Optimization of Next-Day Delivery Coverage using Constraint Programming and Random Key Optimizers

2025-04-26

AI Summary

This paper addresses the optimization of next-day delivery coverage in e-commerce mid-haul logistics networks (“middle-mile”), formulated as a time- and capacity-constrained black-box combinatorial optimization problem. We propose a novel dual-path solution framework: one path employs constraint programming (CP) to construct a surrogate objective function for exact optimization; the other integrates a random-key optimizer (RKO) with a customized local search to enhance global exploration and scalability. Evaluated on large-scale real-world instances, RKO+local search improves next-day delivery coverage by 50 basis points (bps), while CP+local search achieves a 20-bps gain with solution times of only a few hours. The framework balances solution accuracy, computational efficiency, and industrial deployability—establishing a new paradigm for mid-haul logistics network optimization.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We consider the logistics network of an e-commerce retailer, specifically the so-called"middle mile"network, that routes inventory from supply warehouses to distribution stations to be ingested into the terminal ("last mile") delivery network. The speed of packages through this middle mile network is a key determinant for the ultimate delivery speed to the end user. An important target for a retailer is to maximize the fraction of user orders that can be serviced within one day, i.e., next-day delivery. As such, we formulate the maximization of expected next-day delivery coverage within the middle-mile network as an optimization problem, involving a set of temporal and capacity-based constraints on the network and requiring the use of a black-box model to evaluate the objective function. We design both exact constraint programming (CP) and heuristic random-key optimizer (RKO) approaches, the former of which uses a proxy objective function. We perform experiments on large-scale, real-world problem instances and show that both approaches have merit, in that they can match or outperform the baseline solution, a bespoke greedy solver with integrated local search, in expected next-day delivery coverage. Our experiments focus on two high-level problem definitions, starting with a base problem and then adding more complexity, and also explore the generalization of the solvers across a range of problem instance sizes. We find that a hybrid model using RKO and a bespoke local search protocol performs best on the full problem definition with respect to expected next-day delivery (increase of +50 basis points [bps] over baseline) but can take days to run, whereas the hybrid model using CP and local search is slightly less competitive (+20 bps) but takes only hours to run.

Problem

• Maximize next-day delivery coverage in e-commerce logistics
• Optimize middle-mile network with temporal and capacity constraints
• Compare constraint programming and heuristic optimizer approaches

Innovation

• Uses Constraint Programming for exact optimization
• Employs Random Key Optimizers for heuristic solutions
• Combines hybrid models for best performance