Optimization of the total present value of profits under semi Markov conditions with applications in the optimal ferry dispatch problem

Authors:
Michael N. Katehakis;Ioannis Baltzakis;Victoria Ungureanu
Affiliations:
Rutgers Business School, Department of MSIS, University Newark, New Jersey;Technological Institute of Crete, School of Administration and Finance, Iraklio, Greece;Standard & Poor's, New York, NY
Venue:
CONTROL'08 Proceedings of the 4th WSEAS/IASME international conference on Dynamical systems and control
Year:
2008

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Abstract

In this paper we have surveyed theory related to optimization of SemiMarkov processes and we have applied these techniques to a simple dynamic ferry dispatch problem, when the customers arrive at a Ferry according to a Poisson process with rate λ 0. We have formulated this dispatch problem as a two action semi-Markov decision process and we have illustrated computationally that an optimal dispatch policy is characterized by a single critical number x0 such that it is optimal to wait until there are at least x0 customers on the ferry before a departure occurs.