Two Efficient Meta-Heuristic Algorithms for the Robust Inventory Routing Problem with Backhaul

Abstract

The inventory routing problem (IRP) involves the integration and coordination of two components of the logistics value chain: inventory management and vehicle routing. Therefore, consideration of this issue can be effective in decision making of the organization and will lead to lower costs or other goals. Our objective in this article is to examine a new inventory-routing model and solve it with meta-heuristic methods. For more flexibility of the model, and approaching the real world, the model of this article is considered multi-period and multi-product. Also, two objective functions, including minimizing system costs and transportation risk, are included in this model. Given that the main parameter of the model, that is, demand, is uncertain, we have used a robust optimization approach to solve it, and since this model is in the classification of NP-Hard problems, we have used two meta-heuristic algorithms consisting of non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective imperialist competitive algorithm (MOICA). By examining the model in two deterministic and robust conditions, according to two criteria, the mean values of the objective function and its standard deviation, it has been determined that in almost all cases, the robust optimization model produces better solutions. Also, between the two meta-heuristics method, the NSGA-II algorithm has shown better quality according to the mentioned criteria. Obviously, taking into account the different features of a model increases its efficiency. But this, obviously, makes the model even more complex. However, this complexity of models can work like a real system. Our attention in this article has been to this subject. To analyze such models, exact methods do not have the required performance and paying attention to heuristic and meta-heuristic methods is very effective. In this paper, a robust optimization and meta-heurictic approaches focus on these goals.

Keywords

• inventory routing problem with backhaul
• meta-heuristic algorithm
• multi-objective model
• robust optimization