Optimal ATM replenishment policies under demand uncertainty

  • Yeliz EkinciEmail author
  • Nicoleta Serban
  • Ekrem Duman
Original Paper


The use of Automated Teller Machines (ATMs) has become increasingly popular throughout the world due to the widespread adoption of electronic financial transactions and better access to financial services in many countries. As the network of ATMs is becoming denser while the users are accessing them at a greater rate, the current financial institutions are faced with addressing inventory and replenishment optimal policies when managing a large number of ATMs. An excessive ATM replenishment will result in a large holding cost whereas an inadequate cash inventory will increase the frequency of the replenishments and the probability of stock-outs along with customer dissatisfaction. To facilitate informed decisions in ATM cash management, in this paper, we introduce an approach for optimal replenishment amounts to minimize the total costs of money holding and customer dissatisfaction by taking the replenishment costs into account including stock-outs. An important aspect of the replenishment strategy is that the future cash demands are not available at the time of planning. To account for uncertainties in unobserved future cash demands, we use prediction intervals instead of point predictions and solve the cash replenishment-planning problem using robust optimization with linear programming. We illustrate the application of the optimal ATM replenishment policy under future demand uncertainties using data consisting of daily cash withdrawals of 98 ATMs of a bank in Istanbul. We find that the optimization approach introduced in this paper results in significant reductions in costs as compared to common practice strategies.


Automated teller machines Replenishment policy Demand uncertainty 



This research was supported by the Scientific and Technological Research Council of Turkey scholarship, awarded for a postdoctoral research position for Dr. Yeliz Ekinci. Dr. Serban’s research was supported by the Coca-Cola Professorship in H. Milton Stewart School of Industrial and Systems Engineering at Georgia Tech. The authors are also thankful to the anonymous bank that supplied the data and expert opinion. The interpretation and conclusions revealed in this study do not represent the official perspectives of the institutes stated above.


