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Decision Analysis

2 tools in the Operations Research area.

Decision Analysis

Decision making under uncertainty from a payoff table of alternatives against states of nature: the classical criteria (maximax, maximin, minimax regret, Hurwicz, Laplace, maximum likelihood), the Bayes decision rule on the prior probabilities and the expected value of perfect information; with a likelihood table for a test, survey or sample, Bayes' theorem gives the posterior probabilities, the best decision after each outcome, the expected value of sample information, its efficiency and whether the test is worth its cost; the decision tree is drawn and rolled back, the best decision is traced against one prior probability with the crossover points, the risk profiles of the leading alternatives are plotted, and a risk tolerance turns the payoffs into exponential utilities with certainty equivalents and risk premiums. Written for strategy, legal, medical, policy and project-risk work.

2 worked examples reproduced, listed on the tool page.

Multi-Criteria Decision (AHP, TOPSIS)

Ranks alternatives against several criteria from one decision matrix: the analytic hierarchy process with pairwise comparison matrices (principal eigenvector by the power method and the exact eigen-solve, row geometric mean, lambda max, consistency index and ratio, group aggregation of several judges, per-criterion comparisons or direct scores, synthesis), TOPSIS (vector normalisation, ideal and anti-ideal, separations, closeness coefficient), the weighted sum and weighted product, ELECTRE I concordance and discordance with a kernel, PROMETHEE II net flows with six preference functions, entropy and rank-order-centroid weights, a rank comparison across methods and a weight sensitivity sweep with the rank-flip points. Written for trade studies, analyses of alternatives, vendor and site selection and project prioritisation.

1 worked example reproduced, listed on the tool page.

Other Operations Research sections

Optimization · Queueing and Simulation · Scheduling · Inventory and Supply Chain · Networks and Routing