Stochastic linear programming with scarce information: an approach from expected utility and bounded rationality applied to the textile industry

摘要

Potential users of this article are engineers who can estimate mean values, standard deviations, and maybe correlations, but nothing else. By accepting analytical limitations of bounded rationality, the proposed method relies on expected utility to evaluate and control risk from each constraint. In this framework, disutility is close to zero when the constraint holds, while it strongly increases as the shortfall between both sides of the constraint increases. By ensuring high expected utility levels, the method yields either linear deterministic equivalents (very helpful for solving large-scale problems) or deterministic equivalents which are quadratic in the constraints but linear in the objective function. A case study of textile blends is developed for seven types of textile fibre and two random constraints, one concerning tensile strength and the other light fastness. A sensitivity analysis shows the consistency of the solutions.