Abstract: Last mile delivery (LMD) problems have become increasingly prominent with the rapid development of e-commerce. And traditional home delivery service can't meet customers' demand. Pickup service provides customers with a more flexible distribution solution, gaining scale benefit of LMD and reducing the delivery pressure of the city logistics system. Pickup point location is a strategic decision for enterprises to broaden customers' pickup mode and promote market share of LMD. In contrast with other logistics facilities, pickup point is a direct terminal to customers, and customers have a choice in whether to receive service from pickup point in the region or not. In order to maximize the customers' total pickup demand, it is necessary to put emphasis on how customers choose the pickup points to patronize. To this end, assuming that customers' pickup distance and pickup points' attraction are two important attractiveness attributes considered by customers. Based on the competitive location and gradual coverage theory, a piecewise utility function between customer and pickup point is constructed. Under this circumstance, two alternative models are respectively presented with the MNL model and demand elasticity function:in the "probabilistic-choice model", a customer may patronize each pickup point with a certain probability, which increases with the attractiveness of available pickup point. In contrast, the "optimal-choice model" stipulates that each customer will go to the most attractive pickup point. Both models are formulated as a mixed-integer program. To solve the problems efficiently, an immune algorithm is proposed and a random example is used for verification. The results show that pickup point's coverage distance, customer rational degree and demand elasticity coefficient affect the location decisions. In particular, the comparison between the two models indicates that the choice behavior of the customer has a significant impact on the pickup point location decisions, and a thorough empirical investigation of this behavior prior to choosing a model is necessary.

Key words: pickup point, customers' choice behavior, facility location, utility function, immune algorithm