The authors examine a variant of the uncapacitated lot-sizing model of Wagner-Within involving sales instead of fixed demands, and lower bounds on stocks. Two extended formulations are presented, as well as a dynamic programming algorithm and a complete description of the convex hull of solutions.

After reviewing some of the basic preprocessins techniques for handling safety stocks and multilevel problems, we discusss a variety of aspects arising particularly in small and large bucket (time period) models such as stars-ups, changeovers, minimum batch sizes, choice of one or two set-ups...

Two basic properties concerning the dynamic behavior of competitive equilibria of exchange economies with complete markets are derived essentially from the fact that the Walras correspondence has no knots.

We analyze the problem of competitive mechanism design within the context of a model of product differentiated oligopoly. In an oligopoly setting, participation by an agent in any one firm's catalog is endogenously determined. This facts leads naturally to a modification of the classical notion...