Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry

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Highlights

  • A hybrid neural network and runner root meta-heuristic algorithm is proposed.

  • A new method for calculating the risk parameter is developed based on artificial intelligence.

  • Two robust counterpart formulation are proposed for multi-objective product portfolio problem.

  • An exact solution algorithm is developed and implemented to reduce the solution time of the proposed model.

  • Statistical tests and sensitivity analyses are used to evaluate the performance of robust product portfolio models.

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 artificial 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 effect 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 confidence 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 finding 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 effectiveness.

Introduction

The multi-product institutes always face challenges to modify, remove or add products, indicating that the management should arrange a set of products which would it yield the optimal efficiency of profitability (Amadini, Gabbrielli, & Mauro, 2016). With respect to different features of the products, like the profitability and raw material supply rate, product portfolio design should be planned in a manner where the optimal profitability 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 and Pala, 2018, Goli et al., 2019, Ha et al., 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 first drawback is the assumptions underlying these theories. If they do not reveal real conditions, they will yield different results (Sadjadi & Karimi, 2018). The second drawback is the investment trade-off between the investment risk and return, which makes achieving a single optimal solution impossible (Aksaraylı & Pala, 2018).

According to Cardozo & Smith (1983) financial portfolio theory can be adopted for optimal management of the product portfolio. Accordingly, in this study, attend is made to apply the basics of financial portfolio theory in designing an optimal product portfolio. In this theory, risk and return are always considered as the two main objectives in the portfolio optimization models, consequently, the simultaneous risk and return optimization in the design of the product portfolio is discussed here.

Designing a product portfolio is a strategic decision, where the return 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 artificial intelligence and robust optimization is proposed hereto find the best portfolio under return uncertainty. This joint approach is implemented in the dairy industry of Iran and the results are analyzed.

This study is organized as follows: the literature review is presented in Section 2 presents; the methodology is introduced in Section 3; the case study is introduced in Section 4; the numerical results are exposed in Section 5 and the article is concluded in Section 6.

Section snippets

Literature review

In the past researches, most of researched developing financial portfolio models. Some of the most contributed ones are presented as follow. Geum, Shin, & Park (2011) developed a systematic framework for improving the productivity of hospital services through a portfolio approach, where, the failure mode and effect analysis (FMEA) is used to find the optimal portfolio. Fernandes, Gouveia, & Pinho (2012) presented a new strategy for investing in the product portfolio, considering the production

Methodology

To optimize the product portfolio with a financial portfolio approach, the two key parameters of risk and return are of concern. The risk reflects the changes and returns of the present portfolio profit (Lejeune & Shen, 2016). Due to fluctuations in different economic indicators, these parameters are not predetermined in the exact sense. For this reason, it is necessary to consider an appropriate method for measuring the value of these parameters. Moreover, as observed in Fig. 1, the necessity

Case study

The Pegah Golpayegan Company, Isfahan province, Iran is considered for implementing this newly proposed product portfolio optimization. The lack of making proper decisions on the product portfolio is one of the main problems in this company, which lead to high set-up costs. This drawback is followed by high risk in production and lack of return which forces the managers to update the product portfolio for the future. This fact is justified with the following brief statistics: Products of 335

Numerical results

In this prediction network, 5 neurons are applied in the first hidden layer and 5 neurons in the second one. Here, 70% of data is considered for training and 30% for testing the network. In MLP + RRA, RRA is applied to the training data to find the best value for weights between different network layers, and to achieve the minimum MSE value. After implementing RRA, we will have the best possible MSE for training data. Then it will apply for the test data to monitor the performance of RRA. For

Conclusion and future researches

This paper has addressed the product portfolio optimization using hybrid artificial intelligence and robust optimization using risk and return concepts. First, the future demand for each product type has been predicted by using a hybrid MLP and RRA meta-heuristic algorithm. Next, a new technique for calculating product risk has been developed. Then, two optimization models based on the Ben-Tal and Nemirovski model and Bertsimas and Sim model were presented. As the portfolio selection is a

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