Replenishment and denomination mix of automated teller machines with dynamic forecast demands

Lieke Heide, van der*, Leandro Callegari Coelho, Iris Vis, Roel G. van Anholt

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
150 Downloads (Pure)


In the inventory management of automated teller machines (ATMs) many activities affect the total costs, such as forecasting, replenishments and the denomination mix used. The denomination mix is the combination of bills used to fulfill a customer's demand. We investigate whether allowing the denomination mix to vary over time based on the forecast withdrawals at an ATM reduces actual operating costs of an ATM. To verify this, we propose a time-varying denomination mix strategy, which is validated by benchmarking it against the case of a bank's denomination mix strategy. The bank's predetermined strategy typically consists of a least note strategy or a one-smallest strategy. In all strategies we simultaneously optimize denomination mixes and replenishment decisions. We define the problem and solution strategies as mixed integer programming formulations and solve them via a rolling horizon algorithm using different frequencies of denomination mix updates, rolling horizon lengths, numbers of ATMs, cost parameters, and forecast qualities. By implementing the time-varying denomination mix, we show that the operational costs of managing an ATM can be reduced by 21% or €153.77 per ATM per month on average, which can represent over €10 million per year in the Netherlands only.

Original languageEnglish
Article number104828
JournalComputers & Operations Research
Publication statusPublished - Feb-2020


  • Inventory management
  • Automated teller machine
  • Denomination mix
  • Optimization
  • Replenishment
  • Cash logistics
  • Prescriptive analytics
  • CASH

Cite this