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An equilibrium solution to supply chain synchronisation.

Pearson, Mike


Mike Pearson


The classical two-echelon problem, {(C, V), (Q, R)}, is stated as follows. A producer (manufacturer) attempts to determine the cost to charge a distributor (wholesaler/retailer) and the credit/unit to pay for unsold units returned. A distributor determines the amount of inventory to order from the producer and the retail price to charge the customer. Both the producer and the distributor attempt to maximize profit. There is no generalized equilibrium solution to this problem. The manufacturer predicts supply in order to supply demand. That is, the manufacturer allocates demand that supplies the customer. On the other hand, the retailer predicts demand in order to demand supply. That is, the retailer allocates supply that the customer demands. We observe a natural duality in the relationship between the manufacturer and the retailer. We introduce an equilibrium solution to the two-echelon problem through prediction capability and the primal–dual transformation. The stages required to establish the primal–dual solution are harmonization, cooperation, coordination and synchronization. This changes the emphasis from optimization at the manufacturer and retailer levels to the joint search for capability and optimality based on limited information exchange and coordinated allocation strategy. Previous formulations are special cases. The analysis is extended to the supply chain.


Pearson, M. (2003). An equilibrium solution to supply chain synchronisation. IMA Journal of Management Mathematics, 14, 165-185.

Journal Article Type Article
Publication Date Jul 3, 2003
Deposit Date May 15, 2008
Print ISSN 1471-678X
Electronic ISSN 1471-6798
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 14
Pages 165-185
Keywords inventory; supply chain; newsvendor problem; forecasting; pricing; simultaneous equilibrium;
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