On the computational complexity of uncapacitated multi-plant lot-sizing problems

Competitive Uncapacitated Lot- Sizing Game

A game merging the lot-sizing problem with a Cournot competition model is for the first time theoretically studied. Each player is a producer with her own production facility, modeled as an uncapacitated lot-sizing problem (i.e., production incurs set-up and variable costs and inventories are allowed). A Cournot competition is played in each time period (market) with each player deciding the qu...

Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

In 1958, Wagner and Whitin published a seminal paper on the deterministic uncapacitated lot-sizing problem, a fundamental model that is embedded in many practical production planning problems. In this paper we consider a basic version of this model in which demands (and other problem parameters) are stochastic: the stochastic uncapacitated lot-sizing problem (SULS). We define the production pat...

Uncapacitated Lot-Sizing Problems with Start-Up Costs

Loss of customer goodwill in the uncapacitated lot-sizing problem

Loss of customer goodwill in uncapacitated single level lot-sizing is studied with a mixed integer programming model extending the well-known Wagner-Whitin (WW) model. The objective is to maximize profit from production and sales of a single good over a finite planning horizon. Demand, costs, and prices vary with time. Unsatisfied demand cannot be backordered. It leads to the immediate loss of ...

Uncapacitated lot sizing with backlogging: the convex hull

An explicit description of the convex hull of solutions to the uncapacitated lot-sizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify valid inequalities that subsume all previously known valid inequalities for this problem. We show that these inequalities are enough t...