Multi-outsourcing supply chain coordination under yield and demand uncertainties

As a popular production mode, outsourcing enables the cost saving for original equipment manufacturer (OEM) and the acquisition of advanced technology for contract manufacturer (CM). We consider a multi-outsourcing supply chain within the voluntary compliance regime. The game between one OEM facing uncertain demand and arbitrary CMs owning uncertain yields is modeled to study the interactions regarding lot-sizing decisions. A general method is developed to prove the concavity of profit functions, which is formidable to accomplish based on Hessian Matrix. The optimal ordering and production strategies are subsequently characterized. A revenue sharing with surplus purchase contract with great flexibility in parameter selection is proposed to coordinate the supply chain. We find that there exist threshold outsourcing prices beyond which the CMs are motivated to overproduce, otherwise they tend to produce in consistent with the orders. In a competitive market, price war is not a wise strategy for CM due to profit sacrifice. By contrast, if the selling price charged by the OEM is high, a smart CM can appropriately raise its outsourcing price because the order quantity difference among CMs is relatively small. Although supply stability improvement and outsourcing price reduction are both welcomed by the OEM, the latter is more important for it to consider in allocating orders.