Developing the Inventory Routing Problem with Backhauls, Heterogeneous Fleet and Split Service

One of the most important points in a supply chain is customer-driven modeling, which reduces the bullwhip effect in the supply chain, as well as the costs of investment on the inventory and efficient transshipment of the products. Their homogeneity is reflected in the Inventory Routing Problem, which is a combination of distribution and inventory management. This paper expands the classical Inventory Routing Problem based on the Multiple Delivery Strategy along with one of the functionalities of routing problem, namely, "backhauls", with a priority consideration for linehaul customers.  Then it has been modeled in the form of a problem with Multi-period, multi-product, and multi- vehicle planning horizons in which stock out is not allowed. Moreover, for an optimal use of the vehicle capacity to serve the linehaul and backhaul customers, this study adopted a “split service” problem to the model, which also increases the complexity of the problem. First, considering the above-mentioned assumptions, a new mathematical model is proposed in the form of mixed integer programming for the problem defined in this paper. Then, since the stated problem can be considered among the non-deterministic polynomial-time hard, an efficient meta-heuristic genetic algorithm is provided for solving it. At the end, the numerical results obtained by this algorithm are analyzed using the randomized test problems. The result shows that by adopting a split service approach, 70% of the test problems will demonstrate cost reduction.