Decentralized decision-making and protocol design for recycled material flows

Reverse logistics networks often consist of several tiers with independent members competing at each tier. This paper develops a methodology to examine the individual entity behavior in reverse production systems. We consider two tiers in the network, collectors and processors. The collectors determine individual flow functions that relate the flow they provide each processor to the overall vector of prices that the processors determine. Because the exact final prices are unknown, each collector solves a robust optimization formulation where the prices paid by the processors are assumed to be within given ranges. The processors compete for the flow from the collectors until the Nash equilibrium is reached in this competitive tier, which sets the vector of prices to be offered to the collectors. To demonstrate the approach, a numerical example is given for a prototypical recycling network.