M-natural/S-Convexity and Applications
Abstract
Classical monotone comparative statics in parametric optimization problems establishes the existence of nondecreasing optimal solutions (in parameters) through lattice programming. In this talk, we use M-natural-convexity, one of the key concepts in discrete convex analysis, and introduce a new concept of S-convexity as its extension to develop monotone comparative statics in parallel to lattice programming. Specifically, we show that in a parametric minimization model, the optimal solution (set) is nonincreasing (instead of nondecreasing) in the parameters when the objective function is M-natural/S-convex and the constraint is a box, and M-natural/S-convexity is preserved under the optimization operation. We illustrate their applications on several operations models including a multi-product newsvendor model with a joint capacity and a portfolio contract model.