Rolling schedules for a dynamic lot-sizing problem with start-up cost

This paper considers a dynamic lot size model with start-up cost where backlogging is not allowed. The model incorporates inventory holding cost and two kinds of fixed costs-a start-up cost incurred whenever the machine (production facility) is switched from ‘off’ to ‘on’, and a reservation cost incurred in each production period. The optimal (cost-minimizing) solution over a finite horizon is found in a forward dynamic programming approach, upon which a planning horizon theorem is derived to treat the model in a rolling horizon environment. Accordingly, two procedures for selecting the run length of the first production block and the amount to meet the associated production requirement are developed. The cost effectiveness of the procedures are demonstrated by a set of simulation experiments.