One of the basic assumptions of the classical dynamic lot-sizing model is that the aggregate demand of a given period must be satisfied in that period. Under this assumption, if backlogging is not allowed then the demand of a given period cannot be delivered earlier or later than the period. If backlogging is allowed, the demand of a given period cannot be delivered earlier than the period, but can be delivered later at the expense of a backordering cost. Like most mathematical models, the classical dynamic lot-sizing model is a simplified paraphrase of what might actually happen in real life. In most real life applications, the customer offers a grace period - we call it a demand time window - during which a particular demand can be satisfied with no penalty. That is, in association with each demand, the customer specifies an earliest and a latest delivery time. The time interval characterized by the earliest and latest delivery dates of a demand represents the corresponding time window. This paper studies the dynamic lot-sizing problem with demand time windows and provides polynomial time algorithms for computing its solution. If shortages are not allowed, the complexity of the proposed algorithm is of the order T square. When backlogging is allowed, the complexity of the proposed algorithm is of the order T cube.

dynamic programming, lot-sizing, time windows
hdl.handle.net/1765/1620
Econometric Institute Research Papers
Erasmus School of Economics

Lee, C.Y, Cetinkaya, S, & Wagelmans, A.P.M. (1999). A dynamic lot-sizing model with demand time windows (No. EI 9948-/A). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/1620