A multi-objective approach to the cash management problem

[EN] Cash management is concerned with optimizing costs of short-term cash policies of a company. Different optimization models have been proposed in the literature whose focus has been only placed on a single objective, namely, on minimizing costs. However, cash managers may also be interested in risk associated to cash policies. In this paper, we propose a multi-objective cash management model based on compromise programming that allows cash managers to select the best policies, in terms of cost and risk, according to their risk preferences. The model is illustrated through several examples using real data from an industrial company, alternative cost scenarios and two different measures of risk. As a result, we provide cash managers with a new tool to allow them deciding on the level of risk to take in daily decision-making.Work partially funded by projects Collectiveware TIN2015-66863-C2-1-R (MINECO/FEDER) and 2014 SGR 118.Salas-Molina, F.; Pla Santamaría, D.; Rodriguez Aguilar, JA. (2016). A multi-objective approach to the cash management problem. Annals of Operations Research. 1-15. https://doi.org/10.1007/s10479-016-2359-1S115Baccarin, S. (2009). Optimal impulse control for a multidimensional cash management system with generalized cost functions. European Journal of Operational Research, 196(1), 198–206.Ballestero, E. (1998). Approximating the optimum portfolio for an investor with particular preferences. Journal of the Operational Research Society, 49(9), 998–1000.Ballestero, E. (2005). Mean-semivariance efficient frontier: A downside risk model for portfolio selection. Applied Mathematical Finance, 12(1), 1–15.Ballestero, E., & Pla-Santamaria, D. (2004). Selecting portfolios for mutual funds. Omega, 32(5), 385–394.Ballestero, E., & Romero, C. (1998). Multiple criteria decision making and its applications to economic problems. Berlin: Springer.Bates, T. W., Kahle, K. M., & Stulz, R. M. (2009). Why do US firms hold so much more cash than they used to? The Journal of Finance, 64(5), 1985–2021.Baumol, W. J. (1952). The transactions demand for cash: An inventory theoretic approach. The Quarterly Journal of Economics, 66(4), 545–556.Chen, X., & Simchi-Levi, D. (2009). A new approach for the stochastic cash balance problem with fixed costs. Probability in the Engineering and Informational Sciences, 23(04), 545–562.Constantinides, G. M., & Richard, S. F. (1978). Existence of optimal simple policies for discounted-cost inventory and cash management in continuous time. Operations Research, 26(4), 620–636.da Costa Moraes, M. B., & Nagano, M. S. (2014). Evolutionary models in cash management policies with multiple assets. Economic Modelling, 39, 1–7.da Costa Moraes, M. B., Nagano, M.S., Sobreiro, V. A. (2015). Stochastic cash flow management models: A literature review since the 1980s. In P. Guarnieri (Ed.), Decision models in engineering and management. Decision engineering (pp. 11–28). Switzerland: Springer.Eppen, G. D., & Fama, E. F. (1969). Cash balance and simple dynamic portfolio problems with proportional costs. International Economic Review, 10(2), 119–133.Gao, H., Harford, J., & Li, K. (2013). Determinants of corporate cash policy: Insights from private firms. Journal of Financial Economics, 109(3), 623–639.Girgis, N. M. (1968). Optimal cash balance levels. Management Science, 15(3), 130–140.Gormley, F. M., & Meade, N. (2007). The utility of cash flow forecasts in the management of corporate cash balances. European Journal of Operational Research, 182(2), 923–935.Gregory, G. (1976). Cash flow models: A review. Omega, 4(6), 643–656.Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.McNeil, A. J., Frey, R., & Embrechts, P. (2005). Quantitative risk management: Concepts, techniques and tools. Princeton: Princeton University Press.Melo, M. A., & Bilich, F. (2013). Expectancy balance model for cash flow. Journal of Economics and Finance, 37(2), 240–252.Miller, M. H., & Orr, D. (1966). A model of the demand for money by firms. The Quarterly Journal of Economics, 80(3), 413–435.Myers, S. C., & Brealey, R. A. (2003). Principles of corporate finance (7th ed.). NewYork: McGraw-Hill.Neave, E. H. (1970). The stochastic cash balance problem with fixed costs for increases and decreases. Management Science, 16(7), 472–490.Penttinen, M. J. (1991). Myopic and stationary solutions for stochastic cash balance problems. European Journal of Operational Research, 52(2), 155–166.Pinkowitz, L., Stulz, R. M., & Williamson, R. (2016). Do US firms hold more cash than foreign firms do? Review of Financial Studies, 29(2), 309–348.Pla-Santamaria, D., & Bravo, M. (2013). Portfolio optimization based on downside risk: A mean-semivariance efficient frontier from dow jones blue chips. Annals of Operations Research, 205(1), 189–201.Premachandra, I. (2004). A diffusion approximation model for managing cash in firms: An alternative approach to the Miller–Orr model. European Journal of Operational Research, 157(1), 218–226.Roijers, D. M., Vamplew, P., Whiteson, S., & Dazeley, R. (2013). A survey of multi-objective sequential decision-making. Journal of Artificial Intelligence Research, 48(1), 67–113.Ross, S. A., Westerfield, R., & Jordan, B. D. (2002). Fundamentals of corporate finance (6th ed.). NewYork: McGraw-Hill.Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(1), 119–138.Sharpe, W. F. (1994). The sharpe ratio. The Journal of Portfolio Management, 21(1), 49–58.Srinivasan, V., & Kim, Y. H. (1986). Deterministic cash flow management: State of the art and research directions. Omega, 14(2), 145–166.Steuer, R. E., Qi, Y., & Hirschberger, M. (2007). Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Annals of Operations Research, 152(1), 297–317.Stone, B. K. (1972). The use of forecasts and smoothing in control-limit models for cash management. Financial Management, 1(1), 72–84.Whalen, E. L. (1966). A rationalization of the precautionary demand for cash. The Quarterly Journal of Economics, 80(2), 314–324.Yu, P. L. (2013). Multiple-criteria decision making: Concepts, techniques, and extensions. Berlin: Springer.Zeleny, M. (1982). Multiple criteria decision making. NewYork: McGraw-Hill.Zopounidis, C. (1999). Multicriteria decision aid in financial management. European Journal of Operational Research, 119(2), 404–415

