Provably Good Region Partitioning for On-Time Last-Mile Delivery

40 Pages Posted: 3 Sep 2021

See all articles by John Gunnar Carlsson

John Gunnar Carlsson

University of Southern California - Epstein Department of Industrial & Systems Engineering

Sheng Liu

Rotman School of Management

Nooshin Salari

University of Toronto - Rotman School of Management

Han Yu

University of Southern California - Epstein Department of Industrial & Systems Engineering

Date Written: September 1, 2021

Abstract

On-time last-mile delivery is expanding rapidly as people expect faster delivery of goods ranging from grocery to medicines. Managing on-time delivery systems is challenging because of the underlying uncertainties and combinatorial nature of the routing decision. In practice, the efficiency of such systems also hinges on the driver's familiarity with the local neighborhood. This paper studies the optimal region partitioning policy to minimize the expected delivery time of customer orders in a stochastic and dynamic setting. We allow both the order locations and on-site service times to be random and generally distributed. This policy assigns every driver to a subregion, hence making sure drivers will only be dispatched to their own territories. We characterize the structure of the optimal partitioning policy and show its expected on-time performance converges to that of the flexible dispatching policy in heavy traffic. The optimal characterization features two insightful conditions that are critical to the on-time performance of last-mile delivery systems. We then develop partitioning algorithms with performance guarantees, leveraging ham sandwich cuts and 3-partitions from discrete geometry. This algorithmic development can be of independent interest for other logistics problems. We demonstrate the efficiency of the proposed region partitioning policy via numerical experiments using synthetic and real-world data sets.

Keywords: last-mile delivery, region partitioning, vehicle routing, queueing

Suggested Citation

Carlsson, John Gunnar and Liu, Sheng and Salari, Nooshin and Yu, Han, Provably Good Region Partitioning for On-Time Last-Mile Delivery (September 1, 2021). Rotman School of Management Working Paper No. 3915544, Available at SSRN: https://ssrn.com/abstract=3915544 or http://dx.doi.org/10.2139/ssrn.3915544

John Gunnar Carlsson

University of Southern California - Epstein Department of Industrial & Systems Engineering ( email )

United States

Sheng Liu (Contact Author)

Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Nooshin Salari

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

Han Yu

University of Southern California - Epstein Department of Industrial & Systems Engineering ( email )

United States

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