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Journal of Optimization
Volume 2013 (2013), Article ID 960879, 12 pages
http://dx.doi.org/10.1155/2013/960879
Research Article

Dynamic Optimization Technique for Distribution of Goods with Stochastic Shortages

Department of Mathematics, Faculty of Physical Sciences, University of Benin, P.M.B. 1154, Benin City, Edo State, Nigeria

Received 2 April 2013; Accepted 24 September 2013

Academic Editor: Eric S. Fraga

Copyright © 2013 Charles I. Nkeki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This work considers the distribution of goods with stochastic shortages from factories to stores. It is assumed that in the process of shipping the goods to various stores, some proportion of the goods will be damaged (which will lead to shortage of goods in transit). The cost of the damaged goods is added to the cost of the shipment. A proportion of the total expected cost of the shortage goods is assumed to be recovered and should be deducted from the total cost of the shipment. In order to determine the minimum transportation costs for the operation, we adopt dynamic optimization principles. The optimal transportation cost and optimal control policies of shipping the goods from factories to stores were obtained. We find that the optimal costs of the goods recovered could be determined. It was further found that the optimum costs of distributing the goods with minimum and maximum error bounds coincide only at infinity.