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IMA Journal of Management Mathematics Advance Access originally published online on September 23, 2005
IMA Journal of Management Mathematics 2006 17(3):245-255; doi:10.1093/imaman/dpi040
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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.

Optimization of financial and energy structure of productive capital

N. Hritonenko**,1 and Y. Yatsenko***,2

1 Department of Mathematics, Prairie View A&M University, PO Box 4189, Prairie View, TX 77446-4189, USA, 2 College of Business and Economics, Houston Baptist University, 7502 Fondren Road, Houston, TX 77074-3298, USA

** Email: nahritonenko{at}pvamu.edu

*** Email: yyatsenko{at}hbu.edu

Optimal control of special non-linear Volterra integral equations is used to optimize the structure and lifetime of age-dependent productive capital at an individual enterprise level. The equations describe a multifactor vintage capital model. The optimization problem is to select investment, specific capital cost, specific energy consumption and capital lifetime that maximize net profit on finite and infinite horizons. The structure of optimal trajectories is investigated and relevant relations among technological and financial parameters of the productive capital are established.

Keywords: optimal control; non-linear Volterra integral equations; unknown delay; vintage capital models; endogenous capital lifetime; optimal energy consumption

Received on 2 November 2004. revised on 16 May 2005. accepted on 30 August 2005.


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