Possible new applications of the interactive programming based on aspiration levels—case of pure and mixed strategies

Abstract

The interactive programming (IP) using aspiration levels is a well-known method applied to multi-criteria decision making under certainty (M-DMC). However, some essential analogies between M-DMC and scenario-based one-criterion decision making under uncertainty (1-DMU) have been recently revealed in the literature. These observations give the opportunity to adjust the IP to a totaly new issue. The goal of the paper is to create two novel procedures for uncertain problems on the basis of the IP ideas: the first one for pure strategy searching and the second for mixed strategy searching. In many ways, they allow a better consideration of the decision maker's preferences than classical decision rules. One of their significant advantages consists in analyzing particular scenarios sequentially. Another strong point is that the new procedures can be used by any kind of decision makers (optimists, moderate, pessimists). The new approaches may be helpful when solving problems under uncertainty with partially known probabilities. Both methods are illustrated in the paper on the basis of two fictitious decision problems concerning the choice of an optimal location and the optimization of the stock portfolio structure.

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“…Further generalizations presented in the volume is interactive programming. New possible applications of interactive programming, based on aspiration levels, are provided by Gaspars Wieloch ( 2023 ). Linear fractional programming, more precisely, a new iterative method for solving it, is studied in Perić et al ( 2023 ).…”