A novel exact solution algorithm for a robust product portfolio problem under return uncertainty

Document Type : Article


1 Department of Industrial Engineering, Yazd University, Saffayieh, Yazd, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


This research address the optimization of product portfolio problem under uncertainty using the principles of financial portfolios theory. Since the success of the product portfolio is a strategic decision and it depends on the return’s future changes, the return is best to be considered as an uncertain parameter. The innovation of this research is the use of robust optimization approach and providing an exact solution algorithm based on the model of Bertsimas and Sim. Given the assumption of uncertainty in the returns, the product portfolio model is developed based on the robust counterpart formulation of Bertsimas and Sim. An exact solution algorithm is also presented to reduce the solution time. The results obtained by implementing in a real case study of the dairy industry in Iran show that increasing the confidence level decreases the portfolio’s total returns and increases its total risk. A comparison between the proposed algorithm and similar methods shows that, on average, it makes 3% improvement in the solution time.


1. Jiao J, Zhang Y. "Product portfolio planning with customer-engineering interaction". IIE Transactions, 37 (9), pp. 801-814  (2005).
2. Bazmohammadi S, Foroud AA, Bazmohammadi N. "Portfolio optimization in electricity market using a novel risk based decision making approach", Scientia Iranica Transaction D, Computer Science & Engineering, Electrical, 25 (6), pp. 3569-3583 (2018).
3. Biglova A, Ortobelli S, Rachev ST, Stoyanov S. "Different approaches to risk estimation in portfolio theory", The Journal of Portfolio Management, 31 (1), pp. 103-112 (2004).
4. Cardozo RN, Smith Jr DK. "Applying financial portfolio theory to product portfolio decisions: An empirical study". The Journal of Marketing, pp. 110-119 (1983) .
 5. Geum Y, Shin J, Park Y. "FMEA-based portfolio approach to service productivity improvement", The Service Industries Journal, 31 (11), pp. 1825-1847 (2011).
6. Fernandes R, Gouveia JB, Pinho C. "Product mix strategy and manufacturing flexibility", Journal of Manufacturing Systems, 31 (3), pp. 301-311 (2012).
7. Hajnoori A, Amiri M, Alimi A. "Forecasting stock price using grey-fuzzy technique and portfolio optimization by invasive weed optimization algorithm", Decision Science Letters, 2 (3), pp. 175-184 (2013).
8. Solatikia F, Kiliç E, Weber GW. "Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces", Organizacija, 47 (2), pp. 90-97 (2014).
9. Takami MA, Sheikh R, Sana SS. "Product portfolio optimisation using teaching–learning-based optimisation algorithm: a new approach in supply chain management", International Journal of Systems Science: Operations & Logistics, 3 (4), pp. 236-246 (2015).
10. Esfahani HN, Sobhiyah Mh, Yousefi VR. "Project Portfolio Selection via Harmony Search Algorithm and Modern Portfolio Theory", Procedia - Social and Behavioral Sciences 1 (226), pp. 51-58 (2016).
11. Relich M, Pawlewski P. "A fuzzy weighted average approach for selecting portfolio of new product development projects", Neurocomputing, 1 (231), pp.19-27 (2017).
12. Goli A, Zare HK, Tavakkoli-Moghaddam R, Sadeghieh A. "Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm", Numerical Algebra, Control & Optimization, 9 (2), pp. 187-209 (2019).
13. Yevseyeva I, Lenselink EB, de Vries A, IJzerman AP, Deutz AH, Emmerich MT. "Application of portfolio optimization to drug discovery" Information Sciences, 1 (475), pp. 29-43 (2019).
14. Jiang Z, Wang H, Zhang H, Mendis G, Sutherland JW. "Value recovery options portfolio optimization for remanufacturing end of life product", Journal of Cleaner Production 210, pp. 419-431 (2019).
15. Soyster AL. "Convex programming with set-inclusive constraints and applications to inexact linear programming", Operations research 21 (5), pp. 1154-1157 (1973).
16. Ben-Tal A, Nemirovski A. "Selected topics in robust convex optimization", Mathematical Programming, 112 (1), pp. 125-158 (2008).
17. Bertsimas D, Sim M. "The price of robustness", Operations research, 52 (1), pp. 35-53  (2004).
18. Bertsimas D, Pachamanova D. "Robust multiperiod portfolio management in the presence of transaction costs", Computers & Operations Research, 35 (1), pp. 3-17 (2008).
19. Álvarez-Miranda E, Ljubić I, Toth P. "A note on the Bertsimas & Sim algorithm for robust combinatorial optimization problems", 4OR, 11 (4), pp. 349-360 (2013).
20. Goli A, Babaee Tirkolaee E, Soltani M. "A robust just-in-time flow shop scheduling problem with outsourcing option on subcontractors",  Production & Manufacturing Research7(1), pp. 294-315 (2019).
21. Goli A, Zare H. K, Tavakkoli‐Moghaddam R, Sadegheih A. "Multiobjective fuzzy mathematical model for a financially constrained closed‐loop supply chain with labor employment", Computational Intelligence36(1), pp. 4-34 (2020).