Optimal shipping, collaboration, and outsourcing decisions in a hybrid cross-docking supply chain

Motivated by the supply chain of our oil-field service industry partner, we study shipping, collaboration, and outsourcing decisions in a decentralized, three-stage supply chain consisting of suppliers, a hybrid cross-dock facility, and oil well facilities. Unlike pure cross-docking, which transships arriving products quickly downstream, hybrid cross-docking allows for inventory to remain at the cross-dock for multiple periods. We formulate multi-period, optimization models to minimize costs of different members in a hybrid cross-docking supply chain and establish structural properties of optimal solutions. We make use of those results to identify conditions under which hybrid cross-docking is more cost efficient than pure cross-docking. Our results provide managerial insights regarding when a hybrid cross-dock should be enabled, and the value of the resulting cost savings. We also quantify the value of collaboration among different stages in the supply chain. Upstream collaboration results in 1% to 9% average cost savings for the cross-dock, while downstream collaboration generates 4% to 13% in average cost savings for oil well facilities, depending on the number of products and their holding cost. We also develop a Stackelberg pricing game between a logistics company and oil well facilities seeking to lower their costs by outsourcing their transportation and inventory operations. We identify the structure of oil well facilities’ best response to the price of outsourcing services, as well as the structure of the logistics provider’s optimal pricing policy. Our findings and models, based on current literature, provide application focused tools that allow managers to improve cross-docking operations in their supply chains, realize the benefits of collaborations, and make better outsourcing decisions.