On the formal foundations of cash management systems

[EN] Cash management aims to find a balance between what is held in cash and what is allocated in other investments in exchange for a given return. Dealing with cash management systems with multiple accounts and different links between them is a complex task. Current cash management models provide analytic solutions without exploring the underlying structure of accounts and its main properties. There is a need for a formal definition of cash management systems. In this work, we introduce a formal approach to manage cash with multiple accounts based on graph theory. Our approach allows a formal reasoning on the relation between accounts in cash management systems. A critical part of this formal reasoning is the characterization of desirable and non-desirable cash management policies. Novel theoretical results guide cash managers in the analysis of complex cash management systems.This work is partially funded by projects Logistar (H2020-769142), AI4EU (H2020-825619) and 2017 SGR 172.Salas-Molina, F.; Rodriguez-Aguilar, JA.; Pla Santamaría, D.; Garcia-Bernabeu, A. (2021). On the formal foundations of cash management systems. Operational Research. 21(2):1081-1095. https://doi.org/10.1007/s12351-019-00464-6S10811095212Baccarin S (2009) Optimal impulse control for a multidimensional cash management system with generalized cost functions. Eur J Oper Res 196(1):198–206Bollobás B (2013) Modern graph theory, vol 184. Springer, BerlinBondy JA, Murty USR (1976) Graph theory with applications, vol 290. Macmillan, LondonChartrand G, Oellermann OR (1993) Applied and algorithmic graph theory, vol 993. McGraw-Hill, New YorkConstantinides GM, Richard SF (1978) Existence of optimal simple policies for discounted-cost inventory and cash management in continuous time. Oper Res 26(4):620–636da Costa Moraes MB, Nagano MS, Sobreiro VA (2015) Stochastic cash flow management models: a literature review since the 1980s. In: Guarnieri P (ed) Decision models in engineering and management. Springer, Berlin, pp 11–28de Avila Pacheco JV, Morabito R (2011) Application of network flow models for the cash management of an agribusiness company. Comput Ind Eng 61(3):848–857Golden B, Liberatore M, Lieberman C (1979) Models and solution techniques for cash flow management. Comput Oper Res 6(1):13–20Gormley FM, Meade N (2007) The utility of cash flow forecasts in the management of corporate cash balances. Eur J Oper Res 182(2):923–935Gregory G (1976) Cash flow models: a review. Omega 4(6):643–656Makridakis S, Wheelwright SC, Hyndman RJ (2008) Forecasting methods and applications. Wiley, New YorkRighetto GM, Morabito R, Alem D (2016) A robust optimization approach for cash flow management in stationery companies. Comput Ind Eng 99:137–152Salas-Molina F (2017) Risk-sensitive control of cash management systems. Oper Res. https://doi.org/10.1007/s12351-017-0371-0Salas-Molina F, Pla-Santamaria D, Rodriguez-Aguilar JA (2018) A multi-objective approach to the cash management problem. Ann Oper Res 267(1):515–529Srinivasan V, Kim YH (1986) Deterministic cash flow management: state of the art and research directions. Omega 14(2):145–166Valiente G (2013) Algorithms on trees and graphs. Springer, Berli

