The effect of workload constraints in linear programming models for production planning

Linear programming (LP) models for production planning incorporate a model of the manufacturing system that is necessarily deterministic. Although these deterministic models are the current state-of-the-art, it should be recognized that they are used in an environment that is inherently stochastic. This fact should be kept in mind, both when making modeling choices and when setting the parameters of the model. In this paper we study the effect of a workload constraint on the efficiency of resource usage and on the reliability of production planning in a stochastic environment represented by a queueing model. The main novelty of the queueing model is the fact that jobs are admitted to the production facility periodically but are processed continuously. We show that there may not be an acceptable trade-off between efficiency and reliability if planned lead times are not explicitly modeled. The impact of production uncertainty on the design and parametrization of the LP model is demonstrated by numerical examples