Optimization and Coordination in Decentralized Supply Chains with Vertical Cross-Shareholding

Abstract

We consider a decentralized supply chain in which an upstream firm sells a product to a downstream firm, who faces a random demand. The upstream firm and the downstream firm are linked by vertical cross-shareholding. This enables each firm to share the the other firm's operating earning as determined by the shares held, but does not change control rights over managerial decisions. The upstream firm and the downstream firm seek to maximize their own excepted profits, after dividends. We investigate both the push and the pull supply chains. We first derive the optimal pricing and production decisions of the two firms, and observe that the impacts of vertical shareholding on efficiencies of push and pull supply chains are very different. We then study supply chain coordination. We find that to achieve a win-win coordination, one of the two firms may need to get a negative operating earning first, and then share the other firm's operating earning. We propose linear transfer payment to coordinate the supply chains. The proposed mechanisms are parameter rich, each contains three parameters. We show that the proposed mechanisms can coordinate the supply chains with vertical cross-shareholding, and result in a win-win situation.