Multiple-criteria cash-management policies with particular liquidity terms

[EN] Eliciting policies for cash management systems with multiple assets is by no means straightforward. Both the particular relationship between alternative assets and time delays from control decisions to availability of cash introduce additional difficulties. Here we propose a cash management model to derive short-term finance policies when considering multiple assets with different expected returns and particular liquidity terms for each alternative asset. In order to deal with the inherent uncertainty about the near future introduced by cash flows, we use forecasts as a key input to the model. We express uncertainty as lack of predictive accuracy and we derive a deterministic equivalent problem that depends on forecasting errors and preferences of cash managers. Since the assessment of the quality of forecasts is recommended, we describe a method to evaluate the impact of predictive accuracy in cash management policies. We illustrate this method through several numerical examples.Salas-Molina, F.; Pla Santamaría, D.; Garcia-Bernabeu, A.; Mayor-Vitoria, F. (2020). Multiple-criteria cash-management policies with particular liquidity terms. IMA Journal of Management Mathematics. 31(2):217-231. https://doi.org/10.1093/imaman/dpz010S217231312Abdelaziz, F. B., Aouni, B., & Fayedh, R. E. (2007). Multi-objective stochastic programming for portfolio selection. European Journal of Operational Research, 177(3), 1811-1823. doi:10.1016/j.ejor.2005.10.021Aouni, B., Ben Abdelaziz, F., & La Torre, D. (2012). The Stochastic Goal Programming Model: Theory and Applications. Journal of Multi-Criteria Decision Analysis, 19(5-6), 185-200. doi:10.1002/mcda.1466Aouni, B., Colapinto, C., & La Torre, D. (2014). Financial portfolio management through the goal programming model: Current state-of-the-art. European Journal of Operational Research, 234(2), 536-545. doi:10.1016/j.ejor.2013.09.040Baccarin, S. (2009). Optimal impulse control for a multidimensional cash management system with generalized cost functions. European Journal of Operational Research, 196(1), 198-206. doi:10.1016/j.ejor.2008.02.040Ballestero, E. (2001). Stochastic goal programming: A mean–variance approach. European Journal of Operational Research, 131(3), 476-481. doi:10.1016/s0377-2217(00)00084-9Ballestero, E., & Romero, C. (1998). Multiple Criteria Decision Making and its Applications to Economic Problems. doi:10.1007/978-1-4757-2827-9Bemporad, A., & Morari, M. (1999). Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3), 407-427. doi:10.1016/s0005-1098(98)00178-2Cabello, J. G. (2013). Cash efficiency for bank branches. SpringerPlus, 2(1). doi:10.1186/2193-1801-2-334García Cabello, J., & Lobillo, F. J. (2017). Sound branch cash management for less: A low-cost forecasting algorithm under uncertain demand. Omega, 70, 118-134. doi:10.1016/j.omega.2016.09.005Charnes, A., & Cooper, W. W. (1959). Chance-Constrained Programming. Management Science, 6(1), 73-79. doi:10.1287/mnsc.6.1.73Charnes, A., & Cooper, W. W. (1977). Goal programming and multiple objective optimizations. European Journal of Operational Research, 1(1), 39-54. doi:10.1016/s0377-2217(77)81007-2Constantinides, G. M., & Richard, S. F. (1978). Existence of Optimal Simple Policies for Discounted-Cost Inventory and Cash Management in Continuous Time. Operations Research, 26(4), 