Operations Research and Quantitative Methods
This domain tests the ability to formulate and solve decision models. Candidates must recognize problem types and their solution methods: linear programming (graphical and simplex), transportation and assignment models, decision analysis (expected monetary value, decision trees, utility), queuing, simulation, and network models (PERT/CPM, shortest path, minimal spanning tree).
Linear programming traps are common. In the graphical method, the optimum occurs at a corner point of the feasible region (or along an edge if the objective is parallel to a constraint). Know how to convert inequalities to equalities with slack and surplus variables, and how to read a sensitivity report (shadow price = marginal value of one unit of a binding resource). Transportation problems test the northwest-corner, least-cost, and Vogel's approximation methods for initial solutions, and the stepping-stone or MODI method for optimality; check degeneracy (m + n − 1 basic cells).
Decision analysis: compute EMV as the probability-weighted sum of payoffs; the expected value of perfect information (EVPI) equals the expected payoff with perfect information minus the best EMV. Queuing: for M/M/1, utilization ρ = λ/μ; average number in system L = λ/(μ − λ); average wait W = 1/(μ − λ). A frequent trap is confusing λ (arrival rate) with μ (service rate) or using L where W is asked.
PERT versus CPM: PERT uses three time estimates (optimistic, most likely, pessimistic) and computes expected time te = (a + 4m + b)/6 with variance ((b − a)/6)²; CPM uses deterministic times and focuses on cost-time tradeoff (crashing). The critical path is the longest path; crashing shortens the project only while the critical path remains critical.
Worked example
M/M/1 with λ = 8/hr, μ = 10/hr: ρ = 0.8; L = 8/(10−8) = 4 customers; W = 1/(10−8) = 0.5 hr.