Balancing the cardinality of clusters with a distance constraint: a fast algorithm

Herminia I. Calvete (), Carmen Galé () and José A. Iranzo ()
Additional contact information
Herminia I. Calvete: Universidad de Zaragoza
Carmen Galé: Universidad de Zaragoza
José A. Iranzo: Universidad de Zaragoza

Annals of Operations Research, 2025, vol. 351, issue 1, No 24, 629-651

Abstract: Abstract Logistics companies partition the customers they serve into delivery zones as a tactical decision and manage the customers assigned to each zone as a cluster for the purpose of routing, workload allocation, etc. Frequently, this partition is made in accordance with customers’ geographical location, which can result in very unbalanced clusters in terms of the number of customers they include. In addition, in the day-to-day operations, not necessarily all customers need to be served every day so, even if the clusters originally created are balanced, daily needs may lead to unbalanced clusters. Given an a priori assignment of customers to clusters, improving the balance between clusters in advance of workload management is therefore a key issue. This paper addresses the problem of balancing clusters, when there is a distance constraint that prevents reassigning customers to clusters far away from their original pre-assignment. This problem is formulated as a lexicographic biobjective optimization model. The highest priority objective function minimizes the variance of the number of customers in the clusters. The second ranked objective function minimizes the total distance resulting from all reassignments. A fast and effective heuristic algorithm is developed, based on exploring customer reassignments, either by comparing clusters two by two or by extending the search to allow for sequential customer swaps among clusters. Both the quality of the solution and the computational time required encourage the use of this algorithm by logistics companies to balance clusters in real scenarios.

Keywords: Balancing clusters; Distance constraint; Heuristic algorithm (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-024-06017-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:351:y:2025:i:1:d:10.1007_s10479-024-06017-1

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-024-06017-1

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().