Multi-objective Mathematical Programming Research Articles

RETRACTED: Selecting and balancing market portfolio using artificial intelligence and fuzzy multiobjective decision-making model

Most enterprises focus on product portfolio management (PPM) and exclude market portfolio management, and individual markets are selected solely based on financial performance which may not be appropriate because other factors may dictate the outcome of the market selection. This study proposes a market portfolio model that considers market share, market growth, market competition, market risk, and market cost to maximize overall profit. A three-stage approach is proposed to identify potential product markets using an AI algorithm. A set of the most promising market is then determined based on the results of Stage 1 using a fuzzy multi-objective mathematical programming model by concurrently maximizing the total market share and market growth, and minimizing the market competition and market risk. A single-objective mathematical programming model is then used to determine a market portfolio to maximize the total profit using the results for Stage 2. The single-objective model is tested using two sets of threshold constraints. The balance of the market portfolio is discussed and the results are compared. The novelty of the article: (1) the first study involves a product market portfolio, (2) the decision of market selection is scientific (using AI instead of personal judgment), holistic (factors include market share, growth, competition, risk, cost, and profit) and optimized (using mathematical optimization), and (3) the market portfolio maximizes total profit. (4) the proposed method produces a portfolio with a higher profit than the TOPSIS method.

Trust and personalized individual semantics based fusion method for heterogeneous multi-criteria group decision making and application to live streaming commerce

This paper develops a new trust and personalized individual semantics (PISs) based fusion method for heterogeneous multi-criteria group decision making (HMCGDM) and applies to the selection of live streaming commerce plan. Firstly, a consistency-driven optimization model is built to determine the PIS of linguistic terms in linguistic preference relation of criteria given by the trustor and recommenders. Secondly, this paper defines a harmony degree to reflect the degree of difference in the evaluation information of different recommenders in HMCGDM problem. Then, considering the trust relationship between trustor and recommenders and between the recommenders themselves, two multi-objective mathematical programming models are constructed. One purpose is to produce values to positions that are not assigned, and the other purpose is to fuse the evaluation information of recommenders. In addition, combining the preference information of criteria given by trustor and Shannon entropy based on the collective evaluation information, the subjective and objective weights of criteria can be determined respectively. The comprehensive criteria’s weights are acquired by an optimization model which aims at minimizing the Jenson-Shannon divergence between the subjective and objective weights. Finally, an example of selection of influencer or celebrity in live streaming commerce for promoting new products sales is offered to verify the effectiveness of the proposed method.

Collaborative multicenter reverse logistics network design with dynamic customer demands

The vehicle routing problem for waste recycling has been created to improve resource utilization and reduce environmental pollution as a result of the rapid consumption of natural resources and the negative impact of waste on the environment. This study investigates a collaborative multicenter vehicle routing problem with time windows and dynamic customer demands. The collaboration among logistics facilities is an effective mechanism to reduce the number of vehicles and improve resource utilization in a multicenter reverse logistics network. A multi-objective mathematical programming model is proposed to coordinate static and dynamic customer demands while minimizing the total operating cost, the number of vehicles, and the total waiting time. A hybrid heuristic algorithm comprising an improved k-medoids clustering algorithm and an extended reference point-based non-dominated genetic algorithm- III, is designed to solve the multi-objective optimization model. The clustering algorithm is implemented to reduce the network complexity. The extended reference point-based non-dominated genetic algorithm- III with a dynamic insertion strategy is proposed to adjust service routes for dynamic customer demands and find the Pareto optimal solution for the multi-objective optimization model. The performance of the proposed algorithm is evaluated, and results suggest that the extended reference point-based non-dominated genetic algorithm- III has superior solutions in solving the collaborative multicenter vehicle routing problem with time windows and dynamic customer demands compared with other algorithms. The cost savings resulting from optimization are fairly distributed among participants in a collaborative alliance via the minimum cost remaining savings and principle of strictly monotonic path selection. The proposed methods are applied in a case study of a realistic reverse logistics network in Chongqing City, China. Different service periods and optimization strategies are discussed and compared to verify the effectiveness of the proposed solution methods. The optimization results indicate that the collaborative mechanism and dynamic insertion strategy can improve resource utilization and transportation efficiency and contribute to a sustainable urban logistics transportation system.

