Production Planning Under Demand and Endogenous Supply Uncertainty

We study the problem of determining how much finished goods inventory to source from different capacitated facilities in order to maximize profits resulting from sales of such inventory. We consider a problem wherein there is uncertainty in demand for finished goods inventory and production yields at facilities. Further, we consider that uncertainty in production yields is endogenous, as it depends on both the facilities where a product is produced and the volumes produced at those facilities. We model the problem as a two stage stochastic program and propose an exact, Benders-based algorithm for solving instances of the problem. We prove the correctness of the algorithm and with an extensive computational study demonstrate that it outperforms known benchmarks. Finally, we establish the value in modeling uncertainty in both demands and production yields.