Operational Research Course

Lesson 1 • Classification of OR Models

Categorizes deterministic, stochastic, static, and dynamic models by structure. Guides model selection based on problem characteristics and data availability.

Lesson 2 • Mathematical Preliminaries

Reviews linear algebra, calculus, and probability concepts essential for OR models. Ensures students can manipulate equations and interpret quantitative results.

Lesson 3 • History and Scope of OR

Traces OR from wartime origins to modern industry applications. Establishes why systematic quantitative analysis outperforms intuitive decision-making.

Lesson 4 • The OR Problem-Solving Process

Introduces the seven-phase OR methodology from problem formulation to implementation. Connects structured process to reliable, repeatable decision outcomes.

Lesson 1 • Graphical Solution Method

Solves two-variable LPs by plotting feasible regions and iso-profit lines. Builds geometric intuition before algebraic methods are introduced.

Lesson 2 • Duality Theory

Derives the dual LP and explains primal-dual relationships and complementary slackness. Provides economic interpretation of shadow prices and dual variables.

Lesson 3 • Sensitivity Analysis in LP

Examines how optimal solutions change with parameter perturbations. Equips students to assess solution robustness and communicate risk to decision-makers.

Lesson 4 • Formulating Linear Programs

Defines decision variables, objective functions, and constraints for LP models. Connects real-world resource allocation problems to standard LP form.

Lesson 1 • Minimum Cost Network Flow

Unifies transportation, assignment, and flow problems under a single LP framework. Demonstrates how network simplex exploits problem structure for speed.

Lesson 2 • The Transportation Problem

Formulates supply-demand balance problems as LP with a cost matrix. Introduces the northwest corner, minimum cost, and Vogel's approximation methods.

Lesson 3 • Maximum Flow and Min-Cut

Determines maximum throughput in capacitated networks using augmenting paths. Applies the max-flow min-cut theorem to bottleneck identification.

Lesson 4 • Shortest Path and Spanning Tree

Finds minimum-cost paths and spanning trees in weighted graphs. Connects graph algorithms to infrastructure planning and network design decisions.

Lesson 1 • Heuristics and Metaheuristics

Introduces greedy, local search, and population-based methods for large IPs. Balances solution quality against computational time in practice.

Lesson 2 • Branch-and-Bound Method

Solves IPs by systematically partitioning the feasible region and pruning subproblems. Demonstrates bounding strategies that limit computational effort.

Lesson 3 • Classic Combinatorial Problems

Models the traveling salesman, knapsack, and set-covering problems as IPs. Builds a library of formulation patterns applicable across industries.

Lesson 4 • Cutting-Plane Methods

Tightens LP relaxations by adding valid inequalities that cut off fractional solutions. Covers Gomory cuts and their role in modern IP solvers.

Lesson 1 • Nonlinear Programming Concepts

Defines convexity, local vs. global optima, and KKT optimality conditions. Establishes theoretical foundations before algorithmic methods are introduced.

Lesson 2 • DP Applications and Limitations

Applies DP to inventory, resource allocation, and shortest-path problems. Addresses the curse of dimensionality and introduces approximate DP strategies.

Lesson 3 • Unconstrained Optimization Methods

Applies gradient descent, Newton's method, and quasi-Newton algorithms to smooth objectives. Connects convergence rates to practical computational efficiency.

Lesson 4 • Constrained Nonlinear Optimization

Solves NLP with equality and inequality constraints using penalty and barrier methods. Introduces sequential quadratic programming for engineering applications.

Lesson 1 • Markov Chains

Defines discrete-time Markov chains, transition matrices, and steady-state behavior. Applies Markov analysis to inventory and reliability systems.

Lesson 2 • Queuing Network and Design

Extends single-queue models to networks of queues and optimal server allocation. Connects queuing analysis to service system design decisions.

Lesson 3 • Standard Queuing Models

Derives performance formulas for M/M/1, M/M/c, M/G/1, and finite-capacity queues. Enables direct calculation of wait times, queue lengths, and utilization.

Lesson 4 • Probability Review for Stochastic OR

Reinforces random variables, expectation, and key distributions used in OR models. Bridges earlier probability review to stochastic model construction.

Lesson 1 • Random Number Generation

Explains pseudo-random number generators and inverse-transform variate generation. Ensures students can produce correct stochastic inputs for simulation models.

Lesson 2 • Statistical Analysis of Simulation Output

Addresses warm-up bias, run length, and confidence interval construction for simulation. Enables statistically rigorous comparison of system design alternatives.

Lesson 3 • Model Verification and Validation

Distinguishes verification from validation and applies structured testing techniques. Ensures simulation output faithfully represents the real system before analysis.

Lesson 4 • Simulation Concepts and Types

Distinguishes discrete-event, continuous, and Monte Carlo simulation paradigms. Clarifies when simulation is preferred over analytical OR models.

Lesson 1 • Decision Theory Foundations

Defines decision environments: certainty, risk, and uncertainty. Introduces maximin, maximax, and minimax regret criteria for structured choice.

Lesson 2 • Multi-Criteria Decision Making

Applies weighted scoring, TOPSIS, and AHP to rank alternatives on multiple criteria. Addresses criteria weighting and consistency checking in group decisions.

Lesson 3 • Decision Trees and Bayesian Updating

Constructs decision trees with chance nodes and applies backward induction. Integrates Bayes' theorem to update probabilities with new information.

Lesson 4 • Multi-Objective Optimization

Formulates problems with competing objectives and generates Pareto-efficient frontiers. Connects MCDM preference elicitation to multi-objective LP and goal programming.