A hybrid scenario cluster decomposition algorithm for supply chain tactical planning under uncertainty

Abstract

We propose a Hybrid Scenario Cluster Decomposition (HSCD) heuristic for solving a large-scale multi-stage stochastic mixed-integer programming (MS-MIP) model corresponding to a supply chain tactical planning problem. The HSCD algorithm decomposes the original scenario tree into smaller sub-trees that share a certain number of predecessor nodes. Then, the MS-MIP model is decomposed into smaller scenario-cluster multi-stage stochastic sub-models coordinated by Lagrangian terms in their objective functions, in order to compensate the lack of non-anticipativity corresponding to common ancestor nodes of sub-trees. The sub-gradient algorithm is then implemented in order to guide the scenario-cluster sub-models into an implementable solution. Moreover, a Variable Fixing Heuristic is embedded into the sub-gradient algorithm in order to accelerate its convergence rate. Along with the possibility of parallelization, the HSCD algorithm provides the possibility of embedding various heuristics for solving scenario-cluster sub-models. The algorithm is specialized to lumber supply chain tactical planning under demand and supply uncertainty. An ad-hoc heuristic, based on Lagrangian Relaxation, is proposed to solve each scenario-cluster sub-model. Our experimental results on a set of realistic-scale test cases reveal the efficiency of HSCD in terms of solution quality and computation time.