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| Concept | What to Remember | Typical Formula / Rule | |---------|------------------|------------------------| | | Convex polytope defined by constraints. | ( x \ge 0 \mid Ax \le b) | | Basic feasible solution (BFS) | Vertex of the polytope; basis = set of basic variables. | (B^-1b) where (B) is a non‑singular sub‑matrix of (A). | | Shadow price | Marginal worth of a resource (dual variable). | (\pi_j = \frac\partial Z\partial b_j) | | Reduced cost | How much objective coefficient must improve before a non‑basic variable enters basis. | (c_j - \pi^T a_j) | | Optimality condition (LP) | All reduced costs ≤ 0 (max) or ≥ 0 (min). | | Degeneracy | More than one basic variable equals zero → possible cycling. Use Bland’s rule to avoid. | | Network optimality | No negative‑cost cycles (for min‑cost flow). | | Little’s Law (queues) | (L = \lambda W) – average number in system = arrival rate × average time. | | EOQ | (Q^* = \sqrt\frac2DSH) where (D) = demand, (S) = setup cost, (H) = holding cost/unit. | | Expected value of perfect information (EVPI) | Maximum amount worth paying for perfect info. | (EVPI = \textEMV (with perfect info) - \textEMV (without)). |

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