multi-objective optimization

Diversifying investment portfolios by incorporating a variety of assets is a well-established strategy for mitigating risk and enhancing returns. Traditionally, mathematical models for portfolio optimization have primarily focused on stock investments within the capital market. However, this study extends the scope of portfolio optimization to encompass both project and stock investments. This is a critical advancement as investors increasingly grapple with allocating budgets across these two asset types simultaneously. Therefore, this paper proposes a novel mixed portfolio optimization model that uses the Mean-SemiVariance-SemiEntropy approach. By incorporating project investments alongside traditional stocks, the proposed model offers more efficient portfolios that can lead to improved return/risk ratios for investors seeking to optimize their overall financial strategy.

Design/methodology/approach:

 An attempt has been made to bridge the gap between the distinct spaces of projects and stocks to facilitate their joint analysis. Subsequently, a Mean-SemiVariance-SemiEntropy approach has been employed to develop a model within a probabilistic framework. For validating this model, a numerical experiment involving three projects and five stocks from the capital market has been tackled, considering the preferences of an investor. Finally, the optimization problem has been solved using three metaheuristic algorithms: Genetic Algorithm (GA), Imperialist Competitive Algorithm (ICA), and Gray Wolfs Optimization (GWO).

The results obtained by solving the model using the above-mentioned metaheuristic algorithms demonstrated that despite the high speed of the GWO algorithm, the solutions provided by the GWO algorithm were not satisfactory compared to the GA and ICA algorithms. On the other hand, the acceptable speed with nondominated solutions was the advantage of the ICA algorithm over the GA algorithm. The evaluation of various performance metrics also revealed that the ICA algorithm outperformed the GA and GWO algorithms in this problem. Also, the inclusion of semi-entropy as a risk assessment metric led to an improvement in the return on the investment portfolios.

Research limitations/implications: 

Incorporating investor constraints and preferences, such as cardinality and boundary constraints, into the model forms an NP-hard problem. Consequently, exact solution methods are replaced by non-exact methods, such as metaheuristic algorithms. Given the diversity of project contracts, this study concentrated solely on projects with cost-plus contracts, where the entire project or a portion can be selected for partnership. Similar to the Markowitz model, the projects' returns such as stocks' returns were assumed to be normally distributed.Practical implications: This study significantly enhanced diversification, increased potential returns, and reduced risk for investors by introducing a novel mixed project-and-stock portfolio optimization model. The proposed approach can be implemented by a wide range of investors and managers of investment units in various organizations, bringing a new perspective to investment management.

Social implications: 

The far-reaching implications of this study extend beyond the realm of investment management, permeating social, economic, and political areas. The innovative mixed project-and-stock portfolio problem has the potential to positively transform society using fostering innovation, stimulating economic growth, and enhancing financial knowledge. This paper can foster economic growth and job creation by providing new investment opportunities and increasing investment in productive ventures. In summary, this study has taken a significant step towards improving social and economic well-being by introducing an innovative model for resolving investment challenges.

Originality/value:

 The innovation and strength of this research lies in incorporating projects as a new asset class into the traditional portfolio model. This goes beyond simply adding a new asset to an investment portfolio, as the nature of the projects introduces new complexities to the portfolio management process. For this purpose, this study employs a probabilistic approach based on historical data. In addition, the simultaneous use of two risk measures, i.e., semi-variance and semi-entropy, significantly improves the performance of the model by focusing on different risk aspects. This provides a more comprehensive picture of the risks associated with the portfolio and helps investors make more informed and wise decisions.

This paper presents a multi-objective mathematical model for the reverse supply chain of hospital waste management in Iran during the COVID-19 pandemic, incorporating dimensions of sustainability. The objectives of the model are as follows: 1) Minimizing the costs associated with building facilities and waste treatment centers, vehicle fuel costs, and environmental costs due to pollutant emissions; 2) Maximizing the energy generated from the waste combustion process; 3) Minimizing the risk of virus transmission resulting from inadequate waste management; and 4) Maximizing the number of job opportunities in the established centers. It is important to note that existing uncertainties are addressed through the application of fuzzy set theory. Given the multi-objective nature of the model, two multi-objective algorithms, namely the Pareto archive-based Krill Herd Algorithm and Non-dominated Sorting Genetic Algorithm II (NSGA-II), are employed to solve the defined problem. The results indicate that the proposed Krill Herd Algorithm converges to a solution with higher quality and dispersion compared to NSGA-II. Additionally, through a comparison of the spacing index and running time of the two algorithms, it is observed that NSGA-II explores the solution space with higher uniformity and solves the model in less time.

