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Last-mile delivery: Optimal locker location under multinomial logit choice model

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  • Lin, Yun Hui
  • Wang, Yuan
  • He, Dongdong
  • Lee, Loo Hay

Abstract

One innovative solution to the last-mile delivery problem is the self-service locker system. Motivated by a real case in Singapore, we consider a POP-Locker Alliance who operates a set of POP-stations and wishes to improve the last-mile delivery by opening new locker facilities. We propose a quantitative approach to determine the optimal locker location with the objective to maximize the overall service provided by the alliance. Customer’s choices regarding the use of facilities are explicitly considered. They are predicted by a multinomial logit model. We then formulate the location problem as a multi-ratio linear-fractional 0–1 program and provide two solution approaches. The first one is to reformulate the original problem as a mixed-integer linear program, which is further strengthened using conditional McCormick inequalities. This approach is an exact method, developed for small-scale problems. For large-scale problems, we propose an alternating algorithm, i.e., Quadratic Transform with Linear Alternating (QT-LA). The numerical experiment indicates that QT-LA is an efficient approach that yields high-quality solutions. Finally, we conducted a case study. The results highlighted the importance of considering the customers’ choices. Under different parameter values of the multinomial logit model, the decisions could be completely different. Therefore, the parameter value should be carefully estimated in advance.

Suggested Citation

  • Lin, Yun Hui & Wang, Yuan & He, Dongdong & Lee, Loo Hay, 2020. "Last-mile delivery: Optimal locker location under multinomial logit choice model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:transe:v:142:y:2020:i:c:s1366554520307109
    DOI: 10.1016/j.tre.2020.102059
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    19. Bayliss, Christopher & Bektaş, Tolga & Tjon-Soei-Len, Vernon & Rohner, Remo, 2023. "Designing a multi-modal and variable-echelon delivery system for last-mile logistics," European Journal of Operational Research, Elsevier, vol. 307(2), pages 645-662.
    20. Kim, Woojung & Wang, Xiaokun Cara, 2022. "The adoption of alternative delivery locations in New York City: Who and how far?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 158(C), pages 127-140.
    21. Yuan, Yuan & Cattaruzza, Diego & Ogier, Maxime & Semet, Frédéric & Vigo, Daniele, 2021. "A column generation based heuristic for the generalized vehicle routing problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
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