# Optimizing Nursing Care Taxi Dispatch Leveraging Integer Linear Programming Solvers and Machine Learning

arXiv: https://arxiv.org/abs/2606.29725 · HTML: https://mlsanity.com/paper/2606.29725/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation](https://mlsanity.com/paper/2210.07686/) (2022)
- [Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy](https://mlsanity.com/paper/2308.14104/) (2023)
- [Unsupervised Learning for Solving the Travelling Salesman Problem](https://mlsanity.com/paper/2303.10538/) (2023)
- [UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems](https://mlsanity.com/paper/2407.00312/) (2024)
- [A Deep Reinforcement Learning Algorithm Using Dynamic Attention Model for Vehicle Routing Problems](https://mlsanity.com/paper/2002.03282/) (2020)
- [Learning to Handle Complex Constraints for Vehicle Routing Problems](https://mlsanity.com/paper/2410.21066/) (2024)

## Abstract (arXiv)

In this paper, we formulate a new vehicle dispatch optimization problem, called Nursing Care Taxi Dispatch, as a variant of the Vehicle Routing Problem, considering constraints related to wheelchair use, user compatibility, pick-up and drop-off times, and vehicle limitations. Previous neural-based methods for Vehicle Routing Problems have typically addressed a few simple constraints, while our new problem involves multiple complex constraints, resulting in having fewer destinations to select. This complexity makes it more difficult to obtain solutions that allow all nodes to be visited with a limited number of vehicles. To balance low violation rate, computational efficiency, and solution quality, we propose a supervised machine learning approach based on the Transformer architecture. We first obtain a set of high-quality solutions using an integer linear programming solver for given inputs and then train our learning model through supervised learning. Additionally, we introduce the post-processing of the paths generated by the learning model, ensuring that all constraints are satisfied. We compared each instance's objective function value (operating time), execution time, and constraint violation rate across different methods: our proposed method and some existing methods including integer linear programming and machine learning-based methods, using real-world facility data. Our method successfully produced balanced solutions regarding operating time, execution time, and constraint violation rate. Notably, we observed a decrease in the operating time for all problem sizes and regions, while keeping constraint violations to a minimum compared to existing methods. Especially, the decrease reached up to 8% for problem sizes with fewer than 30 users.