A distributed coordination for a single warehouse-multiple retailer problem under private information

In this paper, we consider a distributed coordination for single warehouse and multiple retailer problems. The objective is to minimize the sum of the setup cost and inventory holding cost incurring among warehouse and retailers in a distributed manner. We propose two algorithms based on the alternating direction method (ADM) and diagonal quadratic approximation method (DQAM) that utilize Augmented Lagrangian function and multiplier updating scheme. The ADM-based algorithm solves the problem by communicating partial information between a coordinator, the warehouse and retailers. The DQAM-based algorithm does not require a coordinator. The cooperation to minimize the system-wide cost is performed by the direct communication of the warehouse and retailers. The proposed algorithms guarantee 6% deviation from optimal solution in the worst case. The computational experiments and the comparison with existing decentralized approaches are presented.