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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 85103, 24 pages

Modelling and analysis of a network organization for cooperation of manufacturers on production capacity

Graduate School of Business, KoƧ University, Rumelifeneri Yolu Saryer, Istanbul 34450, Turkey

Received 28 November 2005; Accepted 2 January 2006

Copyright © 2006 Bariş Tan. 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 present an analytical model to analyze the operation of a productive cooperation network where producers cooperate on production capacity. Producers have limited capacity and have access to subcontractors at a higher cost. A single-unit auction-based allocation mechanism is proposed to allocate an arriving order based on the producers' cost structures and their current loads to maximize the total profit. We show that when the costs are private information, producers are willing to cooperate in order to increase their expected profit. Furthermore, it is shown that there is an equilibrium where producers bid their actual costs. The cooperation can also generate extra profit to cover a part of its operating expenses with this allocation mechanism. A continuous-time Markov chain model is utilized to evaluate the performance of the allocation mechanism where producers submit their myopic best response bids. The cooperation case is also compared with the no-cooperation case and also with the centralized operation of producers.