A Variable Neighborhood Decomposition Search Methodology for Production-distribution Planning in Supply Chain Management

The planning and scheduling of the inventory, production and distribution functions remains an open research area, since few studies have developed models allowing their integrated management. In this paper, we consider a three-stage supply chain, for which a sustainable inventory-production-distribution plan over a multi-period horizon is constructed. The associated program takes the form of a general mixed-integer program, for which the sole reliance upon exact methods is shown to be insufficient. We propose a solving methodology based on the variable neighborhood decomposition search metaheuristic, that can be seen as a stagewise exploration of increasingly large neighborhoods. The stages are related to the decomposition scheme, i.e., the order on which integrality conditions are restored. Within each stage, a sequence of increasingly large neighborhoods is defined relying on the variable neighborhood search metaheuristic, while the exploration of the successive neighborhoods is performed using a branch-and-bound algorithm. The methodology is validated through its application to a problem faced by a North American supply chain. Empirical results show that (i) the methodology is most performing when the decomposition scheme accounts for the possibility of resources bottleneck, (ii) the primary source of savings is the distribution function, and (iii) congestion must be defined with respect to the availability of the distribution resources at the periods with high requirements.