Designing an oil supply chain network considering sustainable development paradigm and uncertainty

This study proposes a multi-objective mathematical programming model to design an oil supply chain network at three levels: upstream, midstream and downstream. It includes oil wells, gas injection wells, production units, refineries, gas injection centers, distribution centers, export and import terminals. The proposed model optimizes all three economic, social and environmental goals at the same time. Drilling injection and production wells, transportation costs, production costs, gas injection center costs, as well as fixed and annual costs of refineries and distribution centers are all minimized in the economic dimension. The environmental dimension of sustainability reduces greenhouse gas emissions, while the social dimension of sustainability increases job opportunities. The optimization of associated petroleum gas injection operations into the reservoir is also taken into account in this study. The proposed model considers the uncertainty of critical parameters and employs a robust possibilistic hybrid approach to deal with it, as well as an interactive fuzzy approach to solve it. A case study in Iran is used to evaluate the suggested model's performance. In comparison to the single-objective economic model, the results of solving the model show that taking sustainability into account has reduced greenhouse gas emissions and increased job opportunities. The crude oil extraction potential increases in each period when gas injection optimization and reservoir pressure are taken into account. Furthermore, the cost of the supply chain grows as the amount of uncertainty in the suggested model rises. As a result, the uncertainty of system parameters must be considered.

A sustainability approach to vehicle modular platform design: A mathematical model

Today, sustainability and its economic, social, and environmental pillars are the main elements of new product market development. Therefore, manufacturers, considering all stages of a product life-cycle, consider it necessary to have a framework for producing sustainable products. Moreover, new product design and development processes especially sub-process of product definition and detailed design processes can play a very critical role in developing product sustainability. This paper considers the role that the car platform can play in creating a family of products and with regard to various data related to the environmental, economic, and social pillars of each of the 15 modules of a car platform and also, using the best–worst method technique and multi-objective mathematical programming with the augmented epsilon constraint method, we were able to achieve a set of platforms with maximum sustainability. The present study explores the possibility of determining the most efficient combinations of modules for every one of the 23 cars’ platforms to produce a collection of products. Through these methods, the 54 efficient solutions in the Pareto front were achieved, and out of this number, after considering all the factors and weights of the objective functions, solution no. 51 was selected as the most efficient. Subsequently, all the 15 module variants of the 23 platforms were determined for solution no. 51. Finally, these variants were ranked on the basis of the SAW technique, and finally, sensitivity analysis is done.

Increasing the sustainability of a fresh vegetables supply chain through the optimization of funding programs: A multi-objective mathematical programming approach

Purpose: This research develops a model to improve the quality and freshness of sold vegetables through a funding program between farmers and retailers. Through this program, retailers who are interested in the distribution of first quality vegetables provide funds to farmers to increase their production this type of vegetables through the acquisition of new machinery, technology, or training.Design/methodology/approach: The problem is solved through a multi-objective mathematical programming model that simultaneously optimizes the supply chain profits, the waste of vegetables, the economic unfairness among farmers, the unfairness in the distribution of funds, and the freshness of sold vegetables. The ?-constraint method is used to obtain several non-dominated solutions to the problem after linearizing the non-lineal equations related to the unfairness objectives.Findings: Results show that it is possible to improve the indicators related to the vegetable waste, the economic unfairness, the unfairness in the distribution of funds and the freshness of vegetables while maintaining similar to optimal profits for the supply chain. Interesting trade-offs between the five objectives are identified, which can be used by supply chain members to select the most appropriate solution to be implemented in the real supply chain.Originality/value: This research models aspects relevant to the agri-food sector that have not been previously modelled for the problem under study. The main novelties of this paper are the consideration of the limited shelf life of the vegetables as well as the requirement of ensuring a minimum freshness at the moment of their sale, the price dependence on the quality and freshness of vegetables, the optimization of vegetable waste and the freshness of vegetables sold, as well as the joint optimization of the five previously defined objectives.

Coordinated routing system for fire detection by patrolling trucks with drones

Vehicle routing problem with drones (VRPD) is an extension of classical vehicle routing, which involves the usage of trucks and drones. Nowadays, bushfires are taken into account as a major global challenging subject. Indeed, forests are very vulnerable to fires, and the classical patrol systems cannot patrol all areas of the forest and pastures due to the difficult crossing of some routes.The literature survey demonstrated that the mathematical models are an efficient approach for planning forest and rangeland patrols. Drones and trucks are used in cooperation for forest monitoring in this study, with drones acting as an efficient and accurate means of monitoring routes that are impassable to ground vehicles. However, this novel approach deals with several substantial challenges, including limitation in the drone's battery and the routing problem in an integrated truck-drone system based on considering hard-to-reach areas and creating a trade-off between time and cost of the patrol process. These issues make significant differences between the proposed novel approach and the classical vehicle routing problem. Thus, it is essential to develop a comprehensive approach to resolve these crucial issues. The present study develops a multi-objective mathematical programming model as mixed-integer programming for simultaneous patrolling of trucks and drones. The augmented epsilon constraint (AEC) method has been considered to solve the two-objective mathematical programming model. Besides, Benders' decomposition (BD) algorithm has been employed to evaluate the achieved results in large-size problems. The performance of the BD algorithm has been confirmed in this study. The findings indicated that the proposed model efficiently protected the forest via monitoring all areas, including impassable areas where ground patrolling is impossible (e.g., the lack of roads due to dense vegetation). Also, it was proved that this system was a novel, cost-effective patrol, which prevents uncontrollable fires in the shortest possible time.

