Abstract

The movable unit equipped with a set of lockers has been recently developed as a new mode to improve the efficiency of the last mile delivery. Locating a set of movable parcel locker units appropriately is a fundamental factor to promote the merits of movable parcel lockers. However, the difficulty in determining where to locate movable parcel locker units arises from the stochastic characteristics of demands. Therefore, we propose a robust optimization approach to determine the number of movable parcel locker units and their locations simultaneously with the aim to minimize the operating cost under stochastic demands and mobility restrictions. To reduce the complexity of the optimization model, the non-linear constraints have been transformed into the linear counterparts, resulting in an integer linear programming (ILP) model that can be solved by commercially available mathematical programming solvers. The results from the numerical examples indicate the proposed approach can obtain high robustness with a small extra cost within reasonable time. In addition, it is found that if each unit is equipped with more lockers, fewer movable parcel locker units are required to accommodate the demands with less operating cost, as the demand points can be clustered into a few intensive self-pickup sites.

Highlights

  • The rapid development of e-commerce has led to great changes in people’s shopping mode, and the market share of business-to-consumer (B2C) continues to increase [1,2]

  • The work presented in this paper aims to develop an optimization model to locate movable parcel locker units and determine the number of units under stochastic demands

  • An integer linear programming (ILP) model has been established based on a robust optimization approach

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Summary

Introduction

The rapid development of e-commerce has led to great changes in people’s shopping mode, and the market share of business-to-consumer (B2C) continues to increase [1,2]. Online shopping transactions of global consumers reached ¥15.57307 trillion in 2015, an increase of 19.9% compared to. According to Francke and Visser [4], the scale of e-commerce in Europe, North America and. Asia Pacific, including the proportion of online consumers, the share of online goods and the amount of online transactions, is considerable. In China, online sales on the day of “double 11” accounted for. ¥410.1 billion in 2019, an increase of 30.5% compared to 2018 [5]. The direct impact is that there is a large demand for the last mile delivery. A large number of orders cannot be efficiently delivered only through home delivery

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