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A stochastic programming approach to cash management in banking

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  • Castro, Jordi

Abstract

The treasurer of a bank is responsible for the cash management of several banking activities. In this work, we focus on two of them: cash management in automatic teller machines (ATMs), and in the compensation of credit card transactions. In both cases a decision must be taken according to a future customers demand, which is uncertain. From historical data we can obtain a discrete probability distribution of this demand, which allows the application of stochastic programming techniques. We present stochastic programming models for each problem. Two short-term and one mid-term models are presented for ATMs. The short-term model with fixed costs results in an integer problem which is solved by a fast (i.e. linear running time) algorithm. The short-term model with fixed and staircase costs is solved through its MILP equivalent deterministic formulation. The mid-term model with fixed and staircase costs gives rise to a multi-stage stochastic problem, which is also solved by its MILP deterministic equivalent. The model for compensation of credit card transactions results in a closed form solution. The optimal solutions of those models are the best decisions to be taken by the bank, and provide the basis for a decision support system.

Suggested Citation

  • Castro, Jordi, 2009. "A stochastic programming approach to cash management in banking," European Journal of Operational Research, Elsevier, vol. 192(3), pages 963-974, February.
    • Handle: RePEc:eee:ejores:v:192:y:2009:i:3:p:963-974
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    References listed on IDEAS

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    1. J. G. Kallberg & R. W. White & W. T. Ziemba, 1982. "Short Term Financial Planning under Uncertainty," Management Science, INFORMS, vol. 28(6), pages 670-682, June.
    2. Willem Klein Haneveld & Maarten van der Vlerk, 1999. "Stochastic integer programming:General models and algorithms," Annals of Operations Research, Springer, vol. 85(0), pages 39-57, January.
    3. Jacek Gondzio & Roy Kouwenberg, 2001. "High-Performance Computing for Asset-Liability Management," Operations Research, INFORMS, vol. 49(6), pages 879-891, December.
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    Cited by:

    1. Wong, Man Hong, 2013. "Investment models based on clustered scenario trees," European Journal of Operational Research, Elsevier, vol. 227(2), pages 314-324.
    2. Francisco Salas-Molina, 2024. "Fitting random cash management models to data," Papers 2401.08548, arXiv.org.
    3. Robert Ferstl & Alex Weissensteiner, 2010. "Cash management using multi-stage stochastic programming," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 209-219.
    4. Alaeddine Faleh, 2011. "Un modèle de programmation stochastique pour l'allocation stratégique d'actifs d'un régime de retraite partiellement provisionné," Working Papers hal-00561965, HAL.
    5. Venkatesh, Kamini & Ravi, Vadlamani & Prinzie, Anita & Poel, Dirk Van den, 2014. "Cash demand forecasting in ATMs by clustering and neural networks," European Journal of Operational Research, Elsevier, vol. 232(2), pages 383-392.
    6. Bruno Karoubi & R駩s Chenavaz, 2015. "Prices for cash and cash for prices? Theory and evidence on convenient pricing," Applied Economics, Taylor & Francis Journals, vol. 47(38), pages 4102-4115, August.
    7. Mike G. Tsionas & Dionisis Philippas & Constantin Zopounidis, 2023. "Exploring Uncertainty, Sensitivity and Robust Solutions in Mathematical Programming Through Bayesian Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 205-227, June.
    8. Yeliz Ekinci & Nicoleta Serban & Ekrem Duman, 2021. "Optimal ATM replenishment policies under demand uncertainty," Operational Research, Springer, vol. 21(2), pages 999-1029, June.
    9. V. Kamini & V. Ravi & A. Prinzie & D. Van Den Poel, 2013. "Cash Demand Forecasting in ATMs by Clustering and Neural Networks," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 13/865, Ghent University, Faculty of Economics and Business Administration.

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