A Linear Programming Framework for the Control of Tandem Production Lines
We consider the problem of production control and stock rationing in a make-to- stock production system with several customer classes that generate independent Poisson demands. The system consists of a tandem production line with a finished goods buffer at the end. The tandem line is composed of reliable/unreliable workstations with exponential production times and intermediate buffers. At decision epochs, in conjunction with the stock allocation decision for the finished goods, the control specifies whether to continue or stop production at each workstation. We model the system as a Markov Decision Process and then propose an equivalent linear programming formulation. This formulation enables us to solve larger models in reasonable times by harnessing the power of the state-of-art optimization solvers. Furthermore, this approach provides us with the flexibility to use our MDP model to find the optimal parameters to well-known control policies such as Kanban.
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