An augmented Tabu search algorithm for the green inventory-routing problem with time windows

Abstract Transportation allocates a significant proportion of Gross Domestic Product (GDP) to each country, and it is one of the largest consumers of petroleum products. On the other hand, many efforts have been made recently to reduce Greenhouse Gas (GHG) emissions by vehicles through redesigning and planning transportation processes. This paper proposes a novel Mixed-Integer Linear Programming (MILP) mathematical model for Green Inventory-Routing Problem with Time Windows (GIRP-TW) using a piecewise linearization method. The objective is to minimize the total cost including fuel consumption cost, driver cost, inventory cost and usage cost of vehicles taking into account factors such as the volume of vehicle load, vehicle speed and road slope. To solve the problem, three meta-heuristic algorithms are designed including the original and augmented Tabu Search (TS) algorithms and Differential Evolution (DE) algorithm. In these algorithms, three heuristic methods of improved Clarke-Wright algorithm, improved Push-Forward Insertion Heuristic (PFIH) algorithm and heuristic speed optimization algorithm are also applied to deal with the routing structure of the problem. The performance of the proposed solution techniques is analyzed using some well-known test problems and algorithms in the literature. Furthermore, a statistical test is conducted to efficiently provide the required comparisons for large-sized problems. The obtained results demonstrate that the augmented TS algorithm is the best method to yield high-quality solutions. Finally, a sensitivity analysis is performed to investigate the variability of the objective function.