Multiobjective Mathematical Optimization Model for Municipal Solid Waste Management with Economic Analysis of Reuse/Recycling Recovered Waste Materials

Municipal solid waste management in developing countries like Nigeria did not consider benefits from reuse/recycling recovered waste materials during solid waste evacuation and disposal. The benefits from recovered waste materials mostly go to informal waste vendors and scavengers. This study developed a multiobjective mathematical programming model for waste evacuation and disposal, considering the benefits of reuse/recycling recovered waste materials. Data were collected from the Abuja environmental protection board (AEPB), personal interviews, and other stakeholders. The formulated model was solved using spreadsheet solver version 14.0. The study uses various daily budgetary provisions for solid waste evacuation and disposal at a 15% recovery level of solid waste materials to observe the responses of the model. The solution shows that at 71.5% recovery of reuse/recycling recovered waste material; no budgetary provision is required to evacuate and dispose of the waste at the collection centers. Benefits realized from recovered waste materials are sufficient to evacuate and dispose of the wastes. After a 71.5% level of recovery, the net benefit of $1,108.17 from recovered waste materials starts to accrue until the percentage recovery level reaches 100%. The volume of waste shifted to the disposal sites was reduced to 74.5 tons (i.e., unrecoverable waste material) which is 16.82% of the total waste generated per day, and 368.33 tons (83.18%) of waste materials were recovered. The study will give the policymakers viable information to aid proper planning while budgeting and controlling solid-waste-associated problems in the Abuja municipal area in particular and the country as large.

Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

In this paper, we establish Fritz John stationary conditions for nonsmooth, nonlinear, semidefinite, multiobjective programs with vanishing constraints in terms of convexificator and introduce generalized Cottle type and generalized Guignard type constraints qualification to achieve strong S—stationary conditions from Fritz John stationary conditions. Further, we establish strong S—stationary necessary and sufficient conditions, independently from Fritz John conditions. The optimality results for multiobjective semidefinite optimization problem in this paper is related to two recent articles by Treanta in 2021. Treanta in 2021 discussed duality theorems for special class of quasiinvex multiobjective optimization problems for interval-valued components. The study in our article can also be seen and extended for the interval-valued optimization motivated by Treanta (2021). Some examples are provided to validate our established results.

Application of Three Metaheuristic Algorithms to Time-Cost-Quality Trade-Off Project Scheduling Problem for Construction Projects Considering Time Value of Money

Time, cost, and quality have been known as the project iron triangles and substantial factors in construction projects. Several studies have been conducted on time-cost-quality trade-off problems so far, however, none of them has considered the time value of money. In this paper, a multi-objective mathematical programming model is developed for time-cost-quality trade-off scheduling problems in construction projects considering the time value of money, since the time value of money, which is decreased during a long period of time, is a very important matter. Three objective functions of time, cost, and quality are taken into consideration. The cost objective function includes holding cost and negative cash flows. In this model, the net present value (NPV) of negative cash flow is calculated considering the costs of non-renewable (consumable) and renewable resources in each time period of executing activities, which can be mentioned as the other contribution of this study. Then, three metaheuristic algorithms including multi-objective grey wolf optimizer (MOGWO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective particle swarm optimization (MOPSO) are applied, and their performance is evaluated using six metrics introduced in the literature. Finally, a bridge construction project is considered as a real case study. The findings show that considering the time value of money can prevent cost overrun in projects. Additionally, the results indicate that the MOGWO algorithm outperforms the NSGA-II and MOPSO algorithms.

