A Generalization of Dynamic Programming for Pareto Optimization in Dynamic Networks

Abstract

The Algorithm in this paper is designed to find theshortest path in a network given time-dependent cost functions. It hasthe following features: it is recursive; it takes place bath in abackward dynamic programming phase and in a forward evaluation phase; itdoes not need a time-grid such as in Cook and Halsey and Kostreva andWiecek's "Algorithm One”; it requires only boundedness (above andbelow) of the cost functions; it reduces to backward multi-objectivedynamic programming if there are constant costs. This algorithm has beensuccessfully applied to multi-stage decision problems where the costsare a function of the time when the decision is made. There are examplesof further applications to tactical delay in production scheduling andto production control.