A dynamic lot-sizing model with demand time windows
Management Science p. 1384- 1395
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 it 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 acceptable 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 backlogging is not allowed, the complexity of the proposed algorithm is O(T²) where T is the length of the planning horizon. When backlogging is allowed, the complexity of the proposed algorithm is O(T³).
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Lee, C.Y, Cetinkaya, S, & Wagelmans, A.P.M. (2001). A dynamic lot-sizing model with demand time windows. Management Science, 1384–1395. Retrieved from http://hdl.handle.net/1765/14411