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

Saifallah Benjaafar, Diwakar Gupta

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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 minimizes the total expected Work-In-Progress (WIP) inventory. Demands are assumed to arrive according to independent Poisson processes, but the setup and the processing times can have arbitrary distributions. Whenever a machine produces more than one product type, production batch sizes are determined by a group scheduling policy; which is also known as the cyclic-exhaustive polling policy. We formulate the workload allocation problem as a nonlinear optimization problem and then provide several insights gleaned from first order necessary conditions, from numerical examples, and from a close examination of the objective function. For example, we show that increasing either the load or the number of products assigned to a machine, or both, does not necessarily increase its contribution to total WIP. These insights are then used to devise a heuristic workload allocation as well as a lower bound. The heuristic allocation is further refined using a nonlinear optimization algorithm.

Original languageEnglish (US)
Pages (from-to)339-352
Number of pages14
JournalIIE Transactions (Institute of Industrial Engineers)
Issue number4
StatePublished - 1999

Bibliographical note

Funding Information:
University of Minnesota Graduate School. Diwakar Gupta was supported in part by the Department of Mechanical Engineering, University of Minnesota, (via a visiting appointment) and in part by the Natural Sciences and Engineering Research Council of Canada through research grant number OGP0045904. The authors a1 so acknowledge Mehdi Sheikhzadeh, a Ph.D. candidate at the University of Minnesota, for his help in computer implementation of the two-stage heuristic.

Funding Information:
Saifallah Benjaafar was supported in part by the National Science Foundation under grant DDM-9309631 and the


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