  1. Ágoston KC, Benedek G, Gilányi Z (2016) Pareto improvement and joint cash management optimisation for banks and cash-in-transit firms. Eur J Oper Res 254(3):1074–1082CrossRefGoogle Scholar
  2. Altunoglu Y (2010) Cash ınventory management at automated teller machines under ıncomplete ınformation. Master Thesis, The Department of Industrial Engineering and The Institute of Engineering and Sciences of Bilkent UniversityGoogle Scholar
  3. Andrawis RR, Atiya AF, El-Shishiny H (2011) Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition. Int J Forecast 27(3):672–688CrossRefGoogle Scholar
  4. ATM Industry Association (2016) Accessed 06 November 2016
  5. Baker T, Jayaraman V, Ashley N (2013) A data-driven inventory control policy for cash logistics operations: an exploratory case study application at a financial institution. Decis Sci 44(1):205–226CrossRefGoogle Scholar
  6. Batı Ş, Gözüpek D (2017) Joint optimization of cash management and routing for new-generation automated teller machine networks. IEEE Trans Syst Man Cybern Syst 99:1–15CrossRefGoogle Scholar
  7. Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805CrossRefGoogle Scholar
  8. Bertsimas D, Zhao J (2013) Adaptive robust optimization for the security constrained unit commitment problem. IEEE Trans Power Syst 28(1):52–63CrossRefGoogle Scholar
  9. Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev 53(3):464–501CrossRefGoogle Scholar
  10. Boukani FH, Moghaddam BF, Pishvaee MS (2016) Robust optimization approach to capacitated single and multiple allocation hub location problems. Comput Appl Math 35(1):45–60CrossRefGoogle Scholar
  11. Brentnall AR, Crowder MJ, Hand JH (2010) Predictive-sequential forecasting system development for cash machine stocking. Int J Forecast 26(4):764–776CrossRefGoogle Scholar
  12. Brockwell PJ, Davis RA, Calder MV (2002) Introduction to time series and forecasting, vol 2. Springer, New YorkCrossRefGoogle Scholar
  13. Castro J (2009) A stochastic programming approach to cash management in banking. Eur J Oper Res 192(3):963–974CrossRefGoogle Scholar
  14. Chen J, Chen H, Wu Z, Hu D, Pan JZ (2017) Forecasting smog-related health hazard based on social media and physical sensor. Inf Syst 64:281–291CrossRefGoogle Scholar
  15. Chiou S-W (2015) A bi-level decision support system for uncertain network design with equilibrium flow. Decis Support Syst 69:50–58CrossRefGoogle Scholar
  16. Coyle D, Prasad G, McGinnity TM (2010, July) On utilizing self-organizing fuzzy neural networks for financial forecasts in the NN5 forecasting competition. In: Proceedings of: international joint conference on neural networks, IJCNN 2010. IEEE, Barcelona, pp 1–8Google Scholar
  17. Crone S (2008a) Results of the NN5 time series forecasting competition. In: Presentation at the IEEE world congress on computational ıntelligence: WCCI’2008. Hong KongGoogle Scholar
  18. Crone S (2008b) Time series forecasting competition for computational intelligence. Accessed Jan 2013
  19. Diao Y, Sarkar R, Jan EE (2016, April) Optimizing ATM cash flow network management. In: Network operations and management symposium (NOMS), 2016 IEEE/IFIP. IEEE, pp 1073–1078Google Scholar
  20. Ekinci Y, Lu JC, Duman E (2015) Optimization of ATM cash replenishment with group-demand forecasts. Expert Syst Appl 42(7):3480–3490CrossRefGoogle Scholar
  21. Gabriel V, Cecile M, Thiele A (2014) Recent advances ın robust optimization: an overview. Eur J Oper Res 235(3):471–483CrossRefGoogle Scholar
  22. Gal A, Mandelbaum A, Schnitzler F, Senderovich A, Weidlich M (2017) Traveling time prediction in scheduled transportation with journey segments. Inf Syst 64:266–280CrossRefGoogle Scholar
  23. Gneiting T (2011) Making and evaluating point forecasts. J Am Stat Assoc 106(494):746–762CrossRefGoogle Scholar
  24. Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J Am Stat Assoc 102(477):359–378CrossRefGoogle Scholar
  25. Hahn GJ, Kuhn H (2012) Designing decision support systems for value-based management: a survey and an architecture. Decis Support Syst 53(3):591–598CrossRefGoogle Scholar
  26. Hladik M (2012) Interval linear programming: a survey. In: Linear programming-new frontiers in theory and applications, pp 85–120. Accessed 06 November 2016
  27. Karimi N, Davoudpour H (2016) Integrated production and delivery scheduling for multi-factory supply chain with stage-dependent inventory holding cost. Comput Appl Math 36(4):1529–1544CrossRefGoogle Scholar
  28. Kibekbaev A, Duman E (2016) Benchmarking regression algorithms for income prediction modeling. Inf Syst 61:40–52CrossRefGoogle Scholar
  29. Lau HCW, Nakandala D (2012) A pragmatic stochastic decision model for supporting goods trans-shipments ın a supply chain environment. Decis Support Syst 54(1):133–141CrossRefGoogle Scholar
  30. Lütkepohl H (2005) New ıntroduction to multiple time series analysis. Helmut Springer, ViennaCrossRefGoogle Scholar
  31. Ramezani M, Kimiagari AM, Karimi B, Hejazi TH (2014) Closed-loop supply chain network design under a fuzzy environment. Knowl Based Syst 59:108–120CrossRefGoogle Scholar
  32. Shumway RH, Stoffer DS (2006) Time series analysis and ıts applications (with R examples). Springer, New YorkGoogle Scholar
  33. Silver E, Peterson R (1985) Decision systems for inventory management and production planning, 2nd edn. Wiley, New YorkGoogle Scholar
  34. Simutis R, Dilijonas D, Bastina L, Friman J (2007) A flexible neural network for ATM cash demand forecasting. In: 6th WSEAS international conference on computational intelligence, man-machine systems and cybernetics. Tenerife, Spain, December 14–16, pp 162–166Google Scholar
  35. Taieb SB, Bontempi G, Atiya AF, Sorjamaa A (2012) A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition. Expert Syst Appl 39(8):7067–7083CrossRefGoogle Scholar
  36. Tay AS, Wallis KF (2000) Density forecasting: a survey. J Forecast 19:235–254CrossRefGoogle Scholar
  37. The Interbank Card Center (2016) Accessed 06 November 2016
  38. Tobler W (1970) A computer movie simulating urban growth in the detroit region. Econ Geogr 46(2):234–240CrossRefGoogle Scholar
  39. Tutuncu R, Cornuejols G (2007) Optimization methods in finance. Cambridge University Press, New York, NYGoogle Scholar
  40. Vairaktarakis GL (2000) Robust multi-item newsboy models with a budget constraint. Int J Prod Econ 66(3):213–226CrossRefGoogle Scholar
  41. Van Anholt RG, Coelho LC, Laporte G, Vis IF (2016) An inventory-routing problem with pickups and deliveries arising in the replenishment of automated teller machines. Transp Sci 50(3):1077–1091CrossRefGoogle Scholar
  42. Wan SP, Wang F, Lin LL, Dong JY (2015) An intuitionistic fuzzy linear programming method for logistics outsourcing provider selection. Knowl Based Syst 82:80–94CrossRefGoogle Scholar
  43. Wang L, Dun CX, Bi WJ, Zeng YR (2012) An effective and efficient differential evolution algorithm for the integrated stochastic joint replenishment and delivery model. Knowl Based Syst 36:104–114CrossRefGoogle Scholar
  44. Wasserman L (2006) All of nonparametric statistics. Springer, New YorkGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Business AdministrationIstanbul Bilgi UniversityIstanbulTurkey
  2. 2.Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Industrial EngineeringOzyegin UniversityIstanbulTurkey

Personalised recommendations