In the present unstable business environment, supply chains are considerably impacted by disruptions, necessitating the implementation of resilience strategies. These strategies, however, pose significant financial challenges for companies. Therefore, financing is essential in developing resilient supply chain networks. In addition to utilizing existing capital, options such as bank loans and trade credit can be employed to alleviate the financial burden and enhance working capital.  The present scholarship has failed to address the issue of financial strain resulting from the adoption of resilience strategies. Additionally, the significance of trade credit and repayment scheduling in all levels of the supply chain network also left under-researched. To fill this research gap, this paper proposes a three-tiered supply chain network consisting of main/support suppliers, factories, and distribution centers under uncertain demand conditions. The network is developed to effectively handle demand uncertainty and achieve optimal net present value and demand estimation. To solve the bi-objective model of the study, a preemptive fuzzy ideal programming approach accompanied by the implementation of the CPLEX solver is utilized. The findings lend support to the importance of securing financial support for support suppliers and establishing effective trade credit agreements across all levels of the supply chain.

Providing financial resources is necessary for the survival of any business. In supply chain networks, bank loans and commercial credits play a crucial role in financing. Supply chain networks are always affected by financial disturbances under uncertainty condition, therefore, the design of supply chain networks considering financial flows leads to the improvement of working capital. In this research, the supply chain network is designed and developed considering commercial credibility. Considering commercial credit at all levels in a three-level supply chain network including suppliers, factories and distribution centers can be stated as the main contribution of this study. In addition, considering the timing for the repayment of commercial credits by the factories and distribution centers in uncertainty conditions is another challenge of the present research. Due to the uncertainty of demand, supply chain planning should be done in such a way that the necessary financial resources for the production operations are incorporated. In this regard, the demand is considered under scenario-based uncertainty in the proposed model in which the maximization of the net present value as well as the demand estimate are the main objectives. The CPLEX solver was used for solving the model in small-sized instances and the Bee Colony and Wale multi-objective metaheuristic algorithms were used for solving the large-sized problems. The results show how commercial credit affects physical flow. Also, the Wale metaheuristic algorithm has a better performance than the other algorithm.

Today, due to the increase and complexity of customers' needs, the products available in the market do not satisfy the needs of the customers. Hence, the most effective way for an organization to achieve its objectives is to create distinction through both developing new products and bringing about variations in those products. This study, while pursuing the objective of evaluating product development design, aims to propose a multi-objective design. This model analyzes the developed design from two perspectives of general criteria and variation capacity norms.
Design/methodology/approach: The current research embarks on identifying general criteria using Balanced Scorecard (BSC). The proposed model offers criteria according to which the required standard measures for the evaluation of the product development design are customized and extracted. After determining the evaluation criteria related to each perspective – general and variation capacity- the mentioned criteria have been validated. Then, by using the existing methods, these criteria have been quantified. Finally, the identified standard measures have been employed in the proposed multi-purpose optimized model. 
In this paper, a real case was studied in the Iran Electronics Industries, and the result of the configuration was illustrated. Quantitative values ​​of validated criteria were determined with the help of academic and industry experts and existing methods. After calculating the quantitative values ​​of the criteria for the evaluation of phased array radar development designs, these values were used in the multi-objective optimization model and measured in terms of the amount of risk, revenue, organizational strategy and the amount of effort towards redesign. Finally, by solving the optimization model using GAMZ win 64 25.1.12 software and the weighted sum method, the best development plan was selected.
Research limitations/implications: The main limitation of this study is the lack of accurate information in the early stages of product development. In this research, it was assumed that the information provided by the experts and designers of the relevant industry is correct and real. It is suggested to use fuzzy data in future studies so that the result has more reliability. For future research, the following subjects can be attractive and the present study can provide the necessary background for researchers who seek to work on such subjects: i) In the current research, the time parameter was not considered. It is suggested to consider time in future research; ii) to identify non-common components between the two current and future generations, the method of calculating the priority of standardization of components and considering the technical and financial ability of the producer was used. It is suggested to decide according to possible technologies in the future; iii) another perspective can be used to categorize and identify criteria; iv) to calculate reliability and maintainability, the lifetime of systems was assumed to be exponential and with a constant failure rate. It is suggested to use Weibull distribution with variable failure rate for a more realistic calculation, and v) it is suggested to compare the results of this study with other studies.
Practical implications: Finding comprehensive criteria to evaluate product development designs and providing an effective mathematical model for evaluation can lead to selecting the best product development designs. Selecting an optimal design can prevent the increase in product modification costs and the effort to redesign and reduce the time to supply new products to the market.
Originality/value: Based on the literature review, particularly the internal research, a method that evaluates product development designs with comprehensive criteria including finance, customer, business and internal work, growth and learning, and variation capacity has not been found. Also, the Design for Variety approach has not been used in the initial phases of research and it is applied when the product is made and released to the market.

