Note--On Madigan's Approach to the Deterministic Multi-Product Production and Inventory Problem

The deterministic multi-product single-machine production and inventory problem is one of the simplest models in which production and inventory factors interact. There is at present no algorithm available which solves the problem optimally, and several different types of approaches have been presented in the literature. Madigan's heuristic method [Madigan, J. G. 1968. Scheduling a multi-product single machine system for an infinite planning period. Management Sci. 14(11, July) 713-719.] avoided some of the drawbacks characteristic of other methods, but there are some errors and limitations in his original presentation, to which this note is addressed.