Operations Research
What to master
Model formulation plus solution mechanics. Linear programming: decision variables, objective, constraints, graphical corner points, simplex logic, duality, shadow prices, and sensitivity ranges. Networks: shortest path, minimum spanning tree, maximum flow/min cut, and transportation and assignment models (including the Hungarian method). Project management: CPM/PERT, expected time (a + 4m + b)/6, variance ((b - a)/6)^2, critical path with zero slack, and crashing at minimum cost per unit of time. Decision analysis: payoff tables, EMV, EVPI, decision trees, and utility. Queueing: M/M/1 with rho = lambda/mu, Lq = rho^2/(1 - rho), and Wq = Lq/lambda. Add integer programming and simulation basics.
Traps
- Reporting a shadow price as a reduced cost, or the reverse.
- Assuming an LP optimum is unique or integral.
- Summing PERT variances for activities that are not on the critical path.
- Applying steady-state queue formulas when rho is not less than 1.
- Minimizing when the problem asks for a maximum (objective sign errors).
- Using the transportation method when routes have capacities - that needs a general LP.
Worked example
An M/M/1 queue with lambda = 6/hr and mu = 8/hr: rho = 0.75, Lq = 0.5625/0.25 = 2.25 customers, and Wq = 2.25/6 = 0.375 hr, about 22.5 minutes.
Rule of thumb
Draw the network before computing anything. The critical path is the longest path, its length equals project duration, and only activities on it are worth crashing.