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.