# GREAT-ESDD: Graph Edge Attention Network for Effectively Steered Delivery Decisions

arXiv: https://arxiv.org/abs/2610.14792 · HTML: https://mlsanity.com/paper/2610.14792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 20 of 20)

- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [Matrix Encoding Networks for Neural Combinatorial Optimization](https://mlsanity.com/paper/2106.11113/) (2021)
- [GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time](https://mlsanity.com/paper/2312.08224/) (2023)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [PyVRP: a high-performance VRP solver package](https://mlsanity.com/paper/2403.13795/) (2023)
- [Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem](https://mlsanity.com/paper/2304.09407/) (2023)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization](https://mlsanity.com/paper/2503.16159/) (2025)
- [RADAR: Learning to Route with Asymmetry-aware DistAnce Representations](https://mlsanity.com/paper/2603.03388/) (2026)
- [Learning for routing: A guided review of recent developments and future directions](https://mlsanity.com/paper/2507.00218/) (2025)
- [Fast Approximate Solutions using Reinforcement Learning for Dynamic Capacitated Vehicle Routing with Time Windows](https://mlsanity.com/paper/2102.12088/) (2021)
- [Learning Dynamic Selection and Pricing of Out-of-Home Deliveries](https://mlsanity.com/paper/2311.13983/) (2023)
- [Assortment Control Unlocks the Value of Dynamic Pricing in Mixed Last-Mile Delivery](https://mlsanity.com/paper/2609.13539/) (2026)

## Abstract (arXiv)

Online, same-day delivery requires operators to constantly update their routes, and the routing cost for deliveries increases with the number of customers. Out-of-home (OOH) delivery options can help companies handle increasing customer numbers while keeping delivery costs low. We develop a dynamic pricing-and-routing framework for this online ordering scenario with home and OOH delivery options. First, we develop a neural solver for the capacitated vehicle routing problem (CVRP) based on the Graph-Edge-Attention-Network (GREAT). We train it to solve CVRP with varying instance sizes and starting conditions, allowing it to reoptimize partially executed routes under changing conditions. It is fast while achieving solution quality competitive with traditional baselines. Our solver processes several CVRP instances in parallel in batches and we use it to solve the candidate routing problems that arise from an incoming customer's choice of home or OOH delivery. This provides an estimate of the delivery cost increase per option, which we use to set dynamic prices. Further, it directly provides the updated route once the customer decides. We trade off delivery fees against routing costs and steer customers toward OOH delivery when home delivery would be costly. However, effective steering requires us to know the customer preferences. To learn those online, we use Thompson sampling with a Laplace-approximated posterior. We call the resulting framework GREAT-ESDD (GREAT for Effectively Steered Delivery Decisions). Compared to a traditional routing solver, it increases profit by around 11% under a similar pricing decision time budget. Moreover, we show that we can estimate customer preferences successfully, outperforming a static pricing strategy after only 5 days of simulated operations.