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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 301309, 12 pages
Research Article

Optimal Control of a Make-to-Stock System with Outsourced Production and Price-Sensitive Demand

1Business School, Hohai University, No. 8 Fochen West Road, Jiangning District, Nanjing City 211100, China
2Department of Management Science, City University of Hong Kong, Kowloon, Hong Kong

Received 31 March 2014; Accepted 27 May 2014; Published 6 July 2014

Academic Editor: Xiaolin Xu

Copyright © 2014 Liuxin Chen et al. 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.


We consider a make-to-stock system with controllable demand rate (by varying product selling price) and adjustable service rate (by outsourcing production). With one outsourcing alternative and a choice of either high or low price, the system decides at any point in time whether to produce or even outsource for additional capacity as well as which price to sell the product at. We show in the paper that the optimal control policy is of dynamic threshold type: all decisions are based on the product inventory position which represents the state of the system; there is a state dependent base stock level to decide on production and a higher level on outsourcing; and there is a state dependent threshold which divides the choice of high and low prices.