Satisficing Models Under Uncertainty

Satisficing, as an approach to decision making under uncertainty, aims at achieving solutions that satisfy the problem’s constraints as well as possible. Mathematical optimization problems that are related to this form of decision making include the P-model. In this paper, we propose a general framework of satisficing decision criteria and show a representation termed the S-model, of which the P-model and robust optimization models are special cases. We then focus on the linear optimization case and obtain a tractable probabilistic S-model, termed the T-model, whose objective is a lower bound of the P-model. We show that when probability densities of the uncertainties are log-concave, the T-model can admit a tractable concave objective function. In the case of discrete probability distributions, the T-model is a linear mixed integer optimization problem of moderate dimensions. Our computational experiments on a stochastic maximum coverage problem suggest that the T-model solutions can be highly competitive compared with standard sample average approximation models.