Multi-objective Mathematical Programming Model for Optimum Stratification in Multivariate Stratified Sampling

Multi-objective Mathematical Programming Model for Optimum Stratification in Multivariate Stratified Sampling

An urban metro network-based method to evaluate carbon emission and distribution cost of express delivery

A novel green delivery method for express delivery based on the urban metro network, referred to as Green metro express delivery (GMED), is presented. A multi-objective mathematical programming model is first proposed to maximize the search for the best transportation costs and lowest carbon emissions. To solve the GMED model e-ciently, a two-layer coding method is used to encode the path and the non-dominated sorting genetic algorithm II (NSGA-II) is adopted. Finally, a numerical experiment was conducted with Ningbo Metro Network as a case to prove the effectiveness and stability of NSGA-II in solving the GMED model. The result shows that: (a) Compared with the vehicle express delivery method (VED), GMED has lower carbon emissions and vehicle mileage. (b) For the same quantity of express delivery, the transportation costs of GMED and VED have their own advantages over different transportation distances. (c) For delivery distances with the same transportation cost, the lager the quantity of express delivery, the lower the transportation cost of GMED compared to VED.

NSGA-II algorithm for hub location-allocation problem considering hub disruption and backup hub allocation

Purpose One of the practical issues in the area of location and allocation is the location of the hub. In recent years, exchange rates have fluctuated sharply for a number of reasons such as sanctions against the country. Natural disasters that have occurred in recent years caused delays in hub servicing. The purpose of this study is to develop a mathematical programming model to minimize costs, maximize social responsibility and minimize fuel consumption so that in the event of a disruption in the main hub, the flow of materials can be directed to its backup hub to prevent delays in flow between nodes and disruptions in hubs. Design/methodology/approach A multi-objective mathematical programming model is developed considering uncertainty in some parameters, especially cost as fuzzy numbers. In addition, backup hubs are selected for each primary hub to deal with disruption and natural disasters and prevent delays. Then, a robust possibilistic method is proposed to deal with uncertainty. As the hub location-allocation problem is considered as NP-Hard problems so that exact methods cannot solve them in large sizes, two metaheuristic algorithms including a non-dominated sorting genetic algorithm non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are applied to tackle the problem. Findings Numerical results show the proposed model is valid. Also, they demonstrate that the NSGA-II algorithm outperforms the MOPSO algorithm. Practical implications The proposed model was implemented in one of the largest food companies in Iran, which has numerous products manufactured in different cities, to seek the hub locations. Also, due to several reasons such as road traffic and route type the difference in the rate of fuel consumption between nodes, this model helps managers and decision-makers to choose the best locations to have the least fuel consumption. Moreover, as the hub set up increases the employment rate in that city and has social benefits as it requires hiring some staff. Originality/value This paper investigates the hub location problem considering backup hubs with multiple objective functions to deal with disruption and uncertainty. Also, this study examines how non-hub nodes are assigned to hub nodes.

COMPARATIVE STUDY ON DIFFERENT TECHNIQUES FOR SOLVING MULTI OBJECTIVE PROBLEMS OF OPTIMIZATION

During the last 15 years, multi-objective mathematical programming has been one of the fastest developing fields of personal view. Following the use of evolutionary methods over single-objective optimization for a longer period of time, more than two decades, the wellness industry has incorporated several goals. The function has finally gained attention as a field of science. As a result, many people variations of current strategies and new evolutionary-based methods have been developed. In the scientific articles, it was recently written. In this paper, we suggest a multi-objective optimization algorithm that is based on antibody production theorem (either constrained or unconstrained). The aim of this paper is to summarise and compile details on these existing methods, stressing the relevance of analyzing operations analysis strategies, which are used by the majority of them. In an effort to entice scholars to explore these problems, they are focused. Approaches to mathematical analysis for new ways to utilize the scope evolved algorithms’ features. An overview of the key algorithms behind these methods is also given, as well as a short critique that includes their benefits and drawbacks, applicability, and some recommendations applications that are well-known. Finally, future developments in this field are discussed, as well as any potential future directions, additional analysis is also being considered. According to the findings, the suggested strategy seems to be a feasible solution for solving multi-objective optimization problems.

A New Mathematical Model for Redesigning the Reverse Supply Chain with Social Sustainability

The flow of goods in the supply chain is divided into two types of direct and reverse flows. Recently, more attention has been paid to the reverse supply chain because it can create benefit in waste products. In this paper, a nonlinear integer mixed integer multi-objective mathematical programming model for inverse and sustainable supply chain is presented. The objective functions of this model are economic, social and environmental goals. In addition, this model covers four levels including suppliers, collection centers, recycling centers and consumers. The purpose of this article is to assist managers in making decisions at strategic and tactical levels such as choosing a suitable location for the establishment of collection and recycling centers, selecting production technology, determining the amount of production in each recycling center and the use of available vehicles. To solve this mathematical model, a method based on linearization as well as foal planning is developed. Finally, in order to validate and evaluate the performance, the model is examined using a numerical example and sensitivity analysis is performed on its various parameters.

