Optimal fleet composition via dynamic programming and golden section search

Ryan Loxton; Qun Lin

doi:10.3934/jimo.2011.7.875

Article Contents

2011, Volume 7, Issue 4: 875-890. Doi: 10.3934/jimo.2011.7.875

This issue Previous Article Uniform estimates for ruin probabilities in the renewal risk model with upper-tail independent claims and premiums Next Article A full-Newton step interior-point algorithm for symmetric cone convex quadratic optimization

Optimal fleet composition via dynamic programming and golden section search

Ryan Loxton^1, and
Qun Lin^1,

1.
Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845

Received: August 31, 2010

Revised: April 30, 2011

Published: September 2011

Abstract Related Papers Cited by

Abstract

In this paper, we consider an optimization problem arising in vehicle fleet management. The problem is to construct a heterogeneous vehicle fleet in such a way that cost is minimized subject to a constraint on the overall fleet size. The cost function incorporates fixed and variable costs associated with the fleet, as well as hiring costs that are incurred when vehicle requirements exceed fleet capacity. We first consider the simple case when there is only one type of vehicle. We show that in this case the cost function is convex, and thus the problem can be solved efficiently using the well-known golden section method. We then devise an algorithm, based on dynamic programming and the golden section method, for solving the general problem in which there are multiple vehicle types. We conclude the paper with some simulation results.

Keywords:

Mathematics Subject Classification: Primary: 90B06, 90C25, 90C39; Secondary: 90C10.

Citation:

Related Papers

Cited by

References

[1]	M. S. Bazaraa, H. D. Sherali and C. M. Shetty, "Nonlinear Programming: Theory and Algorithms," 3^rd edition, Wiley-Interscience [John Wiley & Sons], Hoboken, New Jersey, 2006.
[2]	R. Bellman, "Dynamic Programming," Dover Publications, Inc., Mineola, New York, 2003.
[3]	J. Couillard, A decision support system for vehicle fleet planning, Decision Support Systems, 9 (1993), 149-159.doi: 10.1016/0167-9236(93)90009-R.
[4]	G. Ghiani, G. Laporte and R. Musmanno, "Introduction to Logistics Systems Planning and Control," John Wiley, Chichester, 2004.
[5]	A. Hoff, H. Andersson, M. Christiansen, G. Hasle and A. Løkketangen, Industrial aspects and literature survey: Fleet composition and routing, Computers & Operations Research, 37 (2010), 2041-2061.doi: 10.1016/j.cor.2010.03.015.
[6]	A. Imai and F. Rivera, Strategic fleet size planning for maritime refrigerated containers, Maritime Policy & Management, 28 (2001), 361-374.doi: 10.1080/03088830010020629.
[7]	D. Kirby, Is your fleet the right size?, Operational Research Quarterly, 10 (1959), 252.doi: 10.1057/jors.1959.25.
[8]	M.-Y. Lai, C.-S. Liu and X.-J. Tong, A two-stage hybrid meta-heuristic for pickup and delivery vehicle routing problem with time windows, Journal of Industrial & Management Optimization, 6 (2010), 435-451.doi: 10.3934/jimo.2010.6.435.
[9]	D. G. Luenberger and Y. Ye, "Linear and Nonlinear Programming," 3^rd edition, International Series in Operations Research & Management Science, 116, Springer, New York, 2008.
[10]	H. L. Royden, "Real Analysis," 3^rd edition, Macmillan Publishing Company, New York, 1988.
[11]	I. F. A. Vis, R. B. M. de Koster and M. W. P. Savelsbergh, Minimum vehicle fleet size under time-window constraints at a container terminal, Transportation Science, 39 (2005), 249-260.doi: 10.1287/trsc.1030.0063.