A Robust Optimization Method for Location Selection of Parcel Lockers under Uncertain Demands

Abstract

Parcel lockers have continuously growing in popularity as an alternative mode for last-mile delivery services due to their capability of effectively alleviating the risk of a delivery failure, increasing the possibility of delivery consolidation, and reducing the number of drop-off sites. However, poorly located of parcel lockers be less efficient. When determining the parcel locker location, inadequate consideration of uncertain demands can potentially increase the risk of unsatisfied demands. To remedy this issue, a robust optimization model is proposed in this paper with consideration of the demand uncertainties, including the large and small parcels to be received and sent. Not only can the collection locations be optimally determined, but so can the number of large and small parcel lockers for each location at the same time under various robust levels. Meanwhile, the sites whose demands are covered by one of the collection locations are also determined by the constraints of acceptable walking distance. A series of numerical experiments has been performed to evaluate the proposed model, with the main focus being on the solution robustness. Since the set of non-linear constraints are transformed into the linear counterparts, the robust solution can be obtained by the existing solvers within a reasonable time with moderate computing power. The experimental results also provide useful guidance for the practical application of the method, as slightly more conservative decision making can secure the solution robustness with only a marginal increase in costs.