Parallelism of continuous- and discrete-time production planning problems

Abstract

We consider a capacitated production-inventory problem in both discrete- and continuous-time, stationary settings. In the discrete-time setting we analyze the infinite horizon capacitated dynamic lot-sizing problem, find the optimal solution and characterize its properties. For the continuous-time setting we formulate a new problem, which we claim to be an appropriate counterpart of the above discrete-time problem. No other counterpart model was found in the literature, including the vast literature on optimal control, which presumably deals with similar problems but in a continuous-time framework. The new problem formulation is the basis for a new class of models, which forms an alternative way of analyzing certain dynamic lot-sizing problems. This new alternative could sometimes be simpler than the analysis in the discrete case.

Acknowledgement

The authors wish to thank the participants of the Research Forum in the Department of Industrial Engineering at Tel Aviv University for their comments on an earlier draft of this paper.