The stochastic Economic Lot Scheduling Problem: Cyclical base-stock policies with idle times

In this paper we discuss stochastic Economic Lot Scheduling Problems (ELSP), i.e., settings where several items need to be produced in a common facility with limited capacity, under significant uncertainty regarding demands, production times, setup times, or combinations thereof. We propose a class of production/inventory strategies for stochastic ELSPs and describe how a strategy which minimizes holding, backlogging, and setup costs within this class can be effectively determined and evaluated. The proposed class of strategies is simple but rich and effective: when the facility is assigned to a given item, production continues until either a specific target inventory level is reached or a specific production batch has been completed; the different items are produced in a given sequence or rotation cycle, possibly with idle times inserted between the completion of an item's production batch and the setup for the next item. An optimal strategy within the class can be determined, and all relevant performance measures can be evaluated in just a few CPU seconds, using a 486-based PC. We also derive a number of easily computable lower bounds for the optimal cost value and establish a comparison with deterministic ELSPs.