Abstract
We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.
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Presman, E.L., Sethi, S.P., Zhang, H. et al. Average Cost Optimality for an Unreliable Two-Machine Flowshop with Limited Internal Buffer. Annals of Operations Research 98, 333–351 (2000). https://doi.org/10.1023/A:1019272811055
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DOI: https://doi.org/10.1023/A:1019272811055