Title: A linear dynamic model of production-inventory with debt repayment: optimal-choice management strategies

Authors: Ekaterina Tuchnolobova; Victor Terletskiy; Olga Vasilieva

Addresses: Institute for Mathematics, Economics, and Informatics, Irkutsk State University, Bulvar Gagarina 20, Irkutsk 664003, Russia ' Institute for Mathematics, Economics, and Informatics, Irkutsk State University, Bulvar Gagarina 20, Irkutsk 664003, Russia ' Department of Mathematics, Universidad del Valle, Calle 13, No. 100-00, Cali, Colombia

Abstract: In this paper, we present a simple microeconomic model with linear continuous-time dynamics that describes a production-inventory system with debt repayment. This model is formulated in terms of optimal control and its exact solutions are derived by prudent application of the maximum principle under different sets of initial conditions (scenarios). For a potentially profitable small firm, we also propose some alternative (and not exactly bang-bang) short-term control strategies resulting in a positive final profit and prove their optimality. Practical implementation of such strategies is also discussed.

Keywords: production-inventory systems; debt repayment; optimal choice strategies; not purely bang-bang strategies; linear modelling; microeconomic models; continuous-time dynamics; optimal control; small firms.

DOI: 10.1504/IJMOR.2014.064846

International Journal of Mathematics in Operational Research, 2014 Vol.6 No.5, pp.610 - 630

Received: 08 Dec 2012
Accepted: 07 Jun 2013
Published online: 11 Oct 2014 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article