A variable neighborhood decomposition search method for supply chain management planning problems

Few models have been developed for the integrated planning and scheduling of the inventory, production and distribution functions. 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 use a solution algorithm based on the variable neighborhood decomposition search metaheuristics, 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 neighborhoods is defined relying on the variable neighborhood search metaheuristics, 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 large supply chain. Empirical results show that (i) the methodology performs best when the decomposition scheme accounts for the possibility of resources bottleneck, (ii) the primary source of savings originates from the distribution function and (iii) congestion must be defined with respect to the availability of the distribution resources at the periods with high requirements.