Production allocation with dual provisioning

Consider a manufacturer that has existing in-house capacity to produce certain products. However, due to recent growth in demand, the existing capacity is insufficient to meet the total requirements over a finite planning horizon. As a short term solution, the manufacturer has decided to order part of the total requirements from an external supplier. This paper presents a model that focuses on the issue of allocating a production quantity among the in-house facility and an external supplier. We construct a product allocation problem that determines an optimal allocation so that the total relevant cost (in-house production cost, ordering cost, etc.) is minimized. In addition, we analyze the complexity of the problem and develop two different Lagrangian heuristics for generating near-optimal allocations.