Operations Research Foundations and Model Formulation
This domain tests whether you can translate a messy decision into a defensible mathematical model and recognize its limits. Expect questions on variable definition, objective and constraint logic, deterministic versus stochastic models, model classes, validation, and sensitivity.
Core rules
- Define decision variables with units and index sets before writing equations.
- Separate parameters (given) from decisions (chosen); state the objective direction.
- Every constraint must encode a real restriction; check feasible region, scaling, and omitted links.
- Use LP for linear continuous decisions, MILP for integrality or on-off logic, and simulation for complex stochastic dynamics.
- Validate with extreme cases and sensitivity, not just solver status.
Worked example
A workshop makes chairs C and tables T. Profit is 40C+70T. Labor is 2C+3T≤120 hours; wood is 4C+5T≤200 board-feet; demand is T≤18; C,T≥0. At T=18, wood gives C≤27.5 and labor gives C≤33, so the wood limit binds at C=27.5. Profit there is 40(27.5)+70(18)=2360. At C=30,T=10 profit is 1900, so the demand-constrained point is better. The formulation is complete because each resource and market limit is represented.
Traps
Treating T≤18 as unnecessary, mixing hours with board-feet, using profit per unit as a decision variable, or reporting a solver answer without checking feasibility. A model that is feasible is not automatically valid.
Key points
- Variables need units and index sets.
- Parameters are not decisions.
- Constraints must mirror real restrictions.
- Model class follows assumptions.
- Sensitivity is part of validation.