A hybrid metaheuristic algorithm for location inventory routing problem with time windows and fuel consumption

We introduce a multi-period location-inventory-routing problem with time windows and fuel consumption, which simultaneously optimizes the location, routing, and inventory decisions for both the distribution center and customers in a multi-echelon supply chain. To better reflect reality, the fuel consumption is also incorporated into the variable transportation cost. The problem is formulated as a mixed integer nonlinear programming model. We then propose a two-stage hybrid metaheuristic algorithm to address this problem. In the first stage, a customized genetic algorithm is proposed. In the second stage, a gradient descent algorithm is used to improve the inventory decision to further reduce the total cost. Results of numerical experimentations on generated instances confirm the effectiveness of the algorithm. Results show that inventory management activities contribute considerably to total cost saving. Given the cost trade-off between transportation and inventory, the retailers' inventory level shows more shortages after post-optimization, while the inventory level in the distribution centers can be either reduced or increased, depending on the spatial distribution of retailers in the vicinity of the distribution center. Sensitivity analysis on the model parameters is also conducted to provide managerial insights.