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 of Charnes and Cooper (1963). 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 to standard sample average approximation models.
Jaillet, P., S. D. Jena, T. S. Ng, and M. Sim, 01/2022. Satisficing Models under Uncertainty. Forthcoming in INFORMS Journal on Optimization