Modeling stochastic service time for complex on-demand food delivery

Uncertainty is everywhere in the food delivery process, which significantly influences decision-making for complex on-demand food delivery problems, affecting delivery efficiency and customer satisfaction. Especially, the service time is an indispensable part of the delivery process impacted by various uncertain factors. Due to the simplicity and high accuracy requirement, we model the uncertain service time as a Gaussian mixture model (GMM). In detail, we transform the distribution estimation problem into a clustering problem by determining the probability of each data belonging to each component (each cluster as well). A hybrid estimation of distribution algorithm is proposed to intelligently solve the clustering problem with the criterion to optimize quality and simplicity simultaneously. First, to optimize the simplicity, problem-specific encoding and decoding methods are designed. Second, to generate initial solutions with good clustering results, a Chinese restaurant process-based initialization mechanism is presented. Third, a weighted-learning mechanism is proposed to effectively guide the update of the probability model. Fourth, a local intensification based on maximum likelihood is used to exploit better solutions. The effect of critical parameters on the performances of the proposed algorithm is investigated by the Taguchi design of the experimental method. To demonstrate the effectiveness of the proposed algorithm, we carry out extensive offline experiments on real-world historical data. Besides, we employ the GMMs obtained by our algorithm in a real-world on-demand food delivery platform, Meituan, to assist decision-making for order dispatching. The results of rigorous online A/B tests verify the practical value of introducing the uncertainty model into the real-life application.