Profit-maximizing parcel locker location problem under threshold Luce model

The growth of e-commerce has created increasing complexity in logistics services. To remaincompetitive, logistics and e-commerce companies are exploring new modes as supplements totraditional home delivery, one of which is the self-service parcel locker. This paper studiesa parcel locker location problem where a company plans to introduce the locker service bylocating locker facilities to attract customers. The objective is to maximize the profit, accountingfor the revenue and the cost of facilities, under the competition of other delivery modes. Toestimate the revenue, we use the threshold Luce model (TLM) to predict customers' likelihoodof using the locker service. We then propose a combinatorial optimization model and developexact solution methodologies that are practically implementable according to our extensivecomputational experiments. In effect, our modeling framework generalizes the traditionalfacility location problems based on the binomial logit model (BNL) and the multinomial logitmodel (MNL), both of which impose strong and strict assumptions on the customer's choice sets.That is, they assume that the choice set will either contain only one facility or all facilities.In our numerical experiment, we demonstrate that using the BNL and the MNL could leadto, respectively, pessimistic and optimistic revenue estimation. Consequently, the suggestedlocation decisions will be either conservative or aggressive. Our proposed model, by contrast,can effectively relax these assumptions. Our results also reveal that the aggressive decision dueto the use of the MNL will incur an unnecessarily high facility cost that cannot be compensatedby the additional revenue, leading to profit loss that could be significant in various scenarios.Finally, we conduct sensitivity analysis to shed light on how the relative attraction of lockerservices (compared to other delivery options) affects the location decisions and highlight theimportance of calibrating the input parameters in TLM.

Automated summary

This paper studies a parcel locker location problem in the context of the growing complexity of logistics services in the e-commerce industry. The objective is to maximize profit by attracting customers through the introduction of self-service parcel lockers. The paper proposes a combinatorial optimization model that relaxes the strict assumptions of the binomial logit model and the multinomial logit model. The results show that the use of these models can lead to either conservative or aggressive revenue estimation, highlighting the need for a more flexible approach. Sensitivity analysis is conducted to investigate the impact of the relative attractiveness of locker services on location decisions, emphasizing the importance of calibrating the input parameters.