A coordination mechanism for capacitated lot-sizing in non-hierarchical n-tier supply chains

In the context of an n-tier supply chain, a coalition of agents is considered that has to jointly solve a distributed multi-level capacitated lot-sizing problem in order to minimize the agents joint total costs. Due to asymmetric information between the agents, e.g., with respect to setup costs, inventory holding costs or available machine capacities, this problem cannot be solved by a single, central decision maker. Therefore, this paper introduces a coordination mechanism to enable collaborative planning by taking asymmetric information into account. Furthermore, the coordination mechanism is able to deal with non-hierarchical assignment of items to agents within a mutual bill of material. To evaluate the coordination mechanism, test instances for the classical multi-level capacitated lot sizing problem are extended. A computational study shows that the coordination mechanism works well for instances without setup times. That is, for these instances solution quality for the distributed case deviates on average by less than five percent from best-known solutions in the non-distributed case.