Joint Capacity, Inventory and Demand Allocation Decisions in Manufacturing Systems

What is it about?

We study the demand, inventory and capacity allocation problem in production systems with multiple inventory locations and a production facility operating under linear, convex and concave costs. Independent stochastic demand from multiple sources is fullled from multiple warehouses that are in turn replenished from a shared production facility with stochastic production lead times. We rst start with a novel formulation of the demand allocation problem that avoids the nonlinearity of the previous models in the literature and show that the optimal customer allocations are not necessarily single sourced, as previously used and exploited in the literature. Being linear and exact, the new formulation allows the inclusion of additional decisions alongside demand and inventory allocation, which was not possible with existing models. Capacity decisions are incorporated under three cost structures: linear, concave and convex. We provide structural properties to characterize the optimal solutions. For the concave case, we show that for a given demand and inventory allocation, the optimal capacity of the production facility takes on discrete values within a nite set, which allows the objective to be linearized. We demonstrate numerically that the joint optimization of capacity, inventory and demand allocation decisions has signicant cost savings over a sequential decision and leads to a high utilization of the production facility under linear and convex capacity costs, but relatively low utilization under concave costs. Safety stock, on the other hand at the distribution centers is relatively low under linear and concave cost and moderate under convex cost.

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