A Generalization of Dynamic Programming for Pareto Optimization in Dynamic Networks

The Algorithm in this paper is designed to find the shortest path in a network given time‐dependent cost functions. It has the following features: it is recursive; it takes place bath in a backward dynamic programming phase and in a forward evaluation phase; it does not need a time‐grid such as in Cook and Halsey and Kostreva and Wiecek's "Algorithm One’; it requires only boundedness (above and below) of the cost functions; it reduces to backward multi‐objective dynamic programming if there are constant costs. This algorithm has been successfully applied to multi‐stage decision problems where the costs are a function of the time when the decision is made. There are examples of further applications to tactical delay in production scheduling and to production control.