Abstract
We consider a resource allocation problem where a decision maker (DM) is to distribute a certain budget among alternative projects in order to create the best portfolio. The DM aims to generate a portfolio with (1) a high return and (2) a balanced distribution of resources among categories. We assume that the DM has a quasiconcave value function and provides no explicit value for the target distribution of resources over categories. We develop an interactive approach that requires the DM to make pairwise comparisons among alternative portfolios. We present the developed approach on an illustrative example and conduct an extensive computational experiment. In majority of the instances, the incumbent solution proposed by the algorithm is either equal or very close to the best solution.


Similar content being viewed by others
References
Almeida J, Almeida A, Costa A (2014) Portfolio selection of information systems projects using PROMETHEE V with c-optimal concept. Pesqui Operacional 34(2):275–299
Altunok T, Özpeynirci Ö, Kazançoğlu Y, Yılmaz R (2010) Comparative analysis of multicriteria decision making methods for postgraduate student selection. Eurasian J Edu Res 40:1–15
Archer N, Ghasemzadeh F (1999) An integrated framework for project portfolio selection. Int J Proj Manag 17(4):207–216
Argyris N, Figueira J, Morton A (2011) Interactive multicriteria methods in portfolio decision analysis. In: Salo A, Keisler J, Morton A (eds) Portfolio decision analysis improved methods for resource allocation. Springer, New York, pp 107–130
Argyris N, Morton A, Figueira J (2014) Cut: a multicriteria approach for concavifiable preferences. Oper Res 62(3):633–642
Chien C (2002) A portfolio-evaluation framework for selecting R & D projects. R & D Manag 32(4):359–368
Cranmer A, Baker E, Liesiö J, Salo A (2018) A portfolio model for siting offshore wind farms with economic and environmental objectives. Eur J Oper Res 267:304–314
Earnshaw S, Hicks K, Richter A, Honeycutt A (2007) A linear programming model for allocating HIV prevention funds with state agencies: a pilot study. Health Care Manag Sci 10:239–252
Erkan H (2018) Balance in resource allocation problems: a changing reference approach. MSc Thesis, Bilkent University, Ankara, Turkey
Golabi K, Kirkwood C, Sicherman A (1981) Selecting a portfolio of solar energy projects using multiattribute preference theory. Manag Sci 27(2):174–189
Grushka-Cockayne Y, De Reyck B, Degraeve Z (2008) An integrated decision-making approach for improving European air traffic management. Manag Sci 54(8):1395–1409
Kangaspunta J, Liesiö J, Salo A (2012) Cost-efficiency analysis of weapon system portfolios. Eur J Oper Res 223:264–275
Karasakal E, Aker P (2017) A multicriteria sorting approach based on data envelopment analysis for R & D project selection problem. Omega 73:79–92
Karsu Ö, Erkan H (2020) Balance in resource allocation problems: a changing reference approach. OR Spectr 42:297–326
Karsu Ö, Morton A (2014) Incorporating balance concerns in resource allocation decisions: a bi-criteria modelling approach. Omega 44:70–82
Klapka J, Pinos P (2002) Decision support system for multicriterial R & D and information systems projects selection. Eur J Oper Res 140:434–446
Kleinmuntz D (2007) Resource allocation decisions. In: Edwards W, Miles R, von Winterfeldt D (eds) Advances in decision analysis: from foundations to applications. Cambridge University Press, Cambridge
Korhonen P, Wallenius J, Zionts S (1984) Solving the discrete multiple criteria problem using convex cones. Manag Sci 30:1336–1345
Liesiö J (2014) Measurable multiattribute value functions for portfolio decision analysis. Decis Anal 11(1):1–20
Liesiö J, Mild P, Salo A (2007) Preference programming for robust portfolio modeling and project selection. Eur J Oper Res 181:1488–1505
