ATM cash replenishment under varying population coverage requirements

Andrea Chiussi, Christos Orlis*, Roberto Roberti, Wout Dullaert

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Inspired by an automated teller machine (ATM) cash replenishment problem involving population coverage requirements (PCRs) in the Netherlands, we propose the vehicle tour problem with minimum coverage requirements. In this problem, a set of minimum-cost routes is constructed subject to constraints on the duration of each route and the population coverage of the replenished ATMs. A compact formulation incorporating a family of valid inequalities and an efficient tour-splitting metaheuristic are proposed and tested on 77 instances derived from real-life data involving up to 98 ATMs and 237,604 citizens and on 144 newly generated synthetic instances. Our results for the real-life instances indicate significant cost differences in replenishing ATMs for seven major Dutch cities when the PCRs vary. Additionally, we illustrate the impact of different PCRs on the ATM replenishment costs for seven major cities in the Netherlands by presenting an aggregated cost evaluation of 11 PCRs involving 1,003,519 citizens, 338 ATMs, and 19 cash distribution vehicles.

Original languageEnglish
Pages (from-to)869-887
JournalJournal of the Operational Research Society
Issue number4
Publication statusPublished - 2022

Bibliographical note

Publisher Copyright:
© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Copyright 2021 Elsevier B.V., All rights reserved.


  • cash logistics
  • Covering tour problems
  • metaheuristics
  • networks
  • service level requirements


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