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

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.