Optimization Methods in Business Analytics Course

Lesson 1 • Optimisation Workflow Overview

Maps the end-to-end process from problem scoping to solution deployment. Establishes the iterative cycle used throughout the course.

Lesson 2 • Anatomy of an Optimisation Problem

Breaks down decision variables, objective functions, and constraints. Provides a universal template for structuring any business problem.

Lesson 3 • What Is Optimisation in Business

Defines optimisation as the process of finding the best solution under constraints. Anchors abstract maths concepts to tangible business decisions.

Lesson 4 • Data Requirements and Problem Inputs

Identifies the data needed to parameterise an optimisation model. Clean, well-structured inputs directly determine solution quality.

Lesson 1 • The Simplex Algorithm

Introduces the simplex method as a systematic corner-point traversal. Students trace pivot operations on small tableaux to understand convergence.

Lesson 2 • Sensitivity Analysis in LP

Examines how optimal solutions change when objective coefficients or RHS values shift. Sensitivity ranges guide robust decision-making.

Lesson 3 • Formulating Linear Programmes

Translates word problems into standard LP form with a linear objective and linear constraints. Correct formulation is the prerequisite for any solver.

Lesson 4 • Graphical Solution Method

Solves two-variable LPs by plotting feasible regions and evaluating corner points. Builds geometric intuition before algorithmic methods.

Lesson 1 • Model Debugging and Validation

Diagnoses common solver errors such as infeasibility flags and incorrect optima. Systematic debugging prevents costly errors in production models.

Lesson 2 • Python LP with Open-Source Libraries

Formulates and solves LP models using Python optimisation libraries. Code-based workflows scale to larger, more complex problems than spreadsheets.

Lesson 3 • Interpreting Solver Reports

Reads answer, sensitivity, and limits reports generated by spreadsheet solvers. Report literacy connects raw output to actionable business insight.

Lesson 4 • Scaling and Performance Considerations

Addresses numerical scaling issues that degrade solver accuracy on large models. Proper scaling reduces solve time and improves solution reliability.

Lesson 1 • Formulating MIP Models

Translates logical conditions into binary and integer constraints. Mastering MIP formulation unlocks a wide class of combinatorial business problems.

Lesson 2 • Why Integer Variables Matter

Explains when continuous LP solutions are physically meaningless and integer constraints are required. Motivates MIP with workforce and capital budgeting examples.

Lesson 3 • Branch-and-Bound Algorithm

Traces the branch-and-bound tree to show how MIP solvers find provably optimal integer solutions. Understanding the algorithm aids solver parameter tuning.

Lesson 4 • MIP Applications in Business

Applies MIP to facility location, project selection, and shift scheduling. Case studies reinforce formulation skills with realistic data sets.

Lesson 1 • Network Models in Supply Chain

Integrates transportation, flow, and location decisions into a unified supply chain network model. Students solve multi-echelon distribution problems.

Lesson 2 • Transportation and Assignment Models

Formulates supply-demand matching problems as balanced transportation tableaux. The assignment model solves one-to-one matching at minimum cost.

Lesson 3 • Minimum Spanning Tree Problems

Finds the lowest-cost connected network using Kruskal's and Prim's algorithms. MST models infrastructure rollout and communication network design.

Lesson 4 • Shortest Path and Maximum Flow

Applies Dijkstra's algorithm for routing and the max-flow min-cut theorem for capacity analysis. Both underpin logistics and network design decisions.

Lesson 1 • Convexity and Global Optima

Defines convex functions and sets, guaranteeing that local optima are global. Recognising convexity determines whether a solver result is trustworthy.

Lesson 2 • Constrained Nonlinear Optimisation

Introduces Lagrange multipliers and KKT conditions for constrained NLP. These conditions identify candidates for constrained optima in business models.

Lesson 3 • Calculus Review for Optimisation

Refreshes derivatives, gradients, and Hessians as tools for locating optima. Calculus conditions underpin every nonlinear optimisation algorithm.

Lesson 4 • NLP Solvers and Business Applications

Applies NLP solvers to pricing, portfolio, and production mix problems. Students configure solver options and validate nonlinear solutions.

Lesson 1 • Genetic Algorithms

Evolves a population of solutions using selection, crossover, and mutation operators. GAs handle complex, discontinuous search spaces common in business problems.

Lesson 2 • Tabu Search and Comparison

Uses a memory structure to forbid recently visited solutions and guide search. Comparing metaheuristics on benchmark problems builds practical selection judgment.

Lesson 3 • When Exact Methods Fall Short

Explains computational complexity and NP-hard problem classes that motivate heuristics. Understanding limits of exact solvers justifies approximate methods.

Lesson 4 • Simulated Annealing

Applies probabilistic acceptance of worse solutions to escape local optima. Cooling schedule tuning controls the balance between exploration and exploitation.

Lesson 1 • Uncertainty in Business Optimisation

Distinguishes risk, uncertainty, and variability as sources of model error. Framing uncertainty correctly determines which stochastic method to apply.

Lesson 2 • Stochastic Programming Basics

Formulates two-stage stochastic programmes with recourse for demand and supply uncertainty. Expected value and wait-and-see benchmarks measure the value of stochastic solutions.

Lesson 3 • Robust Optimisation Framework

Constructs uncertainty sets and robust counterparts that immunise solutions against worst-case scenarios. Robust models trade average performance for reliability.

Lesson 4 • Simulation-Optimisation Integration

Combines Monte Carlo simulation with optimisation to evaluate stochastic solutions. This hybrid approach handles complex distributions that resist analytical treatment.