How Idle‑Time Optimization Boosts Robot Sorting Center Efficiency

Introduction

With the rapid development of the Internet, e‑commerce, and global logistics, Chinese industry is upgrading and increasingly applying artificial intelligence and robot clusters to manufacturing and supply‑chain operations. The main goal of robot clusters is to collaborate with humans, freeing them from heavy lifting tasks and focusing on finer operations. Consequently, robot‑cluster scheduling has become a new research direction in Multi‑Agent Systems, aiming to assign tasks and plan efficient paths to maximize overall system efficiency.

Problem Modeling

The sorting‑center model consists of three core elements: stations (orange), robots (green), and sorting bins (blue). The objective is to minimize the total idle time of all stations, which requires solving two sub‑problems: (1) Task Assignment – deciding which robot serves which station, and (2) Multi‑Agent Path Finding (MAPF) – planning collision‑free routes for the robots. Together they form the TAPF (Task Assignment and Path Finding) problem, which can be extended to a lifelong TAPF where assignments and paths are recomputed continuously.

ITO Model

Idle‑Time Optimization (ITO) is formulated as a minimum‑cost maximum‑flow network. Each robot node connects to a blue station node, and each station is expanded into K discrete time‑slot nodes representing possible service intervals. Edges carry (cost, capacity) attributes; the flow solution yields a station‑assignment that minimizes idle time while respecting capacity constraints.

PITO Model

Path‑Finding with ITO (PITO) integrates the ITO network with an anonymous MAPF flow network, allowing simultaneous computation of station assignments and robot paths in a single flow model. Robots are represented by time‑expanded nodes, and auxiliary nodes ensure that at most one robot occupies a location at any time, preventing collisions without explicit edge‑collision constraints.

Lifelong Optimization

For continuous operation, the ITO‑L and PITO‑L extensions incorporate a penalty node P with a decreasing cost function over time slots, encouraging robots to occupy earlier slots. This transforms the problem into a min‑cost max‑flow with penalties, guiding the system toward minimal idle time across successive windows.

Experimental Analysis

Two simulation platforms were used: (1) Agent Simulator – random sorting‑center maps with hundreds of robots, stations, and bins; (2) Industrial Simulator – realistic 2‑D layouts of actual warehouses. Five algorithms were compared: three Hungarian‑based baselines (H(Inf)-L, H(1)-L, H(Q)-L) and the proposed ITO‑L and PITO‑L. Parameters such as station processing time T, time window [0, KT), and recomputation interval W were varied.

Results show that both ITO‑L and PITO‑L consistently outperform the baselines, achieving more than 10% increase in throughput on both simulators. The improvements stem from effectively reducing station idle time and coordinating robot movements.

Conclusion

The study demonstrates that minimizing workstation idle time via ITO and PITO provides a practical and effective solution for lifelong TAPF in logistics robot clusters, delivering significant capacity gains. Future work will continue to refine these algorithms and explore their deployment in real‑world automated sorting systems.