The Strategic Use of Capacity Slack in the Economic Lot Scheduling Problem with Random Demand

Growing interest in designing systems with capacity slack as one form of flexibility raises many questions about its use and its usefulness. In the framework of the economic lot scheduling problem with stochastic demand, we develop on optimization-based model that considers capacity slack, safety stock, and overtime explicitly, and has the objective of minimizing the expected cost per unit time of inventory, overtime, and, where applicable, setup costs. The solution is a continuous-time production plan that consists of a time-dependent inventory trajectory for each of the parts, including the placement of planned idle time in the schedule. We consider schedule stability to be desirable because of potential effects on upstream and downstream operations in multistage production settings. Thus, the plan also has certain characteristics that contribute to achieving stability. Our results on the relative merits of capacity slack and safety stock indicate that capacity slack in the form of planned idle time is not a cost-effective hedge against demand uncertainty in this context. Thus, it is essential that management carefully identify and evaluate other reasons for including idle time in a plan, and use the idle time effectively. For managers who face situations not fully represented by our model, this paper provides analytic results that will guide them in the placement of planned idle time and the choice of safety stock levels.