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IMA Journal of Management Mathematics Advance Access originally published online on July 4, 2005
IMA Journal of Management Mathematics 2006 17(2):143-158; doi:10.1093/imaman/dpi032
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© The authors 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Dynamic programming approaches for equipment replacement problems with continuous and discontinuous technological change

Joseph C. Hartman** and Jennifer Rogers

Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA 18015, USA

** Email: jch6{at}lehigh.edu

We consider a capital equipment replacement problem where the assets available for purchase evolve over time according to continuous and discontinuous functions of technological change. Discontinuous technological change captures the arrivals of breakthrough technologies over time while continuous technological change models the periodic improvement of available assets between breakthroughs. We present two dynamic programming formulations, developed from the classic equipment replacement models of Bellman and Wagner, and compare them for cases including probabilistic arrivals for technology breakthroughs, probabilistic costs associated with the breakthrough technologies and multiple challengers. We analyse both models in terms of their state space growth according to various parameters, including the horizon, maximum asset service life and the maximum number of challengers in a period. The model developed from Wagner's original method appears to hold more promise in terms of being able to handle larger instances of realistic problems. We also discuss potential approaches to solving this problem as well as the necessary data and sources.

Keywords: capital equipment replacement; technological change; dynamic programming


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