Mohammad Bagher Fakhrzad - Department of Industrial Engineering, Yazd University, Yazd, Iran
Seyed Masoud Hoseini Shorshani - Department of Industrial Engineering, Yazd University, Yazd, Iran
Hasan Hosseininasab - Department of Industrial Engineering, Yazd University, Yazd, Iran
Ali Mostafaeipour - Department of Industrial Engineering, Yazd University, Yazd, Iran

The vehicle routing problem has attracted much attention in the recent decade. Considering the real-world constraints, many extensions have been developed. This paper develops a new model for the green vehicle routing problem with simultaneous pickup and delivery under demand uncertainty. Due to the problem's complexity, the standard solvers are only able to solve small-scale instances. To solve the large-scale problems, a two-stage algorithm based on the modified AVNS is proposed. Extensive computational experiments are conducted using modified versions of Solomon’s benchmark instances to show the performance of the algorithm. The results affirm that the two-stage algorithm is capable of generating optimal solutions for small-size instances and the planned routes generated for large-size instances were significantly more robust against the increase of uncertainty parameters.

Vehicle routing problem, time window, demand uncertainty, simultaneous pickup and delivery