A dynamic lot-sizing model with demand time windows

One of the basic assumptions of the classical dynamic lot-sizing model is that theaggregate demand of a given period must be satisfied in that period. Under thisassumption, if backlogging is not allowed then the demand of a given period cannotbe delivered earlier or later than the period. If backlogging is allowed, the demandof a given period cannot be delivered earlier than the period, but can be deliveredlater at the expense of a backordering cost. Like most mathematical models, theclassical dynamic lot-sizing model is a simplified paraphrase of what might actuallyhappen in real life. In most real life applications, the customer offers a graceperiod - we call it a demand time window - during which a particular demand can besatisfied with no penalty. That is, in association with each demand, the customerspecifies an earliest and a latest delivery time. The time interval characterizedby the earliest and latest delivery dates of a demand represents the correspondingtime window.This paper studies the dynamic lot-sizing problem with demand time windows andprovides polynomial time algorithms for computing its solution. If shortages arenot allowed, the complexity of the proposed algorithm is order T square. Whenbacklogging is allowed, the complexity of the proposed algorithm is order T cube.