Liesiö J, Mild P, Salo A (2008) Robust portfolio modeling with incomplete cost information and project interdependencies. Eur J Oper Res 190:679–695
Liesiö J, Salo A, Keilser J, Morton A (2020) Portfolio decision analysis: Recent developments and future prospects. Eur J Oper Res. https://doi.org/10.1016/j.ejor.2020.12.015
Lokman B, Köksalan M, Korhonen P, Wallenius J (2016) An interactive algorithm to find the most preferred solution of multi-objective integer programs. Ann Oper Res 245:67–95
Lokman B, Köksalan M, Korhonen P, Wallenius J (2018) An interactive approximation algorithm for multi-objective integer programs. Comput Oper Res 96:80–90
Mavrotas G, Makryvelios E (2021) Combining multiple criteria analysis, mathematical programming and monte carlo simulation to tackle uncertainty in research and development project portfolio selection: A case study from greece. Eur J Oper Res 291:794–806
Mild P, Liesiö J, Salo A (2015) Selecting infrastructure maintenance projects with robust portfolio modeling. Decis Support Syst 77:21–30
Morton A, Keisler JM, Salo A (2016) Multicriteria portfolio decision analysis for project selection. In: Greco S, Ehrgott M, Figueira JR (eds) Multiple criteria decision analysis: state of the art surveys. Springer, New York, pp 1269–1298
Nasrabadi N, Dehnokhalaji A, Korhonen P, Wallenius J (2019) Using convex preference cones in multiple criteria decision making and related fields. J Bus Econ 89:699–717
Özpeynirci Ö, Köksalan M (2010) An exact algorithm for finding extreme supported nondominated points of multiobjective mixed integer programs. Manag Sci 56(12):2302–2315
Özpeynirci Ö, Özpeynirci S, Kaya A (2017) An interactive approach for multiple criteria selection problem. Comput Oper Res 78:154–162
Özpeynirci S, Özpeynirci Ö, Mousseau V (2018) An interactive algorithm for multiple criteria constrained sorting problem. Ann Oper Res 267(1–2):447–466
Salo A, Keisler J, Morton A (2011) An invitation to portfolio decision analysis. In: Salo A, Keisler J, Morton A (eds) Portfolio decision analysis improved methods for resource allocation. Springer, New York, pp 3–28
Silberberg E, Suen W (2001) The structure of economics: a mathematical analysis. McGraw-Hill, New York
Stal-Le Cardinal J, Mousseau V, Zheng J (2011) An application of constrained multicriteria sorting to student selection. In: Salo A, Keisler J, Morton A (eds) Portfolio decision analysis improved methods for resource allocation. Springer, New York, pp 213–240
Stewart T (1991) A multi-criteria decision support system for R & D project selection. J Oper Res Soc 42(1):17–26
Stummer C, Heidenberger K (2003) Interactive R & D portfolio analysis with project interdependencies and time profiles of multiple objectives. IEEE Trans Eng Manag 50(2):175–183
Tervonen T, Liesiö J, Salo A (2017) Modeling project preferences in multiattribute portfolio decision analysis. Eur J Oper Res 263:225–239
Vilkkumaa E, Salo A, Liesiö J (2014) Multicriteria portfolio modeling for the development of shared action agendas. Group Decis Negot 23:49–70
Wang J, Hwang W (2007) A fuzzy set approach for R & D portfolio selection using a real options valuation model. Omega 35(3):247–257
Yavuz M (2018) Two approaches for fair resource allocation. MSc Thesis, Bilkent University, Ankara, Turkey
Acknowledgements
Selin Özpeynirci and Özgür Özpeynirci were visiting researchers at MICS, CentraleSupélec, Université Paris-Saclay during this study. These authors acknowledge the support of the Scientific and Technological Research Council of Turkey (TÜBİTAK-2219 programme), İzmir University of Economics and CentraleSupélec.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Özpeynirci, S., Özpeynirci, Ö. & Mousseau, V. An interactive algorithm for resource allocation with balance concerns. OR Spectrum 43, 983–1005 (2021). https://doi.org/10.1007/s00291-021-00632-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00291-021-00632-1