Model-approximated dynamic programming based on decomposable state transition probabilities

Abstract

In this paper, a discrete model of an elevator system and a design of dynamic programming (DP) method based on that model are shown. The method is followed by a modified DP method on approximated state transition models. The discrete model theoretically considers the causes of a system's probabilistic behavior, and leads such approximation by the reduction of the insignificant constituent of them. In computational illustrations, the two DP methods are applied to two problems of small scale. The results show that the policies obtained by DP methods are both statistically better than an existing elevator allocation rule, and the modified method requires less computational time than the another.

Proposal and Progress of a Road-map to Bridge Theoretical and Practical Approaches for Elevator Operation Problems

“…Other studies have no guarantee to yield optimal solutions, due to the incomplete formulation [12], the utilization of the receding horizon approach [11], and the utilization of the genetic algorithm [13]. One of the authors made it possible to yield optimal solutions for the deterministic and stochastic EOPs by deploying the integer linear programming [4,16] and the dynamic programming [15], respectively. However, they are not applicable to real problems, since the problem size becomes exponentially huge on the deterministic, and stochastic EOPs according to the number of passengers and the number of cars, and the number of floors and the number of cars, respectively.…”