Evaluating hierarchical pathfinding A* (HPA*) for multi‑order routing in a small warehouse layout

Wibawa, Ig. Prasetya Dwi, Kallista, Meta, Nugraha, Ramdan, Widayani, Heni ORCID: https://orcid.org/0000-0002-6966-6754, Bhandari, Harish Chandra and Rusdinar, Angga (2026) Evaluating hierarchical pathfinding A* (HPA*) for multi‑order routing in a small warehouse layout. Cauchy: Jurnal Matematika Murni dan Aplikasi, 11 (1). pp. 524-539. ISSN 2086-0382

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Abstract

Hierarchical Pathfinding A* (HPA*) is a hierarchical search framework that partitions grid‑based environments into clusters to reduce computational time while preserving a near-optimal path. The warehouse layout features cross-aisle connectivity, and multi-order optimization is performed using the HPA* algorithm, which integrates travel times with multi-rack picking times to the objective cost function. We simulate by assigning 30 random orders, with a total of 10641 items stored in the warehouse and 10 item types. The travel time is calculated assuming a picker has a constant speed of 1.2 m/s along edges, the picking time is proportional to the number of items picked per rack, and a small warehouse layout. Estimated cycle times of the orders (travel plus picking time) range from 114.4 to 349.9 seconds using the HPA* optimization, with a mean of 232.0 seconds. From the optimization results, orders require an average of 5.2 rack visits, ensuring that the picker travels more than two racks per order. The HPA* reduces the original low‑level graph (50 nodes and 61 edges, including base and stage station) to a graph with 22 nodes and 17 edges, enabling faster route computation while preserving observed cycle‑time patterns when combined with picking-time durations. Compared to A*, given the layout and orders, HPA* demonstrates an efficient warehouse path‑planning method that reduces search computation while maintaining near‑optimal routing performance.

Item Type:	Journal Article
Keywords:	hpa*; hierarchical pathfinding; warehouse routing; multi-order; route optimization
Subjects:	01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified 01 MATHEMATICAL SCIENCES > 0103 Numerical and Computational mathematics > 010303 Optimisation 08 INFORMATION AND COMPUTING SCIENCES > 0803 Computer Software > 080302 Computer System Architecture 09 ENGINEERING > 0906 Electrical and Electronic Engineering > 090699 Electrical and Electronic Engineering not elsewhere classified 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Heni Widayani
Date Deposited:	24 Jun 2026 11:20

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