The capacitated multi-level lot-sizing problem with distributed agents

Cloud manufacturing is an emerging concept that enables the orchestration, matching, and sharing of services or resources among collaboration partners or intra-plant facilities. In this context, we introduce the capacitated multi-level lot sizing problem with transshipments and set up carry-over. We consider components that can only be produced by one specific agent as well as components that can be provided by more than one producer. As capacities are limited, agents might have to share resources and jointly cover required demands. In this case, finished components are transshipped between agents. As an agent can be in charge of producing more than one component, we include the concept of set up carry-over into our modeling. We address a centralized planning approach, where the objective is to find a globally optimized lot sizing plan for all participating agents. Thus, we cover both horizontal and vertical collaboration between agents. The new problem class is formulated mathematically. We propose a matheuristic solution approach based on a fix-and-optimize procedure, where the interrelatedness of decision variables is taken into account. We benchmark the proposed approached against optimal or proven near-optimal solutions. Additionally, a decentralized upstream lot-shifting heuristic is generated, which allows us to compare the results to situations in which no central decision maker is present. Both solution approaches are applied to an extensive set of test instances. We show that the centralized approach is able to reduce the total cost by up to 47%. We assess the different levels of interrelatedness of the decision variables and demonstrate that an increase in interrelatedness can even lead to a decrease in the solution quality. Moreover, we provide valuable managerial insights into the impact of the bill-of-material structure on problem complexity.