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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 365367, 10 pages
Research Article

The Optimization of Transportation Costs in Logistics Enterprises with Time-Window Constraints

School of Economics and Management, North China Electric Power University, Beijing 102206, China

Received 25 November 2014; Revised 26 March 2015; Accepted 27 March 2015

Academic Editor: Delfim F. M. Torres

Copyright © 2015 Qingyou Yan and Qian Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a model for solving a multiobjective vehicle routing problem with soft time-window constraints that specify the earliest and latest arrival times of customers. If a customer is serviced before the earliest specified arrival time, extra inventory costs are incurred. If the customer is serviced after the latest arrival time, penalty costs must be paid. Both the total transportation cost and the required fleet size are minimized in this model, which also accounts for the given capacity limitations of each vehicle. The total transportation cost consists of direct transportation costs, extra inventory costs, and penalty costs. This multiobjective optimization is solved by using a modified genetic algorithm approach. The output of the algorithm is a set of optimal solutions that represent the trade-off between total transportation cost and the fleet size required to service customers. The influential impact of these two factors is analyzed through the use of a case study.