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...

An oligopoly with spatially dispersed producers and consumers and with multi-period demands is modeled in this paper.