The Dial-a-Ride Problem with Synchronized Visits

2026-01-01

AI Summary

This study addresses the routing problem for drones or small modular vehicles with limited payload capacity, which must collaboratively serve large customers requiring synchronized visits and small customers amenable to ride-pooling. The authors propose four mathematical programming formulations: arc-based, event-based, time-space event-based (TSEF), and time-space fragment-based (TSFrag), introducing for the first time the modeling of events and path fragments into the synchronized dial-a-ride problem. Coupled with a dynamic discretization discovery (DDD) algorithm, the TSFrag+DDD approach significantly outperforms the conventional arc-based model under high request density, achieving faster computation and fewer iterations; conversely, the event-based model excels under low request intensity. This framework effectively replaces traditional callback mechanisms in classical dial-a-ride settings.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

The limited capacity of drones and future one- or two-seat modular vehicles requires multiple units to serve a single large customer (i.e., a customer whose demand exceeds a single vehicle's capacity) simultaneously, whereas small customers (i.e., those whose demand can be served by a single vehicle) can be consolidated in one trip. This motivates the Dial-a-Ride Problem with Synchronized Visits, where a fleet of drones must be routed and scheduled to transport orders at minimum cost. We propose four formulations: arc-based, event-based, time-space event-based (TSEF), and time-space fragment-based (TSFrag). An event is defined as a tuple of a location and a set of onboard customers, while a fragment represents a partial path. For TSEF and TSFrag, we also employ the dynamic discretization discovery (DDD) algorithm, which iteratively refines an initial low-resolution time-space network to obtain a continuous-time optimal solution. Computational results show that the event-based formulation performs best under low request intensity (few customers per unit time), whereas TSFrag with DDD excels with high request intensity; both substantially outperform the arc-based formulation. When implemented with DDD, TSFrag also requires less time and fewer iterations than TSEF. We also apply our methods to the classical dial-a-ride problem, where we find that that TSFrag with DDD can replace callbacks in case of high request intensity, and that using DDD is more beneficial to this problem than to the pickup-and-delivery problem with time windows.

Problem

• Dial-a-Ride Problem
• Synchronized Visits
• Limited Capacity
• Drone Routing
• Customer Consolidation

Innovation

• Synchronized Visits
• Time-Space Fragment
• Dynamic Discretization Discovery
• Dial-a-Ride Problem
• Event-Based Formulation