This paper investigates unreliable multi-product assembly lines with mixed (serial-parallel) layout model in which machines failures and repairing probabilities are considered. The aim of this study is to develop a multi-objective mathematical model consisting the maximization of the throughput rate of the system and the minimization of the total cost of reducing mean processing times and the total buffer capacities with respect to the optimal values of the mean processing time of each product in each workstation and the buffer capacity between workstations. For this purpose, in order to configure the structure of the mathematical model, Simulation, Design of Experiments and Response Surface Methodology are used and to solve it, the meta-heuristic algorithms including Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Non-Dominated Ranked Genetic Algorithm (NRGA) are implemented. The validity of the multi-objective mathematical model and the application of the proposed methodology for solving the model is examined on a case study. Finally, the performance of the algorithms used in this study is evaluated. The results show that the proposed multi-objective mathematical model is valid for optimizing unreliable production lines and has the ability to achieve optimal (near optimal) solutions in other similar problems with larger scale and more complexity.

Due to the trend of increasing demand for electricity consumption, the use of current fossil fuel-based electricity production technologies has led to frequent blackouts in the summer and fuel burning in the winter. Therefore, the use of renewable energy sources and especially the construction of solar power plants can be a solution to end the blackout and fuel burning crises. The purpose of this research is the multi-objective optimization of the allocation of solar power plant construction to meet the electricity demand. In the objective functions of the problem of system costs, the amount of disturbances in the lines and the amount of greenhouse gases were minimized, as well as the amount of covered areas was maximized. In this research, the LP metric method has been used to solve the problem of multi-objective optimization in GAMS software. In order to validate the presented mathematical model, the correctness of the presented model was checked by GAMS software.Then, by presenting a numerical example, the complexity of the problem, the effectiveness of the multi-objective genetic algorithm in small and large dimensions were investigated. Finally, a case study regarding the construction of a solar power plant in Kashan, Aran and Bidgol region was investigated  and  According to the given information and the input data of the problem, the situation of the candidate areas for the construction of solar power plants was determined and Also, different areas of demand were assigned to the built solar power plants.

This study aims to optimize the energy supply system of a greenhouse considering twelve different climate conditions in Iran. For this purpose, an integrated two-objective linear energy optimization model has been developed to control the inside temperature and provide the required heating, cooling, and electricity by receiving electricity, gas, and water. The mentioned goals are to minimize operating costs (taking into account the discount rate over twenty years) and the initial cost and minimize the deviation of the inside temperature from the desired value. The initial cost of energy equipment is the result of examining data from domestic manufacturers and obtaining the equipment cost curve. The analysis of the results shows that the best areas for greenhouses construction are Kerman, Tehran, and Arak, respectively, for which the total cost is around ten thousand dollars.

