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Optimal ATM replenishment policies under demand uncertainty

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Abstract

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.

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Notes

  1. We note that this is not a correct scoring rule in evaluating prediction errors. The MAPE can be used when only median predictions are derived. However, for most methods as they are based on L2-norm estimation or least squares estimation, mean square error needs to be used. This fundamental aspect in evaluating predictions is a topic of interest in the statistical literature (Gneiting and Raftery 2007; Gneiting 2011).

References

  • 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):1074–1082

    Article  Google Scholar 

  • 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 University

  • 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):672–688

    Article  Google Scholar 

  • ATM Industry Association (2016) http://www.atmia.com. Accessed 06 November 2016

  • 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):205–226

    Article  Google Scholar 

  • 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 99:1–15

    Google Scholar 

  • Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805

    Article  Google Scholar 

  • Bertsimas D, Zhao J (2013) Adaptive robust optimization for the security constrained unit commitment problem. IEEE Trans Power Syst 28(1):52–63

    Article  Google Scholar 

  • Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev 53(3):464–501

    Article  Google Scholar 

  • Boukani FH, Moghaddam BF, Pishvaee MS (2016) Robust optimization approach to capacitated single and multiple allocation hub location problems. Comput Appl Math 35(1):45–60

    Article  Google Scholar 

  • Brentnall AR, Crowder MJ, Hand JH (2010) Predictive-sequential forecasting system development for cash machine stocking. Int J Forecast 26(4):764–776

    Article  Google Scholar 

  • Brockwell PJ, Davis RA, Calder MV (2002) Introduction to time series and forecasting, vol 2. Springer, New York

    Book  Google Scholar 

  • Castro J (2009) A stochastic programming approach to cash management in banking. Eur J Oper Res 192(3):963–974

    Article  Google Scholar 

  • 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 64:281–291

    Article  Google Scholar 

  • Chiou S-W (2015) A bi-level decision support system for uncertain network design with equilibrium flow. Decis Support Syst 69:50–58

    Article  Google Scholar 

  • 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 1–8

  • Crone S (2008a) Results of the NN5 time series forecasting competition. In: Presentation at the IEEE world congress on computational ıntelligence: WCCI’2008. Hong Kong

  • Crone S (2008b) Time series forecasting competition for computational intelligence. http://www.neural-forecastingcompetition.com. Accessed Jan 2013

  • 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 1073–1078

  • Ekinci Y, Lu JC, Duman E (2015) Optimization of ATM cash replenishment with group-demand forecasts. Expert Syst Appl 42(7):3480–3490

    Article  Google Scholar 

  • Gabriel V, Cecile M, Thiele A (2014) Recent advances ın robust optimization: an overview. Eur J Oper Res 235(3):471–483

    Article  Google Scholar 

  • Gal A, Mandelbaum A, Schnitzler F, Senderovich A, Weidlich M (2017) Traveling time prediction in scheduled transportation with journey segments. Inf Syst 64:266–280

    Article  Google Scholar 

  • Gneiting T (2011) Making and evaluating point forecasts. J Am Stat Assoc 106(494):746–762

    Article  Google Scholar 

  • Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J Am Stat Assoc 102(477):359–378

    Article  Google Scholar 

  • Hahn GJ, Kuhn H (2012) Designing decision support systems for value-based management: a survey and an architecture. Decis Support Syst 53(3):591–598

    Article  Google Scholar 

  • Hladik M (2012) Interval linear programming: a survey. In: Linear programming-new frontiers in theory and applications, pp 85–120. http://www.wikipedia.org/. Accessed 06 November 2016

  • 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):1529–1544

    Article  Google Scholar 

  • Kibekbaev A, Duman E (2016) Benchmarking regression algorithms for income prediction modeling. Inf Syst 61:40–52

    Article  Google Scholar 

  • 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):133–141

    Article  Google Scholar 

  • Lütkepohl H (2005) New ıntroduction to multiple time series analysis. Helmut Springer, Vienna

    Book  Google Scholar 

  • Ramezani M, Kimiagari AM, Karimi B, Hejazi TH (2014) Closed-loop supply chain network design under a fuzzy environment. Knowl Based Syst 59:108–120

    Article  Google Scholar 

  • Shumway RH, Stoffer DS (2006) Time series analysis and ıts applications (with R examples). Springer, New York

    Google Scholar 

  • Silver E, Peterson R (1985) Decision systems for inventory management and production planning, 2nd edn. Wiley, New York

    Google Scholar 

  • 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 162–166

  • 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):7067–7083

    Article  Google Scholar 

  • Tay AS, Wallis KF (2000) Density forecasting: a survey. J Forecast 19:235–254

    Article  Google Scholar 

  • The Interbank Card Center (2016) http://www.bkm.com.tr. Accessed 06 November 2016

  • Tobler W (1970) A computer movie simulating urban growth in the detroit region. Econ Geogr 46(2):234–240

    Article  Google Scholar 

  • Tutuncu R, Cornuejols G (2007) Optimization methods in finance. Cambridge University Press, New York, NY

    Google Scholar 

  • Vairaktarakis GL (2000) Robust multi-item newsboy models with a budget constraint. Int J Prod Econ 66(3):213–226

    Article  Google Scholar 

  • 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):1077–1091

    Article  Google Scholar 

  • Wan SP, Wang F, Lin LL, Dong JY (2015) An intuitionistic fuzzy linear programming method for logistics outsourcing provider selection. Knowl Based Syst 82:80–94

    Article  Google Scholar 

  • 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 36:104–114

    Article  Google Scholar 

  • Wasserman L (2006) All of nonparametric statistics. Springer, New York

    Google Scholar 

Download references

Acknowledgements

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.

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Authors and Affiliations

  1. Business Administration, Istanbul Bilgi University, Istanbul, Turkey

    Yeliz Ekinci

  2. Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA

    Nicoleta Serban

  3. Industrial Engineering, Ozyegin University, Istanbul, Turkey

    Ekrem Duman

Authors
  1. Yeliz Ekinci
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  2. Nicoleta Serban
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  3. Ekrem Duman
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Correspondence to Yeliz Ekinci.

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Appendices

Appendix 1: Independent variables considered in the regression model

See the Table 4.

Table 4 Independent variables considered in the regression model
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Appendix 2: Prediction plots

See the Figs. 5, 6, 7 and 8.

Fig. 5
figure 5

Prediction intervals of the first week

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Fig. 6
figure 6

Prediction intervals of the second week

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Fig. 7
figure 7

Prediction intervals of the third week

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Fig. 8
figure 8

Prediction intervals of the fourth week

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Ekinci, Y., Serban, N. & Duman, E. Optimal ATM replenishment policies under demand uncertainty. Oper Res Int J 21, 999–1029 (2021). https://doi.org/10.1007/s12351-019-00466-4

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