Workload allocation in multi-product, multi-facility production systems with setup times

In this article, we model the problem of assigning work to M heterogeneous servers (machines), which arises from exogenous demands for N products, in the presence of nonzero setup times. We seek a workload allocation which mi nimizes the total expected Work-In-Progress (WIP) inventory. Demands are as sumed to arrive according to independent Poisson processes, but the setup a nd the processing times can have arbitrary distributions. Whenever a machin e produces more than one product type, production batch sizes are determine d by a group scheduling policy; which is also known as the cyclic-exhaustiv e polling policy. We formulate the workload allocation problem as a nonline ar optimization problem and then provide several insights gleaned from firs t order necessary conditions, from numerical examples, and from a close exa mination of the objective function. For example, we show that increasing ei ther the load or the number of products assigned to a machine, or both, doe s not necessarily increase its contribution to total WIP. These insights ar e then used to devise a heuristic workload allocation as well as a lower bo und. The heuristic allocation is further refined using a nonlinear optimiza tion algorithm.