The continuous pollution routing problem

Yiyong Xiao, Xiaorong Zuo, Jiaoying Huang, Abdullah Konak and Yuchun Xu

Applied Mathematics and Computation, 2020, vol. 387, issue C

Abstract: In this paper, we presented an ε-accurate approach to conduct a continuous optimization on the pollution routing problem (PRP). First, we developed an ε-accurate inner polyhedral approximation method for the nonlinear relation between the travel time and travel speed. The approximation error was controlled within the limit of a given parameter ε, which could be as low as 0.01% in our experiments. Second, we developed two ε-accurate methods for the nonlinear fuel consumption rate (FCR) function of a fossil fuel-powered vehicle while ensuring the approximation error to be within the same parameter ε. Based on these linearization methods, we proposed an ε-accurate mathematical linear programming model for the continuous PRP (ε-CPRP for short), in which decision variables such as driving speeds, travel times, arrival/departure/waiting times, vehicle loads, and FCRs were all optimized concurrently on their continuous domains. A theoretical analysis is provided to confirm that the solutions of ε-CPRP are feasible and controlled within the predefined limit. The proposed ε-CPRP model is rigorously tested on well-known benchmark PRP instances in the literature, and has solved PRP instances optimally with up to 25 customers within reasonable CPU times. New optimal solutions of many PRP instances were reported for the first time in the experiments.

Keywords: Vehicle routing problem; Emission reduction; Continuous optimization; Convex programming (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300320300412

DOI: 10.1016/j.amc.2020.125072

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