Derivation of additional probabilistic information for analyzing decisions under risk
Dowling, John Patrick, Jr.
Schrady, David A.
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The problem of analyzing decisions under risk is investigated. The vehicle for this investigation is the single-period inventory model commonly referred to as the "newsboy problem". The maximum expected value of the profit is the criteria most often used in making a decision in this type of problem. This paper analyzes this model in several ways. It is found that, under some conditions, variance of profit provides valuable insight into the problem and could assist the analyst in choosing alternatives for the decision maker. In addition, it is found that in this model, maximizing the expected value of profit does not maximize the probability of attaining at least this maximum expected profit. Appropriate display of this additional information allows the decision maker to implicitly assign his utilities in terms of his preferences when making decisions under risk. A modification of the expected utility function used by Borch is also discussed so that, for managers who exhibit decreasing marginal utility for money, some of this additional information can be simplified to produce a single measure of merit.
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