Subcontracting in a make-to-stock production system, IPA gradients for an SFM

This work extends the single product, single facility and single warehouse make-to-stock (MTS) model (Zhao and Melamed 2004), by allowing subcontracting. In addition to the inventory triggering level employed in their model, a new subcontracting triggering level is used to manage the subcontracted amount. A stochastic fluid model (SFM) is used to model the MTS system with subcontracting. In the current model, the subcontractor is assumed capable of satisfying any difference between the demand and the in-house production to keep the inventory at the subcontracting triggering level. The sensitivity of the inventory on-hand, backorders and amounts subcontracted with respect to the two employed triggering levels are found using infinitesimal perturbation analysis (IPA).