2026/2/20
Arsalan Rahmani

Arsalan Rahmani

Academic rank: Assistant Professor
ORCID:
Education: PhD.
H-Index:
Faculty: Faculty of Science
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E-mail: a.rahmani [at] uok.ac.ir
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Research

Title
The green cold vehicle routing problem with traffic congestion and variable speed
Type
JournalPaper
Keywords
Cold VRP · Fuel consumption · Traffic congestion · Variable speed · Benders decomposition · PSO algorithm
Year
2024
Journal Energy Systems-Optimization Modeling Simulation and Economic Aspects
DOI
Researchers Meysam (Meyssam) Hosseini ، Arsalan Rahmani

Abstract

Cold supply chains produce and distribute goods that perish and deteriorate over time. To keep such goods fresh, the temperature must be constantly and continu ously controlled, which in turn requires more fuel consumption. In this study, a mixed-integer optimization model is presented in which the goal is to minimize costs assuming that vehicle speed can be variable and considering the traffic con gestion. In addition, it is assumed that the travel time and fuel consumption of each route depend not only on the distance travelled but also on the time of day when that route is travelled. In the proposed model, minimizing costs including the fixed cost, transportation, damage to new products, the refrigerator cost, carbon emissions, and penalties is considered. By solving the proposed model, the optimal route and travel time of vehicles are determined. A hybrid method based on Benders decomposition and PSO algorithms is applied to solve the proposed model. Finally, in addition to solving several test instances with different sizes to investigate the performance of the algorithm, a relatively comprehensive sensitivity analysis has been performed on the model. The obtained results indicate that the proposed algorithm can obtain the optimal solution for all small-size cases, and the average optimality gap ranges for medium sizes are from 0 to 0.12. For larger size cases, an optimal solution is not available, by the CPLEX within the given time limit. In most of these cases, the propose