A way to optimally solve a green time-dependent vehicle routing problem with time windows
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A way to optimally solve a green time-dependent vehicle routing problem with time windows Iman Kazemian1 · Masoud Rabbani1 · Hamed Farrokhi-Asl2
Received: 11 March 2016 / Revised: 30 June 2017 / Accepted: 1 July 2017 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017
Abstract This study presents a novel approach to solve the vehicle routing problem by focusing on greenhouse gas emissions and fuel consumption aiming to mitigate adverse environmental effects of transportation. A time-dependent model with time windows is developed to incorporate speed and schedule in transportation planning. The model considers speed limits for different times of the day in a realistic delivery context. Due to the complexity of solving the model, a graph transformation approach is proposed to reduce the complexity of the problem. By means of several steps, the problem is transformed into a vehicle routing problem without time windows. In this way, we can reduce the complexity of the problem. Our method can be used in practice to decrease fuel consumption and greenhouse gas emissions, while total cost is also controlled to some extent. Finally, future research directions and conclusion remarks are provided. Keywords Vehicle routing · Green · Time-dependent · Time windows · Greenhouse gas emissions · Fuel consumption · Graph transformation Mathematics Subject Classification 90B06
Communicated by José Mario Martínez.
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Masoud Rabbani [email protected] Iman Kazemian [email protected] Hamed Farrokhi-Asl [email protected]
1
School of Industrial and Systems Engineering, College of Engineering, University of Tehran, P.O. Box: 11155-4563, Tehran, Iran
2
School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
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I. Kazemian et al.
1 Introduction The essentiality of transportation in distribution activities of logistic systems makes the vehicle routing problem (VRP) a combinatorial question of great importance. The VRP originated in 1959 as an integer programming problem (Dantzig and Ramser 1959) and aims to find the optimal delivery plan for a fleet of vehicles serving a number of customers with predefined demands. The classical version of this problem includes a central depot and a number of vehicles required to deliver orders to customers at minimum cost. Another common variant is the VRP with Time Windows (VRPTW) where customers should be visited within predefined time slots. The literature on the VRP and its variants is rich and the readers are referred to the survey about this field by Cordeau et al. (2007). Green transportation has been interesting topics for researchers and has attracted researchers’ attention in recent years because of the severity of environmental concerns and the undeniable impacts of transportation activities on them. The transportation is the most substantial factor in the depletion of energy resources on Earth. As such, one of the motivations for analyzing VRP stems from the necessity of adopting green practices in transportation plannin
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