The main purpose of this study is to provide three simulation-based risk management models for optimal placement of wind turbines in Khodabandeh city (located in the south of Zanjan province) taking into account the wake effect and uncertainty in wind speed and direction. For this purpose, wind speed and direction data were collected, then wind speed and direction uncertainty was modeled by Monte Carlo simulation and three risk management models presented were optimized with PESA-II, NSGA-II and MOPSO algorithms. Standard deviation and tenth percentile are used as risk criteria. Based on the findings, the maximum output power of the wind farm is about 8.5 MW. Also, according to the tenth percentile risk criterion, in 90% of cases, the production is less than 1.8 MW, which it was found that the construction of a wind farm in the area has a high production risk. Is. Therefore, investing in the study area requires high risk-taking of the investor. The risk management models used in the research provide useful detailed information about the expected power, cost and risk of constructing a wind turbine project. Comparing the performance of algorithms for all three models in terms of proximity of solutions to the ideal solution, PESA-II algorithm and in terms of variety of solutions, NSGA-II algorithm has a better performance than other algorithms

Supply chain network design is one of the most important issues in supply chain management. Therefore, the purpose of this study is to design a closed loop supply chain network in conditions of uncertainty and solve it using meta-heuristic algorithms.

This research is of applied kind. In this research, field and library study methods were used to collect information. Considering the selection of the tire industry as the under study industry for designing the proposed supply chain network, in this study, using field research, the required data from Kian Tire, Iran Tire, Dena Tire, Barez Tire, Kavir Tire, Yazd Tire, Artaville Tire and Pars Tire were collected and used to solve the model.

The modeling of this chain is done based on environmental considerations, minimizing the total cost of the chain and maximizing the response to customer demand. Finally, this model is solved using NRGA and NSGAII meta-heuristic algorithms and the obtained results are compared with each other. Also for credit evaluation suggested model using limitation epsilon method has been implemented in the GAMS software too.

In this research, the design of closed-loop supply chain network in conditions of uncertainty and its solution using meta-heuristic algorithms is considered and based on the research results, executive proposals were presented.

The present study aimed to provide a decision model in Internet advertising planning using multi-objective genetic algorithm. The proposed model is a model for distributing advertising resources through the web to optimize the effect of advertising, based on research literature and according to the characteristics of advertising through the web. This model can simultaneously consider the interests of network managers and advertisers.

The present study is in the category of descriptive research in terms of method and nature and is a survey in terms of implementation and also applied in terms of purpose. In this research, since the proposed model is a multi-objective optimization model with high dimensions, the multi-objective genetic optimization algorithm has been used to solve it. 

In this study, unlike previous studies, by simultaneously considering the conflicting goals of applicants for advertising through the web (reducing advertising costs) and webmasters (increasing profits from the provision of services), about How to better optimize the allocation of advertising resources to the website was discussed and a new decision model was presented that had two conflicting goals. In fact, this multi-objective model not only maximizes website revenue but also reduces the cost to the applicant of advertising; therefore, the mentioned model can be the basis of the work of these two. On the other hand, based on the characteristics of advertising through the web and existing pricing strategies, a hybrid pricing strategy was created based on the variables "cost per thousand views" and "cost per click in this research". Then, a new multi-objective optimization decision model based on this strategy was proposed. In this model, the interests of webmasters and advertisers are considered. Finally, by providing a computational example and numerical results of the simulation, the effectiveness of the model and algorithm is proved.

The simulation results showed that the optimization model and algorithm are justified and feasible. Also, the set of optimal Pareto answers obtained from solving the model can satisfy the webmasters and applicants for advertising. Using this model, they interact and compromise and try to consider the interests of another person. Considering that by solving the proposed model, unlike other models, the interests of both stakeholders have been considered, the answer set is included in the win-win strategy. Therefore, since the validation of this model is done through simulation, in practice, network administrators can when coding ads on web pages by applying the mathematical relationships provided in the proposed model, the method of calculating the cost of applicants for advertising is logical.  And provide a list of possible suggestions to the applicant. In this list, different combinations of simultaneous decision variables at the desired level, by maximizing the income of network managers, minimize the costs of each applicant according to their opinion, which leads to the adoption of more efficient pricing strategies.

