Mathematical Modeling and the Presentation of A Population-Based Meta- Heuristic Algorithm for Multi-Product, Multi-Vehicle Inventory- Routing Problem, With Backhauls

One of the key issues in the operational management of the supply chain is the inventory routing problem, which is a combination of inventory management and transportation planning. According to the literature review, this paper combines one of the practical features of routing problem named as "backhauls" with the multi-product, multi-period, multi-Vehicle inventory- routing problem. The stock out and backlogging is not allowed in this model. The Strategy of routing is Multiple Delivery Strategy. This problem is non-deterministic polynomial-time hard (NP-hard) and the solution time, using the exact methods, increase exponentially with the increase in the dimensionality of the problem. Therefore, after introducing the research background, a new mathematical model is proposed in the form of the mixed integer programming for the problem defined in this paper. As follows, an efficient meta-heuristic genetic algorithm is provided to solve it. At the end, the numerical results obtained by this algorithm are analyzed using the randomized testing problems.