| While stochastic dynamic programming (DP) is a powerful optimization methodology for multi-stage decision processes, its application assumes that the decision maker has a well-defined criterion for evaluating solutions, and a well-defined relationship, albeit probabilistic, between the decision made in a state during each stage of the process and the state that results from that decision. This thesis attempts to remedy those limitations by constructing and validating a stochastic DP model that (a) incorporates the analytical hierarchy procedure (AHP) for assessing the relative desirability of the DP states and (b) recognizes and treats the estimates of the transition probabilities as an approximation of their actual values.; The analytical hierarchy procedure provides the decision-maker with three major benefits: measuring the relative desirability of the DP states, taking into account the varied potential of these states, and taking advantage of the value judgment and expertise of the decision maker.; During the backward recursion, when decisions are compared and selected based upon the expected level of achievement of the criteria, a statistical test of the significance of the differences is included, in consideration of the fact that the expected values are based upon estimated probabilities. When the test fails to find a significant difference, other considerations that were not addressed in the model may be interposed in order to make the selection.; While investigating the applicability of AHP to this class of problems, we also examined a “rule-of-thumb” which has been applied by practitioners since the inception of AHP. This rule provided a criterion (“consistency ratio ≤0.1”) for judging the consistency of the decision-maker while making the pairwise comparisons. We demonstrate that this criterion is flawed, and propose a new criterion based upon the consistency index, and the number of alternatives being compared. |
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