620-636. doi:10.1287/opre.26.4.620Moraes, M. B. da C., & Nagano, M. S. (2014). Evolutionary models in cash management policies with multiple assets. Economic Modelling, 39, 1-7. doi:10.1016/j.econmod.2014.02.010Da Costa Moraes, M. B., Nagano, M. S., & Sobreiro, V. A. (2015). Stochastic Cash Flow Management Models: A Literature Review Since the 1980s. Decision Engineering, 11-28. doi:10.1007/978-3-319-11949-6_2Eppen, G. D., & Fama, E. F. (1969). Cash Balance and Simple Dynamic Portfolio Problems with Proportional Costs. International Economic Review, 10(2), 119. doi:10.2307/2525547Gormley, F. M., & Meade, N. (2007). The utility of cash flow forecasts in the management of corporate cash balances. European Journal of Operational Research, 182(2), 923-935. doi:10.1016/j.ejor.2006.07.041Gregory, G. (1976). Cash flow models: A review. Omega, 4(6), 643-656. doi:10.1016/0305-0483(76)90092-xHerrera-Cáceres, C. A., & Ibeas, A. (2016). Model predictive control of cash balance in a cash concentration and disbursements system. Journal of the Franklin Institute, 353(18), 4885-4923. doi:10.1016/j.jfranklin.2016.09.007Higson, A., Yoshikatsu, S., & Tippett, M. (2009). Organization size and the optimal investment in cash. IMA Journal of Management Mathematics, 21(1), 27-38. doi:10.1093/imaman/dpp015Miller, M. H., & Orr, D. (1966). A Model of the Demand for Money by Firms. The Quarterly Journal of Economics, 80(3), 413. doi:10.2307/1880728Miller, T. W., & Stone, B. K. (1985). Daily Cash Forecasting and Seasonal Resolution: Alternative Models and Techniques for Using the Distribution Approach. The Journal of Financial and Quantitative Analysis, 20(3), 335. doi:10.2307/2331034Penttinen, M. J. (1991). Myopic and stationary solutions for stochastic cash balance problems. European Journal of Operational Research, 52(2), 155-166. doi:10.1016/0377-2217(91)90077-9Prékopa, A. (1995). Stochastic Programming. doi:10.1007/978-94-017-3087-7Salas-Molina, F. (2017). Risk-sensitive control of cash management systems. Operational Research, 20(2), 1159-1176. doi:10.1007/s12351-017-0371-0Salas-Molina, F., Martin, F. J., Rodríguez-Aguilar, J. A., Serrà, J., & Arcos, J. L. (2017). Empowering cash managers to achieve cost savings by improving predictive accuracy. International Journal of Forecasting, 33(2), 403-415. doi:10.1016/j.ijforecast.2016.11.002Salas-Molina, F., Pla-Santamaria, D., & Rodriguez-Aguilar, J. A. (2016). A multi-objective approach to the cash management problem. Annals of Operations Research, 267(1-2), 515-529. doi:10.1007/s10479-016-2359-1Salas-Molina, F., Pla-Santamaria, D., & Rodríguez-Aguilar, J. A. (2017). Empowering Cash Managers Through Compromise Programming. Financial Decision Aid Using Multiple Criteria, 149-173. doi:10.1007/978-3-319-68876-3_7Salas-Molina, F., Rodríguez-Aguilar, J. A., & Pla-Santamaria, D. (2018). Boundless multiobjective models for cash management. The Engineering Economist, 63(4), 363-381. doi:10.1080/0013791x.2018.1456596Srinivasan, V., & Kim, Y. H. (1986). Deterministic cash flow management: State of the art and research directions. Omega, 14(2), 145-166. doi:10.1016/0305-0483(86)90017-4Stone, B. K. (1972). The Use of Forecasts and Smoothing in Control-Limit Models for Cash Management. Financial Management, 1(1), 72. doi:10.2307/3664955Stone, B. K., & Miller, T. W. (1987). Daily Cash Forecasting with Multiplicative Models of Cash Flow Patterns. Financial Management, 16(4), 45. doi:10.2307/366610

