A generalized lot sizing model for the process cycling problem

Most scheduling/lot sizing models for the single‐machine problem assume that aggregate demand equals aggregate production; and that backorders are to be avoided. Where working inventories are low, the scheduler may wish to avoid short production runs and willingly incur some backorder penalties so as to increase the length of production runs and reduce setup costs per unit of time. The model proposed here identifies optimal lot sizes with respect to the backorder/setup cost relationships. Use of the model will result in an optimally balanced inventory even when aggregate inventory levels are changing.