# American Institute of Mathematical Sciences

October  2005, 1(4): 415-432. doi: 10.3934/jimo.2005.1.415

## Optimization of the lifetime of capital equipment using integral models

 1 College of Business and Economics, Houston Baptist University, 7502 Fondren Road, Houston, TX 77074-3298, United States 2 Department of Mathematics, Prairie View A{\&}M University, P.O. Box 4189, Prairie View, TX 77446-4189, United States

Received  February 2005 Revised  September 2005 Published  October 2005

In Operations Research, the equipment replacement process is usually modeled as a discrete sequential decision problem. The alternative approach is developed in vintage capital models, which explicitly involve the lifetime of capital equipment and are described by the integral equations of a special type. The paper exposes a general investigation framework for the optimal control of the integral models with endogenous lags, which is applied to meaningful one- and two-sector vintage models. The analysis leads to nontrivial results such as turnpike properties of the optimal equipment lifetime and corresponding management strategies of equipment replacement.
Citation: Yuri Yatsenko, Natali Hritonenko. Optimization of the lifetime of capital equipment using integral models. Journal of Industrial & Management Optimization, 2005, 1 (4) : 415-432. doi: 10.3934/jimo.2005.1.415
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