Parcel Locker Location Problem under Threshold Luce Model

The growth of e-commerce has created increasing complexity in logistics service. To remain competitive in the market, logistics and e-commerce companies are exploring new modes as supplements to traditional home delivery, one of which is the self-service parcel locker. This paper studies the use of parcel lockers as an innovative solution to the last-mile delivery problem. We consider a logistics company that plans to introduce the locker service by locating a fixed number of lockers in the network. The objective is to attract as many customers to use the locker service as possible, namely, the captured demand rate. Customers' choices on whether to use the locker service or which locker to select are predicted by a discrete choice model. In the literature, a popular approach is to use the multinomial logit model. However, such a model cannot explain zero-probability choices that appear in practice and tends to overestimate the captured demand rate. To overcome the issue, the threshold luce model is applied instead. In its definition, when locker x is dominated by locker y, the probability of selecting x will be zero in the presence of y. We then propose two equivalent formulations for the locker location problem under threshold luce model and derive a valid inequality based on directed acyclic graph theory to improve the formulation. Two solution approaches, i.e., outer approximation and mixed-integer conic quadratic programming approach (MICQP), are developed. Extensive numerical studies reveal that the MICQP approach with improved inequalities outperforms the others. Finally, we conduct a case study and draw managerial implications.