A stochastic goal programming model to derive stable cash management policies

In this paper, we consider cash management systems with multiple bank accounts described by a given particular relationship between accounts and by a linear state transition law. Since cash managers may simultaneously consider a number of possibly conflicting goals, we provide a general stochastic goal programming model that is able to handle multiple goals and also the inherent uncertainty introduced by expected cash flows. We describe in detail an instance of our general model that considers the optimization of three different criteria such as cost, risk and cash balance stability. We claim that cash balance stability is an interesting goal to deal with the inherent uncertainty of expected cash flows. We also provide useful instructions for cash managers to set the main parameters of our model in practice. Our model provides a systematic approach to multiobjective cash management that is ready to be implemented in decision support systems for cash management.

[1]  Jean-Philippe Vial,et al.  Robust Optimization , 2021, ICORES.

[2]  A. Charnes,et al.  Goal programming and multiple objective optimizations: Part 1 , 1977 .

[3]  Asier Ibeas,et al.  Model predictive control of cash balance in a cash concentration and disbursements system , 2016, J. Frankl. Inst..

[4]  Davide La Torre,et al.  Financial portfolio management through the goal programming model: Current state-of-the-art , 2014, Eur. J. Oper. Res..

[5]  Juan A. Rodríguez-Aguilar,et al.  Empowering cash managers through compromise programming , 2018 .

[6]  Stefano Baccarin,et al.  Optimal impulse control for a multidimensional cash management system with generalized cost functions , 2009, Eur. J. Oper. Res..

[7]  Allen L. Soyster,et al.  Technical Note - Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming , 1973, Oper. Res..

[8]  Mehrdad Tamiz,et al.  Practical Goal Programming , 2010 .

[9]  R. Rockafellar,et al.  Conditional Value-at-Risk for General Loss Distributions , 2001 .

[10]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[11]  Francisco Salas-Molina,et al.  Empowering cash managers to achieve cost savings by improving predictive accuracy , 2016, 1605.04219.

[12]  Thomas L. Saaty,et al.  DECISION MAKING WITH THE ANALYTIC HIERARCHY PROCESS , 2008 .

[13]  H. Daellenbach,et al.  A Stochastic Cash Balance Model with Two , 1971 .

[14]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[15]  Marcelo Seido Nagano,et al.  Stochastic Cash Flow Management Models: A Literature Review Since the 1980s , 2015 .

[16]  Miguel A. Mariño,et al.  Multi-Colony Ant Algorithm for Continuous Multi-Reservoir Operation Optimization Problem , 2007 .

[17]  H. Pastijn.  Handbook of critical issues in goal programming: Carlos Romero Pergamon Press, Oxford, 1990, xi + 124 pages, £25.00, ISBN 008 0406610 , 1992 .

[18]  Enrique Ballestero,et al.  Stochastic goal programming: A mean-variance approach , 2001, Eur. J. Oper. Res..

[19]  Fionnuala M. Gormley,et al.  The utility of cash flow forecasts in the management of corporate cash balances , 2007, Eur. J. Oper. Res..

[20]  John W. Labadie,et al.  Optimal Operation of Multireservoir Systems: State-of-the-Art Review , 2004 .

[21]  Markku Penttinen,et al.  Myopic and stationary solutions for stochastic cash balance problems , 1991 .

[22]  C. Romero,et al.  Multiple Criteria Decision Making and its Applications to Economic Problems , 1998 .

[23]  Bernell K. Stone,et al.  The Use of Forecasts and Smoothing in Control-Limit Models for Cash Management , 1972 .

[24]  H. Simon,et al.  A Behavioral Model of Rational Choice , 1955 .

[25]  R. Wets,et al.  Stochastic programming , 1989 .

[26]  V. Srinivasan,et al.  Deterministic cash flow management: State of the art and research directions , 1986 .

[27]  William W.-G. Yeh,et al.  Reservoir Management and Operations Models: A State‐of‐the‐Art Review , 1985 .

[28]  Enrique Ballestero,et al.  Portfolio Selection with Multiple Time Horizons: A Mean Variance—Stochastic Goal Programming Approach , 2012, INFOR Inf. Syst. Oper. Res..

[29]  Nikolaos V. Sahinidis,et al.  Optimization under uncertainty: state-of-the-art and opportunities , 2004, Comput. Chem. Eng..

[30]  Francisco Salas-Molina,et al.  Risk-sensitive control of cash management systems , 2020, Oper. Res..

[31]  Juan A. Rodríguez-Aguilar,et al.  A multi-objective approach to the cash management problem , 2018, Ann. Oper. Res..

[32]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[33]  L..  How To Make A Decision : The Analytic Hierarchy Process , 2003 .

[34]  Alexander Schrijver,et al.  Handbook of Critical Issues in Goal Programming , 1992 .

[35]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[36]  Thomas L. Saaty,et al.  How to Make a Decision: The Analytic Hierarchy Process , 1990 .

[37]  Joseba Quevedo,et al.  Optimal control of a water distribution network in a supervisory control system , 2000 .

[38]  S. Yakowitz,et al.  Constrained differential dynamic programming and its application to multireservoir control , 1979 .

[39]  Fouad Ben Abdelaziz,et al.  Multi-objective stochastic programming for portfolio selection , 2007, Eur. J. Oper. Res..

[40]  Arkadi Nemirovski,et al.  Robust solutions of uncertain linear programs , 1999, Oper. Res. Lett..

[41]  Goal Programming and Multiple Objective Optimization , 2022 .