Home Healthcare provides a wide range of home care services from prevention to rehabilitation and primary care to professional nursing services. This research presents a two-objective mathematical model based on the mixed integer linear programming approach for the home healthcare routing and scheduling problem (HHCRSP) with the objectives of minimization the nurses’ travel costs and the maximal working time difference among nurses. Considering the multimodal transportation, several initial health centers and one final health center and patient and nurse time windows are important features of the studied mathematical model. Small-sized problems have solved by using the Ɛ-constraint method on GAMS software. Also, due to the NP-hardness of the problem, MOPSO and NSGA-II algorithms have used to solve the medium and large-sized problems. The statistical results showed that the NSGA-II performed better than the MOPSO for medium and large sizes of problems in both MID and NOS performance metrics. Overall, Results of the performance metrics on different sizes of problems indicate the efficient and effective performance of NSGA-II in solving the understudied problem.

Over the past decade, there have always been new paradigms in supply chain design. The green supply chain is a new concept that helps organizations deal with unexpected disruptions and minimize environmental impacts. The main purpose of this study is to present a multi-objective optimization model for a green-resilient supply chain network in cement industries. Dashtestan cement industries have been selected for validation and implementation of the model.

After reviewing the theoretical foundations and experimental background, the network was designed. Then, an appropriate mathematical model was developed and validated by a case study. In this study, scenarios were defined in two modes of production surplus and non-production surplus. Data analysis in each scenario was performed with MATLAB software. The CPLEX solver was also used to solve the model.

The results showed that Dashtestan Cement Company's production surplus has no effect on supply chain resilience. Also, it can be concluded that if there is a production surplus, the cost of carbon dioxide emissions is less than the one in the absence of surplus production.

The company's production level has little effect on the cost of carbon dioxide emissions and the amount of that in the designed network is mostly due to the carbon emission rate in the production nodes and arcs. Therefore, the reduction of carbon footprint in these parts of the network should be considered.

Since the resources are limited in each industrial region, it is logical to allocate resources to the most efficient industries. Recently, based on the environmental conditions and geographical position of Tehran, the capital of Iran, this city is in critical environmental situation. Therefore, assessing both environmental and industrial efficiency of Tehran’s production industries is essential. In this regard, network Data Envelopment Analysis is used in order to compare total efficiency of the industries including environmental and operational efficiencies. Network Data Envelopment Analysis is a developed form of standard DEA and looks inside the black-box in order to assess the partial efficiency in addition to the total efficiency which will results to a multi-objective problem. The contribution of this research is introducing a technique for assessing the efficiency of a network structure by means of the developed form of network DEA technique which minimizes the distance from the individuals’ independent efficiency with a linear optimization approach. Results show the advantages of the proposed model.

Despite their achievements, the industrial parks have had a devastating effect on the environment and sometimes did not address social welfare issues. Therefore, it is necessary to improve their design based on the characteristics of sustainable development and ecological principles. One of the effective measures in this regard is Industrial Symbiosis (IS). It is a set of integrated plants aiming to exchange the waste of each plant as the raw material of another plant. Although several models have been presented for the optimization of water or energy exchange, one of the purposes of this research is to simultaneously exchange raw materials and waste in solid, liquid, and gas types. Considering the social characteristic of sustainable development is another necessity of this research that has been less discussed. Also, a significant portion of the waste needs to be recycled and cannot be exchanged directly between plants. Therefore, another purpose of this research is to increase the productivity of the model considering material flow between plants and recovery centres, which did not exist in previous

 In this research, a two-objective mixed-integer linear programming model is proposed considering the characteristics of sustainable development, which simultaneously enables the exchange of all raw materials and waste. Providing recyclable waste exchanges via recovery centres is another strength of the proposed model. The first objective is to minimize the economic costs of the IS network, and the second objective is to maximize social welfare. The environmental characteristic is also controlled by model constraints. Finally, to validate the proposed model, it has been implemented in one of the industrial parks of Alborz province. Also, to solve the model, the ε-Constraint method has been used.

 According to the model’s results, most of the plant's waste was replaced by the input raw materials of other plants, while before IS, all plant waste was disposed and all input materials were supplied through fresh materials. Therefore, the findings of the proposed model are as follows:reducing the volume of disposed and useless plant waste and its costs; reducing the volume of fresh input raw materials plants and its costs; creating 23 job opportunities through the establishment of centres to recover; compensating for lost working days due to the reduction of environmental pollutants to achieve the social characteristics of sustainable development; and improving the characteristics of sustainable development in the industrial park compared to the time before IS.

