Fuzzy Demand Vehicle Routing Problem with Soft Time Windows

Considering the vehicle routing problem with fuzzy demand and fuzzy time windows, a vehicle routing optimization method is proposed considering both soft time windows and uncertain customer demand. First, a fuzzy chance-constrained programming model is established based on credibility theory, minimizing the total logistics cost. At the same time, a random simulation algorithm is designed to calculate the penalty cost of delivery failures caused by demand that cannot be satisfied. In order to overcome the shortcomings of GA, which easily falls into the local optimum in the process of searching, and the slow convergence speed of SA when the population is too large, a hybrid simulated annealing–genetic algorithm is adopted to improve the solution quality and efficiency. Finally, the Solomon standard example is used to verify the effectiveness of the algorithm, and the influence of decision-makers’ subjective cost preference is analyzed