Boundless multiobjective models for cash management

"This is an Accepted Manuscript of an article published by Taylor & Francis in Engineering Economist on 31-05-2018, available online: https://doi.org/10.1080/0013791X.2018.1456596"[EN] Cash management models are usually based on a set of bounds that complicate the selection of the optimal policies due to nonlinearity. We here propose to linearize cash management models to guarantee optimality through linear-quadratic multiobjective compromise programming models. We illustrate our approach through a reformulation of the suboptimal state-of-the-art Gormley-Meade¿s model to achieve optimality. Furthermore, we introduce a much simpler formulation that we call the boundless model that also provides optimal solutions without using bounds. Results from a sensitivity analysis using real data sets from 54 different companies show that our boundless model is highly robust to cash flow prediction errors.Generalitat de Catalunya [2014 SGR 118]; Ministerio de Economia y Competitividad [Collectiveware TIN2015-66863-C2-1-R].Salas-Molina, F.; Rodriguez-Aguilar, JA.; Pla Santamaría, D. (2018). Boundless multiobjective models for cash management. Engineering Economist (Online). 63(4):363-381. https://doi.org/10.1080/0013791X.2018.1456596S363381634Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3), 203-228. doi:10.1111/1467-9965.00068Baccarin, S. (2009). Optimal impulse control for a multidimensional cash management system with generalized cost functions. European Journal of Operational Research, 196(1), 198-206. doi:10.1016/j.ejor.2008.02.040Ballestero, E., & Romero, C. (1998). Multiple Criteria Decision Making and its Applications to Economic Problems. doi:10.1007/978-1-4757-2827-9Bar-Ilan, A., Perry, D., & Stadje, W. (2004). A generalized impulse control model of cash management. Journal of Economic Dynamics and Control, 28(6), 1013-1033. doi:10.1016/s0165-1889(03)00064-2Baumol, W. J. (1952). The Transactions Demand for Cash: An Inventory Theoretic Approach. The Quarterly Journal of Economics, 66(4), 545. doi:10.2307/1882104Bemporad, A., & Morari, M. (1999). Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3), 407-427. doi:10.1016/s0005-1098(98)00178-2Ben-Tal, A., El Ghaoui, L., & Nemirovski, A. (2009). Robust Optimization. doi:10.1515/9781400831050Branke, J., Deb, K., Miettinen, K., & Słowiński, R. (Eds.). (2008). Multiobjective Optimization. Lecture Notes in Computer Science. doi:10.1007/978-3-540-88908-3Chelouah, R., & Siarry, P. (2000). Journal of Heuristics, 6(2), 191-213. doi:10.1023/a:1009626110229Chen, X., & Simchi-Levi, D. (2009). A NEW APPROACH FOR THE STOCHASTIC CASH BALANCE PROBLEM WITH FIXED COSTS. Probability in the Engineering and Informational Sciences, 23(4), 545-562. doi:10.1017/s0269964809000242Constantinides, G. M., & Richard, S. F. (1978). Existence of Optimal Simple Policies for Discounted-Cost Inventory and Cash Management in Continuous Time. Operations Research, 26(4), 620-636. doi:10.1287/opre.26.4.620Moraes, M. B. da C., & Nagano, M. S. (2014). Evolutionary models in cash management policies with multiple assets. Economic Modelling, 39, 1-7. doi:10.1016/j.econmod.2014.02.010Da Costa Moraes, M. B., Nagano, M. S., & Sobreiro, V. A. (2015). Stochastic Cash Flow Management Models: A Literature Review Since the 1980s. Decision Engineering, 11-28. doi:10.1007/978-3-319-11949-6_2De Avila Pacheco, J. V., & Morabito, R. (2011). Application of network flow models for the cash management of an agribusiness company. Computers & Industrial Engineering, 61(3), 848-857. doi:10.1016/j.cie.2011.05.018Girgis, N. M. (1968). Optimal Cash Balance Levels. Management Science, 15(3), 130-140. doi:10.1287/mnsc.15.3.130Golden, B., Liberatore, M., & Lieberman, C. (1979). Models and solution techniques for cash flow management. Computers & Operations Research, 6(1), 13-20. doi:10.1016/0305-0548(79)90010-8Gormley, F. M., & Meade, N. (2007). The utility of cash flow forecasts in the management of corporate cash balances. European Journal of Operational Research, 182(2), 923-935. doi:10.1016/j.ejor.2006.07.041Gregory, G. (1976). Cash flow models: A review. Omega, 4(6), 643-656. doi:10.1016/0305-0483(76)90092-xGurobi Optimization, Inc (2017) Gurobi optimizer reference manual, Houston.Keown, A. J., & Martin, J. D. (1977). A Chance Constrained Goal Programming Model for Working Capital Management. The Engineering Economist, 22(3), 153-174. doi:10.1080/00137917708965174Miller, M. H., & Orr, D. (1966). A Model of the Demand for Money by Firms. The Quarterly Journal of Economics, 80(3), 413. doi:10.2307/1880728Neave, E. H. (1970). The Stochastic Cash Balance Problem with Fixed Costs for Increases and Decreases. Management Science, 16(7), 472-490. doi:10.1287/mnsc.16.7.472PARK, C. S., & HERATH, H. S. B. (2000). EXPLOITING UNCERTAINTY—INVESTMENT OPPORTUNITIES AS REAL OPTIONS: A NEW WAY OF THINKING IN ENGINEERING ECONOMICS. The Engineering Economist, 45(1), 1-36. doi:10.1080/00137910008967534Penttinen, M. J. (1991). Myopic and stationary solutions for stochastic cash balance problems. European Journal of Operational Research, 52(2), 155-166. doi:10.1016/0377-2217(91)90077-9Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. doi:10.1016/s0378-4266(02)00271-6Salas-Molina, F., Martin, F. J., Rodríguez-Aguilar, J. A., Serrà, J., & Arcos, J. L. (2017). Empowering cash managers to achieve cost savings by improving predictive accuracy. International Journal of Forecasting, 33(2), 403-415. doi:10.1016/j.ijforecast.2016.11.002Salas-Molina, F., Pla-Santamaria, D., & Rodriguez-Aguilar, J. A. (2016). A multi-objective approach to the cash management problem. Annals of Operations Research, 267(1-2), 515-529. doi:10.1007/s10479-016-2359-1Srinivasan, V., & Kim, Y. H. (1986). Deterministic cash flow management: State of the art and research directions. Omega, 14(2), 145-166. doi:10.1016/0305-0483(86)90017-4Stone, B. K. (1972). The Use of Forecasts and Smoothing in Control-Limit Models for Cash Management. Financial Management, 1(1), 72. doi:10.2307/3664955Stone, B. K., & Miller, T. W. (1987). Daily Cash Forecasting with Multiplicative Models of Cash Flow Patterns. Financial Management, 16(4), 45. doi:10.2307/3666108Xu, X., & Birge, J. R. (2008). Operational Decisions, Capital Structure, and Managerial Compensation: A News Vendor Perspective. The Engineering Economist, 53(3), 173-196. doi:10.1080/00137910802262887Yu, P.-L. (1985). Multiple-Criteria Decision Making. doi:10.1007/978-1-4684-8395-

