Optimal Control of Supply Chain Systems with Assembly Operation
This chapter considers a supply chain system with assembly operation. The manufacturer has to make the ordering decisions for multiple types of raw materials from different suppliers in parallel and the production decisions on assembling finished goods using all types of raw materials. The system is subject to uncertainties of raw material delivery lead times, assembly processing times, customer demand arrivals, and possible breakdown of the assembly machine. The objective is to minimize the expected discounted cost including raw materials inventory costs, finished goods inventory cost, and demand backlog cost. The optimal integrated ordering and assembly policy is derived. The structural properties of the optimal cost function such as monotonicity and asymptotic behaviors are established explicitly for the special case with the maximum order size one. It is shown that the optimal policy can be characterized by a set of switching manifolds, which lead to a set of control regions to determine the optimal control decisions. This chapter ends with some discussion and notes.
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