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The production-inventory-distribution-routing problem: An integrated formulation and solution framework

Supply chain management includes several functions that are planned and managed to improve the total performance of the supply chain, the general objective is to minimize system-wide costs while satisfying service level requirements. Previously, each function was addressed as an isolated problem, however, it was found that focusing on cost minimization in one area of the supply chain often leads to higher costs in other areas; this is why the integration of different supply chain management functions has received increasing consideration recently. The production-inventory-distribution-routing integrated planning is a step forward towards more integration and realism in supply chain management, as it integrates lot-sizing, inventory management, distribution planning, and vehicle routing problems. In this paper, a review of the recent literature addressing the joint consideration of these aspects is presented and research gaps are highlighted. It was noticed that the existing models tackle relatively simple cases. However, in real life, more complex systems and variants exist. To make a step forward, a generic problem description and a mathematical model are proposed to address the production-inventory-distribution-routing problem. Finally, a conceptual framework is presented to illustrate the existing and potential work in this topic; this framework is expected to provide good directions for researchers to work in this area.