Multiple Product Single Facility Stockout Avoidance Problem (SAP) and Weighted Stockout Problem (WSP)

We study 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 pnelized linearly is also studied. We call this problem the Weighted Stockout Problem (WSP). Both problems are NP-hard in the strong sense. We develop Mixed Integer Linear Programming (MIP) formulations for both the SAP and the WSP. In addition, several heuristic algorithms are presented and performances are tested using computational experiments. We show that there exist polynomial algorithms for some special cases of the SAP and the WSP. We also present a method to phase into a target cyclic schedule for infinite horizon problems. These can be used as a practical scheduling tool for temporarily overloaded facilities or to reschedule production after a disruption.