Multi-project scheduling with 2-stage decomposition

A non-preemptive, zero time lag multi-project scheduling problem with multiple modes and limited renewable and nonrenewable resources is considered. A 2-stage decomposition approach is adopted to formulate the problem as a hierarchy of 0-1 mathematical programming models. At stage one, each project is reduced to a macro-activity with macro-modes resulting in a single project network where the objective is the maximization of the net present value and the cash flows are positive. For setting the time horizon three different methods are developed and tested. A genetic algorithm approach is designed for this problem, which is also employed to generate a starting solution for the exact solution procedure. Using the starting times and the resource profiles obtained in stage one each project is scheduled at stage two for minimum makespan. The result of the first stage is subjected to a post-processing procedure to distribute the remaining resource capacities. Three new test problem sets are generated with 81, 84 and 27 problems each and three different configurations of solution procedures are tested

Client-contractor bargaining on net present value in project scheduling with limited resources

The client-contractor bargaining problem addressed here is in the context of a multi-mode resource constrained project scheduling problem with discounted cash flows, which is formulated as a progress payments model. In this model, the contractor receives payments from the client at predetermined regular time intervals. The last payment is paid at the first predetermined payment point right after project completion. The second payment model considered in this paper is the one with payments at activity completions. The project is represented on an Activity-on-Node (AON) project network. Activity durations are assumed to be deterministic. The project duration is bounded from above by a deadline imposed by the client, which constitutes a hard constraint. The bargaining objective is to maximize the bargaining objective function comprised of the objectives of both the client and the contractor. The bargaining objective function is expected to reflect the two-party nature of the problem environment and seeks a compromise between the client and the contractor. The bargaining power concept is introduced into the problem by the bargaining power weights used in the bargaining objective function. Simulated annealing algorithm and genetic algorithm approaches are proposed as solution procedures. The proposed solution methods are tested with respect to solution quality and solution times. Sensitivity analyses are conducted among different parameters used in the model, namely the profit margin, the discount rate, and the bargaining power weights

Client-contractor bargaining on net present value in project scheduling with limited resources

