Operations Research

Introduction to Operations Research (OR)

Operations Research (OR) is the scientific approach to decision-making and problem-solving using mathematical, statistical, and analytical methods. Its main goal is to optimize performance, reduce costs, and improve efficiency in various fields such as industry, management, logistics, and healthcare.

Key Topics in the Course

Chapter 1: Introduction to Operations Research

  • Definition: OR is the scientific approach to decision-making and problem-solving using mathematical, statistical, and analytical methods.

  • Steps in OR Problem Solving:

    1. Problem identification

    2. Model formulation

    3. Solution of the model

    4. Validation & testing

    5. Implementation & monitoring

  • Applications: Industry, logistics, healthcare, business, military, transport.

Chapter 2: Linear Programming (LP)

  • Definition: Technique for optimizing (maximizing or minimizing) a linear objective function subject to linear constraints.

  • Components:

    • Objective function

    • Decision variables

    • Constraints

    • Non-negativity restrictions

  • Solution Methods:

    • Graphical Method (for 2 variables)

    • Simplex Method (for multiple variables)

  • Key Concepts: Feasible region, basic feasible solutions, optimal solution, infeasibility, unboundedness, alternative solutions.

Chapter 3: Transportation and Assignment Problems

  • Transportation Problem: Minimize the cost of transporting goods from sources to destinations.

  • Assignment Problem: Assign tasks to agents to minimize total cost or time.

  • Methods: North-West Corner, Least Cost, Vogel’s Approximation, Hungarian Method (for assignment).

Chapter 4: Network Models

  • Shortest Path Problem: Find the minimum distance or cost path between nodes.

  • Maximum Flow Problem: Determine the maximum flow possible from a source to a sink in a network.

  • Project Management (PERT/CPM):

    • CPM (Critical Path Method): Focuses on time optimization in deterministic projects.

    • PERT (Program Evaluation Review Technique): Handles uncertainty in project completion times.

Chapter 5: Integer and Nonlinear Programming

  • Integer Programming: Some or all decision variables must take integer values (useful in scheduling, routing).

  • Nonlinear Programming (NLP): Objective function or constraints are nonlinear.

  • Solution Techniques: Lagrange multipliers, KKT conditions, or numerical methods.

Chapter 6: Decision Theory

  • Objective: Make rational decisions under certainty, risk, or uncertainty.

  • Decision Criteria:

    • Maximax (optimistic)

    • Maximin (pessimistic)

    • Minimax regret

    • Expected monetary value (EMV)

Chapter 7: Queueing Theory

  • Focus: Study waiting lines and service systems.

  • Key Measures: Average waiting time, average number of customers, server utilization.

  • Applications: Banks, hospitals, call centers.

Chapter 8: Simulation

  • Purpose: Analyze complex systems using computer models when analytical solutions are hard.

  • Techniques: Monte Carlo simulation, discrete-event simulation.

  • Applications: Manufacturing, logistics, healthcare, service systems.

Chapter 9: Multi-Criteria Decision Making (MCDM)

  • Objective: Solve problems with multiple conflicting objectives.

  • Techniques: Weighted sum model, Analytic Hierarchy Process (AHP), Goal Programming.

Chapter 10: Inventory and Replacement Models

  • Inventory Models: EOQ (Economic Order Quantity), reorder point, safety stock.

  • Replacement Models: Determine optimal replacement of equipment or machinery to minimize costs.

Applications of OR

  • Production & inventory optimization

  • Project scheduling

  • Transportation and logistics planning

  • Resource allocation

  • Service systems optimization (banks, hospitals)