[Paper Review] Fighting the E-commerce Giants: Efficient Routing and Effective Consolidation for Local Delivery Platforms

Albert H. Schrotenboer, Michiel A.J. uit het Broek+2 more|arXiv (Cornell University)|Aug 28, 2021

Urban and Freight Transport Logistics27 references4 citations

TL;DR

This paper proposes a two-parameter Cost-Function Approximation (CFA) with column generation to balance order consolidation and delivery urgency in dynamic local delivery platforms. It significantly improves customer satisfaction, reduces late deliveries and travel time compared to benchmarks, while remaining robust across varying system conditions.

ABSTRACT

Local delivery platforms are collaborative undertakings where local stores offer instant-delivery to local customers ordering their products online. Offering such delivery services both cost-efficiently and reliably is one of the main challenges for local delivery platforms, as they face a complex, dynamic, stochastic dynamic pickup-and-delivery problem. Orders need to be consolidated to increase the efficiency of the delivery operations and thereby enable a high service guarantee towards the customer and stores. But, waiting for consolidation opportunities may jeopardize delivery service reliability in the future, and thus requires anticipating future demand. This paper introduces a generic approach to balance the consolidation potential and delivery urgency of orders. Specifically, it presents a newly developed parameterized Cost-Function Approximation (CFA) approach that modifies a set-packing formulation with two parameters. This CFA approach not only anticipates future demand but also utilizes column generation to search the large decision space related to pickup-and-delivery problems fast. Inspired by a motivating application in the city of Groningen, the Netherlands, numerical experiments show that our CFA approach strongly increases perceived customer satisfaction while lowering the total travel time of the vehicles compared to various benchmark policies. Furthermore, our CFA also reduces the percentage of late deliveries, and their lateness, to a minimum. Finally, our approach may assist managers in practice to manage the non-trivial balance between consolidation opportunity and delivery urgency.

Motivation & Objective

• To address the dynamic, stochastic pickup-and-delivery problem faced by local delivery platforms that must balance order consolidation and delivery urgency.
• To develop a scalable, computationally efficient method for real-time routing decisions under uncertainty and soft deadlines.
• To maximize expected customer satisfaction by modeling it as a general function of delivery time and soft deadlines.
• To enable practical deployment through offline training and interpretable parameters, avoiding costly online simulations.
• To demonstrate robustness across varying order volumes, vehicle counts, and penalty functions.

Proposed method

• A parameterized Cost-Function Approximation (CFA) modifies a set-packing formulation using two parameters to trade off consolidation potential and delivery urgency.
• The CFA approach uses a general penalty function to model customer dissatisfaction based on delivery time relative to soft deadlines.
• Column generation is employed to efficiently explore the vast decision space of pickup-and-delivery routes in real time.
• The method is trained offline using historical data, enabling fast online decisions without real-time scenario evaluation.
• The approach is embedded in a dynamic programming framework that anticipates future demand and consolidates orders strategically.
• The CFA parameters are tuned via numerical experiments to minimize expected penalty costs under various demand and objective conditions.

Experimental results

Research questions

• RQ1 How can a dynamic routing system balance the trade-off between consolidating orders for efficiency and delivering them urgently to meet soft deadlines?
• RQ2 What is the impact of different penalty functions (fixed vs. variable lateness costs) on optimal CFA parameter settings and system performance?
• RQ3 How does the proposed CFA approach compare to benchmark policies in terms of customer satisfaction, late deliveries, and total travel time?
• RQ4 Can the CFA approach be robustly applied across varying system sizes, such as different numbers of vehicles and order volumes?
• RQ5 What is the relationship between the two CFA parameters, and how do they non-linearly affect performance under different objectives?

Key findings

• The CFA approach reduced the percentage of late deliveries by up to 40% compared to the best benchmark policy (DSP), with a 25% reduction in deadline exceedance in the LIML-4 scenario.
• Average lateness for late deliveries was reduced by up to 50% compared to DSP, with the CFA achieving 8 minutes of average lateness versus 18 minutes for DSP in the LIML-4 case.
• Total travel time was reduced by up to 10.4% compared to DSP, with the CFA achieving 918 minutes versus 1084 minutes in the LIML-4 scenario.
• The CFA approach improved customer satisfaction by minimizing penalty costs, especially under penalty functions with high fixed costs for lateness, where urgency was prioritized.
• The optimal CFA parameters showed a non-linear relationship, indicating that manual tuning is ineffective and the method’s automated parameterization is essential.
• The approach remained robust across different order sizes, vehicle counts, and penalty functions, demonstrating strong generalization capability.