Supply Chain Scheduling: Conflict and Cooperation in Assembly Systems

We study conflict and cooperation issues in supply chain manufacturing. Consider an assembly system where suppliers provide parts to a manufacturer. A product cannot be delivered until all its parts have been supplied. The manufacturer performs nonbottleneck operations, for example, outsourced assembly, packaging, and delivery for each product. Two classical scheduling objectives are considered: minimization of the total completion time and of the maximum lateness. We analyze how far from optimal the best schedule for a suppliers' scheduling problem can be for the corresponding manufacturer's problem, and vice versa. To resolve these conflicts, we consider four alternative scenarios for the relative bargaining power of the suppliers and the manufacturer, and in each case describe a practical mechanism for cooperation between the decision makers. Evaluating the cost of conflict and the benefit of cooperation in these scenarios requires the solution of various scheduling problems by the suppliers, the manufacturer, and the overall system. For all these scheduling problems, we provide either an efficient algorithm or a proof of intractability. Moreover, for two problems that we show are intractable, we describe heuristics and analyze their worst case performance or demonstrate asymptotic optimality of their solutions. We demonstrate computationally that the cost saving realized by cooperation between the decision makers is significant in many cases. Extensions of our models to consider bottleneck operations at the manufacturer and transportation times are also developed.