Modern production systems require high levels of flexibility, integration, and efficiency in order to reach economic and environmental sustainability. Tight integration among delocalized production and logistics systems is fundamental for, manufacturing systems based on synchronization and lead time reduction. In this paper we present a mathematical model describing a network in which nodes represent production plants or distribution centers while arc are multimodal connections. Production is considered in modeling with respect to constraints related to the Bill of Material (BOM) of the product to be delivered. The model considers costs, sustainability factors and constraints related to distribution, inventory and production. BOM is considered as additional constraint at operational decisional level. Moreover, sustainability factors are considered in the objective function. The problem is to find the optimal routes for serving customers with a given set of vehicles, production plants, logistics platforms, on the given multimodal network. The logistics platforms can be viewed as the network nodes where transportation modes can be changed. When a product is requested by the customer, an origin destination transportation must be fulfilled. BOM considerations imply that additional intermediate travels for required material are needed. This requirements are considered in the model as additional intermediate origin destination transportations requests. The problem is developed as Mixed Integer Linear Programming (MILP) model, and realistic test instances are exploited for validation purposes of the objective function.
Confessore, G., Galiano, G., Liotta, G., & Stecca, G. (2013). A production and logistics network model with multimodal and sustainability considerations. In Procedia CIRP (Vol. 12, pp. 342–347). Elsevier B.V. https://doi.org/10.1016/j.procir.2013.09.059