Multi-depot open vehicle routing problem with fuzzy time windows

This paper presents one method and one hybrid genetic algorithm for multi-depot open vehicle routing problem with fuzzy time windows (MDOVRPFTW) without maximum time windows. For the method, the degree of customers’ willingness to accept goods (DCWAG) is firstly proposed, it’s one fuzzy vague and determines maximum time windows. Referring to methods to determine fuzzy membership function, the function between DCWAG and the starting service time is constructed. By setting an threshold for DCWAG, the starting service time that the threshold corresponds can be treated as the maximum time window, which meets the actual situation. The goal of the model is to minimize the total cost. For the algorithm, MDOVRPFTW without maximum time windows is an extension of the NP-hard problem, the hybrid genetic algorithm was designed, which is combination of genetic algorithm and Hungarian algorithm. When the hybrid genetic algorithm applied to one pharmaceutical logistics company in Beijing City, China, one optimal scheme is determined. Then the rationality and the stability of solutions by the hybrid genetic algorithm are proved. Finally, sensitivity analyses are performed to investigate the impact of someone factor on DCWAG and some suggestions are proposed.