Applications of ORGitHub
Lecture Notes

Applications of Operations Research

Each lecture takes one real decision problem — routing a fleet, staffing a call centre, pricing airline seats, committing power plants — and works through it the same way: what the decision is, how to write it as a mathematical model, how that model is solved, and what the answer tells you.

Part 1 · Foundations

  1. 1What Is Operations Research?The modelling cycle, the core toolkit, and how the rest of these notes are organized.

Part 2 · Logistics & Supply Chain

  1. 2The Transportation ProblemShipping goods from supply points to demand points at minimum cost, and what the dual prices tell you.
  2. 3Facility LocationChoosing which sites to open and which customers each serves, and why two equivalent MIP formulations can differ greatly in strength.
  3. 4Vehicle RoutingDesigning delivery routes for a capacitated fleet: TSP formulations, the Clarke–Wright savings heuristic, and local search.
  4. 5Inventory ManagementHow much to order and when: the EOQ trade-off, the newsvendor critical ratio, and safety stock under uncertain demand.

Part 3 · Services & Workforce

  1. 6Staff SchedulingCovering staffing requirements with shifts at minimum cost: set covering, the cyclic days-off problem, and the pipeline from forecast to roster.
  2. 7Call Centre StaffingSizing a call centre with the Erlang C queue, service-level targets, and the square-root staffing rule.

Part 4 · Pricing & Finance

  1. 8Revenue ManagementDeciding how many seats to protect for high-fare demand, from Littlewood's rule to network bid prices and overbooking.
  2. 9Portfolio OptimizationTrading off risk against return with Markowitz's mean–variance model, and minimizing tail risk with CVaR as a linear program.

Part 5 · Energy & Transport

  1. 10Unit CommitmentScheduling which power stations run each hour and how much they produce, and how the dual of the demand constraint sets the electricity price.
  2. 11Electric Bus SchedulingCovering a timetable with battery-limited buses and planning when to charge them: vehicle scheduling with range constraints, and charging under time-varying prices and grid limits.
  3. 12Airline Crew SchedulingCovering every flight with legal crew pairings via set partitioning, column generation and branch-and-price, then rostering them to individuals.

Part 6 · Computing & AI Systems

  1. 13Serving AI ModelsPlacing models on GPUs: Mixture-of-Experts placement as load shifts over time, and block placement and request routing across servers spread over the Internet.