Optimizing service-level and relevant cost for a stochastic multi-item cyclic production system

A multi-item make-to-order production system in a stochastic environment is analyzed. Assuming a common cycle production approach, the impact of safety stock, cycle time, demand, processing time and setup time on service-level and total relevant cost (holding, setup and backorder cost) is determined. To illustrate this relationship a trajectory for the service-level with respect to the relevant cost (holding and setup) is presented. Furthermore algorithms to calculate the cycle time which leads to maximum service-level at constant safety stock and to calculate the pair cycle time and safety stock which minimize total relevant cost are introduced.