The client-contractor bargaining problem addressed here is in the context of a multi-mode resource constrained project scheduling problem with discounted cash flows, which is formulated as a progress payments model. In this model, the contractor receives payments from the client at predetermined regular time intervals. The last payment is paid at the first predetermined payment point right after project completion. The second payment model considered in this paper is the one with payments at activity completions. The project is represented on an Activity-on-Node (AON) project network. Activity durations are assumed to be deterministic. The project duration is bounded from above by a deadline imposed by the client, which constitutes a hard constraint. The bargaining objective is to maximize the bargaining objective function comprised of the objectives of both the client and the contractor. The bargaining objective function is expected to reflect the two-party nature of the problem environment and seeks a compromise between the client and the contractor. The bargaining power concept is introduced into the problem by the bargaining power weights used in the bargaining objective function. Simulated annealing algorithm and genetic algorithm approaches are proposed as solution procedures. The proposed solution methods are tested with respect to solution quality and solution times. Sensitivity analyses are conducted among different parameters used in the model, namely the profit margin, the discount rate, and the bargaining power weights

Selecting cash management models from a multiobjective perspective

[EN] This paper addresses the problem of selecting cash management models under different operating conditions from a multiobjective perspective considering not only cost but also risk. A number of models have been proposed to optimize corporate cash management policies. The impact on model performance of different operating conditions becomes an important issue. Here, we provide a range of visual and quantitative tools imported from Receiver Operating Characteristic (ROC) analysis. More precisely, we show the utility of ROC analysis from a triple perspective as a tool for: (1) showing model performance; (2) choosingmodels; and (3) assessing the impact of operating conditions on model performance. We illustrate the selection of cash management models by means of a numerical example.Work partially funded by projects Collectiveware TIN2015-66863-C2-1-R (MINECO/FEDER) and 2014 SGR 118.Salas-Molina, F.; Rodríguez-Aguilar, JA.; Díaz-García, P. (2018). Selecting cash management models from a multiobjective perspective. Annals of Operations Research. 261(1-2):275-288. https://doi.org/10.1007/s10479-017-2634-9S2752882611-2Ballestero, E. (2007). Compromise programming: A utility-based linear-quadratic composite metric from the trade-off between achievement and balanced (non-corner) solutions. European Journal of Operational Research, 182(3), 1369–1382.Ballestero, E., & Romero, C. (1998). Multiple criteria decision making and its applications to economic problems. Berlin: Springer.Bi, J., & Bennett, K. P. (2003). Regression error characteristic curves. In Proceedings of the 20th international conference on machine learning (ICML-03), pp. 43–50.Bradley, A. P. (1997). The use of the area under the roc curve in the evaluation of machine learning algorithms. Pattern Recognition, 30(7), 1145–1159.da Costa Moraes, M. B., Nagano, M. S., & Sobreiro, V. A. (2015). Stochastic cash flow management models: A literature review since the 1980s. In Decision models in engineering and management (pp. 11–28). New York: Springer.Doumpos, M., & Zopounidis, C. (2007). Model combination for credit risk assessment: A stacked generalization approach. Annals of Operations Research, 151(1), 289–306.Drummond, C., & Holte, R. C. (2000). Explicitly representing expected cost: An alternative to roc representation. In Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 98–207). New York: ACM.Drummond, C., & Holte, R. C. (2006). Cost curves: An improved method for visualizing classifier performance. Machine Learning, 65(1), 95–130.Elkan, C. (2001). The foundations of cost-sensitive learning. In International joint conference on artificial intelligence (Vol. 17, pp. 973–978). Lawrence Erlbaum associates Ltd.Fawcett, T. (2006). An introduction to roc analysis. Pattern Recognition Letters, 27(8), 861–874.Flach, P. A. (2003). The geometry of roc space: understanding machine learning metrics through roc isometrics. In Proceedings of the 20th international conference on machine learning (ICML-03), pp. 194–201.Garcia-Bernabeu, A., Benito, A., Bravo, M., & Pla-Santamaria, D. (2016). Photovoltaic power plants: a multicriteria approach to investment decisions and a case study in western spain. Annals of Operations Research, 245(1–2), 163–175.Glasserman, P. (2003). Monte Carlo methods in financial engineering (Vol. 53). New York: Springer.Gregory, G. (1976). Cash flow models: a review. Omega, 4(6), 643–656.Hernández-Orallo, J. (2013). Roc curves for regression. Pattern Recognition, 46(12), 3395–3411.Hernández-Orallo, J., Flach, P., & Ferri, C. (2013). Roc curves in cost space. Machine Learning, 93(1), 71–91.Hernández-Orallo, J., Lachiche, N., & Martınez-Usó, A. (2014). Predictive models for multidimensional data when the resolution context changes. In Workshop on learning over multiple contexts at ECML, volume 2014.Metz, C. E. (1978). Basic principles of roc analysis. In Seminars in nuclear medicine (Vol. 8, pp. 283–298). Amsterdam: Elsevier.Miettinen, K. (2012). Nonlinear multiobjective optimization (Vol. 12). Berlin: Springer.Ringuest, J. L. (2012). Multiobjective optimization: Behavioral and computational considerations. Berlin: Springer.Ross, S. A., Westerfield, R., & Jordan, B. D. (2002). Fundamentals of corporate finance (sixth ed.). New York: McGraw-Hill.Salas-Molina, F., Pla-Santamaria, D., & Rodriguez-Aguilar, J. A. (2016). A multi-objective approach to the cash management problem. Annals of Operations Research, pp. 1–15.Srinivasan, V., & Kim, Y. H. (1986). Deterministic cash flow management: State of the art and research directions. Omega, 14(2), 145–166.Steuer, R. E., Qi, Y., & Hirschberger, M. (2007). Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Annals of Operations Research, 152(1), 297–317.Stone, B. K. (1972). The use of forecasts and smoothing in control limit models for cash management. Financial Management, 1(1), 72.Torgo, L. (2005). Regression error characteristic surfaces. In Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining (pp. 697–702). ACM.Yu, P.-L. (1985). Multiple criteria decision making: concepts, techniques and extensions. New York: Plenum Press.Zeleny, M. (1982). Multiple criteria decision making. New York: McGraw-Hill