 This research, like other studies, has assumptions and limitations in model development. For example, the transmission path of all three types of material and waste was considered the same. The feasibility of situations trade-off and the use of waste of recovery centres was not studied. Also, the expectations of the park and the plants were considered in an integrated manner. Therefore, the following subjects are suggested to improve and develop the model in future studies:design of IS network using bi-level models; development of a model for the use of waste from the recovery centre; for example, methane gas or sludge treatment plant; model development by considering seasonal plants through reliability inventory models and intermittent flows; development of a model for locating and allocating unusable waste in the current network to the new plant; and development of a model based on the different transmission paths for material and waste flow in solid, liquid, and gaseous according to the research assumption 3.

One of the most significant applications of this paper is the simultaneous optimization of exchange material and waste in three types of solid, liquid, and gaseous in IS network to achieve the characteristics of sustainable development. Also, reducing the cost of input material and waste disposal compared to the time before IS are the economic advantages of this research. Social implications - One of the aims of this paper was to reduce the environmental and social impact of the industrial park to achieve the characteristics of sustainable development. For example, reducing the volume of fresh input raw materials and disposed waste plants and job creation were the environmental and social advantages of this study.

The innovations of this research include the following:simultaneous optimization of material and waste flow in three types: solid, liquid, and gaseous; considering the social characteristic of sustainable development; and considering the exchange between recovery centres and plants to use the waste in need of recovery.

Although the construction industry, especially because of its relationship with other economic sectors, is one of the most important sectors that plays a key role in a country's economic growth, the construction supply chain has been considered less attention. Therefore, construction supply chain network design is of great importance for not only the companies but also governments. Thus, presenting an original mixed integer linear programming model, this paper introduces an optimal framework for a multi-project multi-resource multi-supplier construction supply chain network design for large construction companies with a decentralized procurement strategy. The main objective is to design a reliable supply chain model based on the quality of projects under the certain predefined budget, considering the entire supply chain as a single entity. Using a bi-objective approach to formulate the chain and the Lp-metric approach to solve the problem, make it possible to obtain a single-objective structural framework to reliability-quality trade-off consideration. To solve the problem in small and medium scales, GAMS software is employed, and a hybrid algorithm based on Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm is developed to solve the large-scaled problem. The results show the capability of the model to attain optimal size of the chain as well as the quality-reliability trade-off considering a pre-specified budget. And, to the best of authors knowledge this is the first to obtain such a structured integrated framework in the construction supply chain.

In this research, a multi-objective mathematical model is proposed for the airline multi-skilled crew scheduling problem. The multi-skilled crew can be assigned to flights and airplanes according to their skills. The objective functions of the proposed model are: (1) Maximizing the number of leave days planned according to the days announced by the flight crew, and (2) Minimizing the penalty costs associated with violation of minimum and maximum working hours. Several test problems have been designed based on the data acquired by the airline studied in this research. Due to the NP-hard essence of the model, we have employed two meta-heuristics, namely the multi-objective differential evolution (MODE) and Non-dominated Sorting Genetic Algorithm II (NSGA-II). These algorithms are calibrated using the Taguchi method. The algorithms have been compared based on several multi-objective performance measures. Each algorithm has been more successful in terms of some metrics. The comparisons between algorithms and sensitivity analysis show that the proposed model and algorithms can produce appropriate schedules for the airline crew scheduling problem.

Crises are the inevitable realities of human life; which is an accident that occurs naturally or suddenly orincreasingly by human and to address it, there is a need for urgent and fundamental measures. When thecrisis occurs, pre-determined storage locations will play an important role in relief; therefore, the selection ofsuitable places for warehouses is one of our main goals in this research. In this research, a bi-objective linearprograming model with integer variables is developed. The proposed model attempt to minimize total costalong with maximizing the minimum weight of open shelter areas while deciding on the location of shelter areas,the assigned population points to each open shelter area and controls the utilization of open shelter areas.In order to solve proposed model, some of well-known multi-objective, exact methods include a weightedsum method, LP-metric method, and goal programing approach are employed. Finally, the best open shelterareas with considering the minimum cost is obtained, which these results can be useful for crisis organizations.