Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie Hybrid artifcial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry Alireza Goli a, ⁎ , Hasan Khademi Zare a , Reza Tavakkoli-Moghaddam b , Ahmad Sadeghieh a a Department of Industrial Engineering, Yazd University, Saffayieh, Yazd, Iran b School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran ARTICLEINFO Keywords: Artifcial intelligence Runner root algorithm Multi-objective product portfolio problem Robust optimization Exact solution algorithm ABSTRACT The optimization of the product portfolio problem under return uncertainty is addressed here. The contribution of this study is based on the application of a hybrid improved artifcial intelligence and robust optimization and presenting a new method for calculating the risk of a product portfolio. By applying an improved neural network with runner root algorithm (RRA), the future demand of each product is predicted and the risk index of each product is calculated based on its predicted future demand. A two-objective (minimizing risk and maximizing return) mathematical model is proposed where, the efect of investments, reliability and allowable lost sales on the designed product portfolio are of concern. Due to the return uncertainty, two robust counterpart models based on the Bertsimas and Sim and Ben-Tal and Nemirovski approaches are developed. Then, an exact solution method is proposed to reduce the solving time of robust model. The results of the implementation in the dairy industry of Iran indicate that an increase in the confdence level, increase the investment risk and decrease the total return. The obtained results by the statistical tests indicate that the two newly proposed robust models are of similar performance in the fnding the maximum return solutions, while, here the least risky solutions, the Bertsimas model outperforms its counterparts. Moreover, the results of the proposed exact solution method indicate that this method reduces the execution time by an average of 3%, indicative of proposed method efectiveness. 1. Introduction The multi-product institutes always face challenges to modify, re- move or add products, indicating that the management should arrange a set of products which would it yield the optimal efciency of proft- ability (Amadini, Gabbrielli, & Mauro, 2016). With respect to diferent features of the products, like the proftability and raw material supply rate, product portfolio design should be planned in a manner where the optimal proftability is guaranteed. The portfolio management science provides tools and solutions that managers and decision-makers can choose from in order to realize the best product portfolio (Aksaraylı & Pala, 2018; Goli, Zare, Tavakkoli-Moghaddam, & Sadeghieh, 2019; Ha, Yang, & Wang, 2017; Hassanlou, 2017). All of the investment methods and theories are examined in a real- life situation, it is observed that most of these methods have two basic drawbacks in operating phase, in spite of the advantages of selecting each technique and optimizing the product portfolio (Wu & Chuang, 2012). The frst drawback is the assumptions underlying these theories. If they do not reveal real conditions, they will yield diferent results (Sadjadi & Karimi, 2018). The second drawback is the investment trade- of between the investment risk and return, which makes achieving a single optimal solution impossible (Aksaraylı & Pala, 2018). According to Cardozo & Smith (1983) fnancial portfolio theory can be adopted for optimal management of the product portfolio. Accord- ingly, in this study, attend is made to apply the basics of fnancial portfolio theory in designing an optimal product portfolio. In this theory, risk and return are always considered as the two main objec- tives in the portfolio optimization models, consequently, the simulta- neous risk and return optimization in the design of the product portfolio is discussed here. Designing a product portfolio is a strategic decision, where the re- turn of each product may change in the future. Determining the risk of each product in a given portfolio is ambiguous. For this purpose, a joint approach of artifcial intelligence and robust optimization is proposed hereto fnd the best portfolio under return uncertainty. This joint ap- proach is implemented in the dairy industry of Iran and the results are analyzed. This study is organized as follows: the literature review is presented https://doi.org/10.1016/j.cie.2019.106090 Received 16 March 2019; Received in revised form 22 September 2019; Accepted 24 September 2019 ⁎ Corresponding author. E-mail address: A.goli@stu.yazd.ac.ir (A. Goli). Computers & Industrial Engineering 137 (2019) 106090 Available online 25 September 2019 0360-8352/ © 2019 Elsevier Ltd. All rights reserved. T