Judging Customer Satisfaction by Considering Fuzzy Random Time Windows in Vehicle Routing Problems

  • Yanfang Ma
  • Cuiying Feng
  • Jing Zhang
  • Fang YanEmail author
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)


This article puts forward a membership function of the customer satisfaction based on fuzzy random time windows in vehicle routing problems. The objective is to confirm that all the customers are satisfied in an acceptable degree by judging the vehicle arriving time. More specifically, time windows given by customers are taken as fuzzy random variables in this paper. And then, fuzzy random theory has been used to describe customers’ time windows. Finally, a measure function has been given to calculate customers’ satisfaction based on fuzzy random time windows.


Vehicle routing optimization Customer satisfaction Time windows Fuzzy random variable 



This research was supported by National Natural Science Foundation of China (Grant No. 71640013, and Grant No. 71401020), and System Science and Enterprise Development Research Center (Grant No. Xq16C10), National philosophy and Social Science Foundation of Tianjin (TJGL15-007); Provincial Science and Technology Foundation of Hebei Province (16457643D).


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Yanfang Ma
    • 1
    • 2
  • Cuiying Feng
    • 2
  • Jing Zhang
    • 1
    • 2
  • Fang Yan
    • 3
    Email author
  1. 1.School of Economics and ManagementHebei University of TechnologyTianjingPeople’s Republic of China
  2. 2.College of Economics and ManagementZhejiang University of TechnologyHangzhouPeople’s Republic of China
  3. 3.School of Economic and ManagementChongqing Jiaotong UniversityChongqingPeople’s Republic of China

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