Four payment models for the multi-mode resource constrained project scheduling problem with discounted cash flows

In this paper, the multi-mode resource constrained project scheduling problem with discounted cash flows is considered. The objective is the maximization of the net present value of all cash flows. Time value of money is taken into consideration, and cash in- and outflows are associated with activities and/or events. The resources can be of renewable, nonrenewable, and doubly constrained resource types. Four payment models are considered: Lump sum payment at the terminal event, payments at prespecified event nodes, payments at prespecified time points and progress payments. For finding solutions to problems proposed, a genetic algorithm (GA) approach is employed, which uses a special crossover operator that can exploit the multi-component nature of the problem. The models are investigated at the hand of an example problem. Sensitivity analyses are performed over the mark up and the discount rate. A set of 93 problems from literature are solved under the four different payment models and resource type combinations with the GA approach employed resulting in satisfactory computation times. The GA approach is compared with a domain specific heuristic for the lump sum payment case with renewable resources and is shown to outperform it

Pre-emptive resource-constrained multimode project scheduling using genetic algorithm: a dynamic forward approach

Purpose: The issue resource over-allocating is a big concern for project engineers in the process of scheduling project activities. Resource over-allocating drawback is frequently seen after scheduling of a project in practice which causes a schedule to be useless. Modifying an over-allocated schedule is very complicated and needs a lot of efforts and time. In this paper, a new and fast tracking method is proposed to schedule large scale projects which can help project engineers to schedule the project rapidly and with more confidence. Design/methodology/approach: In this article, a forward approach for maximizing net present value (NPV) in multi-mode resource constrained project scheduling problem while assuming discounted positive cash flows (MRCPSP-DCF) is proposed. The progress payment method is used and all resources are considered as pre-emptible. The proposed approach maximizes NPV using unscheduled resources through resource calendar in forward mode. For this purpose, a Genetic Algorithm is applied to solve. Findings: The findings show that the proposed method is an effective way to maximize NPV in MRCPSP-DCF problems while activity splitting is allowed. The proposed algorithm is very fast and can schedule experimental cases with 1000 variables and 100 resources in few seconds. The results are then compared with branch and bound method and simulated annealing algorithm and it is found the proposed genetic algorithm can provide results with better quality. Then algorithm is then applied for scheduling a hospital in practice. Originality/value: The method can be used alone or as a macro in Microsoft Office Project® Software to schedule MRCPSP-DCF problems or to modify resource over-allocated activities after scheduling a project. This can help project engineers to schedule project activities rapidly with more accuracy in practice.Peer Reviewe