Abstract
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 language | English |
|---|---|
| Pages (from-to) | 869-887 |
| Journal | Journal of the Operational Research Society |
| Volume | 73 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
Funding
The support by the Dutch Science Foundation [grant number 407-13-050] is gratefully acknowledged. We would like to thank Geldmaat for providing real-life instances of banknote distribution. The views presented in the article are the sole responsibility of the authors.
| Funders | Funder number |
|---|---|
| Nederlandse Organisatie voor Wetenschappelijk Onderzoek | 407-13-050 |
Keywords
- cash logistics
- Covering tour problems
- metaheuristics
- networks
- service level requirements