Applying Probabilistic Model Checking to Express Delivery Location Selection and Optimization

Abstract

According to our survey about the express delivery from hundreds of campuses, we find that the location of commodity storage places impacts the delivery success rate and service quality. Thus, how to select the proper delivery location is vital to logistics enterprises, which contributes to improve the work efficiency and reduce delivery costs. In this paper, probabilistic model checking is used to verify the delivery fetch system, which evaluates the solution of location distributions in a quantitative way. First, it formalizes the fetch process of express delivery system between business and customer in the form of Discrete-Time Markov Chain (DTMC) when considering the stochastic behavior. Second, Probabilistic Computation Tree Logic (PCTL) is introduced as the verification property to the temporal behavior checking. Third, formal verifications are conducted by the supporting tool PRISM concerning on the transition probabilities computing. Furthermore, verification results are proven to follow the law of Bernouli Large Numbers, which aims to illustrate that the simulation result is close to the actual express delivery situation. Fourth, the express delivery location model is extended as new structure Co-DTMC in order to calculate time consumption and cost consumption, where the punishment factor is designed for the purpose of optimization. Finally, experiments are carried out to show that our approach can effectively select an optimal place for express delivery, which provides an alternative solution to integrate time and cost into the location selection.