DYNAMIC SHORTEST PATHS IN ACYCLIC NETWORKS WITH MARKOVIAN ARC COSTS

PSARAFTIS, HN; TSITSIKLIS, JN

dc.contributor.author	PSARAFTIS, HN	en
dc.contributor.author	TSITSIKLIS, JN	en
dc.date.accessioned	2014-03-01T01:09:22Z
dc.date.available	2014-03-01T01:09:22Z
dc.date.issued	1993	en
dc.identifier.issn	0030-364X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10934
dc.subject	Dynamic Shortest Paths	en
dc.subject.classification	Management	en
dc.subject.classification	Operations Research & Management Science	en
dc.title	DYNAMIC SHORTEST PATHS IN ACYCLIC NETWORKS WITH MARKOVIAN ARC COSTS	en
heal.type	journalArticle	en
heal.identifier.primary	10.1287/opre.41.1.91	en
heal.identifier.secondary	http://dx.doi.org/10.1287/opre.41.1.91	en
heal.language	English	en
heal.publicationDate	1993	en
heal.abstract	We examine shortest path problems in acyclic networks in which arc costs are known functions of certain environment variables at network nodes. Each of these variables evolves according to an independent Markov process. The vehicle can wait at a node (at a cost) in anticipation of more favorable arc costs. We first develop two recursive procedures for the individual arc case, one based on successive approximations, and the other on policy iteration. We also solve the same problem via parametric linear programming. We show that the optimal policy essentially classifies the state of the environment variable at a node into two categories: green states for which the optimal action is to immediately traverse the arc, and red states for which the optimal action is to wait. We then extend these concepts for the entire network by developing a dynamic programming procedure that solves the corresponding problem. The complexity of this method is shown to be O(n2K + nK3), where n is the number of network nodes and K is the number of Markov states at each node. We present examples and discuss possible research extensions.	en
heal.publisher	OPERATIONS RESEARCH SOC AMER	en
heal.journalName	OPERATIONS RESEARCH	en
dc.identifier.doi	10.1287/opre.41.1.91	en
dc.identifier.isi	ISI:A1993KN58200007	en
dc.identifier.volume	41	en
dc.identifier.issue	1	en
dc.identifier.spage	91	en
dc.identifier.epage	101	en