Service Level Constraint Models

Abstract

In this chapter the problem of capacity investment and WAW setting is discussed in a service level constraint context. Since in production systems it is often difficult to identify a cost factor for backorders, a service level target can be defined by management as a strategic decision. To be able to use the models developed in Chaps. 4 and 5 in such an environment, an extension of these models to include a service level constraint is developed. For the single-stage M/M/1 model, an explicit expression for the optimal WAW and the optimality condition for the optimal processing rate are derived. For the two-stage M/M/s model a service level equation is provided to enable its application in such settings. Some additional numerical examples are provided which show that the results of the service level constraint models are similar to the backorder cost models. Additionally, a capacity investment optimization model for a multi-item, single-stage production system with normally distributed demand is developed in this chapter. The capacity investment is optimized under a service level constraint including inventory holding costs.