How to avoid stockouts when producing several items on a single facility? What to do if you can't?

This paper considers the Multiple Product Single Facility Stockout Avoidance Problem (SAP). That is the problem of determining, given initial inventories, whether there is a multiple product single facility production schedule that avoids stockouts over a given time horizon. The optimization version of the SAP where stockouts are penalized linearly is also studied. We call this problem the Weighted Stockout Problem (WSP). Both problems are NP-hard in the strong sense. Mixed Integer Linear Programming (MIP) formulations for both the SAP and the WSP are developed. We show that there exist polynomial algorithms for some special cases of the SAP and the WSP. We have also developed heuristics and computational results.