A stochastic programming approach to cash management in banking
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.
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- Golub, Bennett & Holmer, Martin & McKendall, Raymond & Pohlman, Lawrence & Zenios, Stavros A., 1995. "A stochastic programming model for money management," European Journal of Operational Research, Elsevier, vol. 85(2), pages 282-296, September.
- 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.
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