Multi-item production routing problem with backordering: a MILP approach

• Published in: International journal of production research Vol. 54; no. 4; pp. 1076 - 1093
• Main Authors: Brahimi, Nadjib, Aouam, Tarik
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 16-02-2016; Taylor & Francis LLC
• Subjects: backordering; Decisions; Heuristic; Integer programming; Linear programming; lot sizing problem; Mathematical models; Mixed integer; Optimization; Production planning; production routing problem; relax-and-fix heuristic; Routing; Sales; Solvers; Storage capacity; vehicle routing problem
• ISSN: 0020-7543; 1366-588X
• DOI: 10.1080/00207543.2015.1047971

The aim of this paper is to present mixed integer linear programming formulations for the production routing problem with backordering (PRP-B) and a new hybrid heuristic to solve the problem. The PRP-B is considered in the context of a supply chain consisting of a production facility with limited production and storage capacities and geographically dispersed points of sale with limited storage capacities. The PRP-B integrates multiple item lot sizing decisions and vehicle routing decisions to the points of sale, where backordering of end customer demands is allowed at a penalty. Two integrated mixed integer programming models are formulated and a solution procedure consisting of a relax-and-fix heuristic combined with a local search algorithm is proposed. The numerical results show that this hybrid heuristic outperforms a state-of-the-art MIP commercial solver, in terms of solution quality and CPU times.