Applications

• Resource allocation
• Production planning

3. Integer Programming (IP)

3.1 Introduction

• Difference between LP and IP
• Types: pure, mixed-integer, binary integer programming

3.2 Applications

• Project scheduling
• Network design
• Production planning

3.3 Solution Techniques

• Branch and bound method
• Cutting plane method

4. Nonlinear Programming (NLP)

4.1 Overview

• Characteristics of nonlinear problems
• Examples of nonlinear objective functions and constraints

4.2 Solution Techniques

• Gradient-based methods: steepest descent, Newton's method
• Lagrange multipliers for constrained optimization

4.3 Applications

• Engineering design optimization
• Financial portfolio optimization
• Economic modeling

5. Network Optimization

5.1 Network Models

• Representation of networks: nodes and arcs

5.2 Algorithms

• Shortest path problem (Dijkstra's algorithm)
• Network flow models
• Maximum flow-minimum cut theorem

5.3 Project Management

• Critical path method (CPM)
• Program evaluation and review technique (PERT)

6. Inventory Management

6.1 Inventory Control Models

• Economic order quantity (EOQ) model
• Reorder point determination
• Just-in-time (JIT) inventory systems

6.2 Stochastic Inventory Models

• Demand variability considerations
• Safety stock calculation

6.3 Cost Trade-Offs

• Holding costs
• Ordering costs
• Stockout costs

7. Decision Analysis

7.1 Decision-Making Under Uncertainty

• Probabilistic models
• Decision criteria: maximin, maximax, expected value

7.2 Decision Trees

• Construction and analysis

7.3 Sensitivity Analysis and Risk Assessment

• Impact of parameter changes
• Utility theory basics

8. Simulation and Monte Carlo Methods

8.1 Simulation Modeling

• Purpose and types of simulation

8.2 Monte Carlo Simulation

• Random number generation
• Input modeling techniques

8.3 Output Analysis

• Statistical evaluation of simulation results
• Experimental design for simulations

8.4 Applications

• Complex system analysis
• Risk assessment and management

9. Game Theory

9.1 Fundamentals

• Concepts: players, strategies, payoffs

9.2 Solution Concepts

• Nash equilibrium
• Dominant strategies

9.3 Cooperative vs Non-Cooperative Games

9.4 Applications

• Economics
• Business negotiations
• Conflict resolution

10. Multi-Criteria Decision Making (MCDM)

10.1 Introduction

• Conflicting objectives in decision problems

10.2 Methods

• Analytic Hierarchy Process (AHP)
• Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)
• ELECTRE method

10.3 Applications

• Project selection
• Supplier evaluation
• Strategic planning