Optimal project portfolio selection with reinvestment strategy considering sustainability in an uncertain environment: a multi-objective optimization approach

PurposeThis study aims to develop a model for project portfolio selection considering organizational goals such as budgets, sustainability cash flow and reinvestment strategy under an uncertain environment.Design/methodology/approachA multi-objective mathematical programming model is proposed for project selection, which takes the social, environmental and financial aspects into account as the objectives of the project portfolio selection problem. The project evaluation and selection process in one of the large capitals in the Middle East with numerous urban construction projects was considered as a real case study, in which the subjects of environmental and social sustainability are of great importance. Then, the most significant criteria for project evaluation and selection based on sustainability were identified and ranked using the fuzzy best-worst method (BWM).FindingsThe criterion of “defining clear and real objectives” was ranked first, “project investment return period” was ranked second, “minimum changes in the predicted range” was ranked third, and the other ten sustainability indicators were ranked as well. Next, the presented mathematical programming model was solved using the augmented e-constraint method. The sensitivity analysis indicated that increasing the amount of investments in projects would increase their net present value. Also, increased investment had no effect on sustainability, while decreased investment caused sustainability to not being optimal.Originality/valueThis study focuses on the impact of the amount of investments on projects, and the associated costs of sustainable projects. Further to the authors' knowledge, there has been no relevant study taking uncertainty into account. Also, very few studies proposed a mathematical programming model for the project portfolio selection problem. Moreover, this research uses the brainstorming and Delphi method to identify the sustainability indicators influencing the organization and screens the evaluation indicators. Furthermore, the weights of the evaluation indicators are determined using the fuzzy BWM based on the consistency of opinions.

A multi-objective robust optimization model for upstream hydrocarbon supply chain

The hydrocarbon supply chain (HCSC) is a significant part of the world's energy sector. The energy market has experienced erratic behavior over the last few years results in financial risks such as exceeding certain limits of the budget or not achieving the desired levels of cash in-flow, i.e., revenue. In this work, robust optimization and multi-objective mathematical programming are used to develop a model that eliminates or at least mitigates the impact of uncertain market behavior. Robust optimization provides tactical plans that are feasible and robust over market scenarios. The model assesses the trade-offs between alternatives and guides the decision-maker towards the effective management of the HCSC. The economic objectives are to minimize total cost and maximize revenue, while the non-economic objective is to minimize the depletion rate. The model considers the environmental aspect by limiting the emission of CO2 and the sustainability aspect by reducing the depletion rate of natural resources. Uncertain behavior of the oil market is modeled on scenario representation. A case study based on real data from Saudi Arabia HCSC is provided to demonstrate the model's practicality, and a sensitivity analysis is conducted to provide some managerial insights. The results indicate that Saudi Arabia can cover its entire expenditure, break-even-point, by producing oil at 7.18 MMbbld and gas at 3,543.48 MMcftd. Besides, the robust approach provides a preferred plan with the highest cash inflow and the lowest sustainability over other approaches, e.g., deterministic, stochastic, and risk-based. The differences show that the robust model increases oil production to compensate for the variability of the scenario.

A multi-objective stochastic programming model for post-disaster management

This paper develops a mathematical model for post-disaster planning with human casualties, which can be considered as operational guidance for the proper use of emergency resources. For this purpose, a stochastic mixed-integer programming model is provided to formulate the problem. The objective functions of the model are (1) maximizing the survival probability of patients, (2) minimizing the maximum of completion time of treatment of all patients, and (3) minimizing the total cost of operations. The model is solved with the ϵ-constraint method. Due to the NP-hardness of the problem which is a significant challenge in the literature, two innovative meta-heuristic algorithms are proposed, i.e. a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective simulated annealing (MOSA). Finally, a comprehensive computational analysis is performed for evaluation purposes. Also, a case study is made on the earthquake in Iran, which illustrates the real-world application of the model. Highlights A stochastic multi-objective mathematical programming model to allocate patients to hospitals and treat them. NSGA-II and MOSA are proposed, in addition to ϵ-constraint method as solution methods. Performance of two meta-heuristic algorithms is measured with five evaluation metrics. The study showed that NSGA-II is more effective than MOSA. The model was implemented on a real-world case, Tabriz earthquake in Iran.

Optimization model to support sustainable crop planning for reducing unfairness among farmers

Agri-food production must increase while food waste needs to be reduced for improving the position of farmers. To do so it is necessary to sustainably manage agri-food supply chains beginning with the crop planning decisions. Although the centralized approach has usually been adopted for this purpose, it can lead to unfair solutions due to inequitable distribution of profits among farmers causing their unwillingness to collaborate in the implementation of decisions made. To solve this, in this paper a novel centralized multi-objective mathematical programming model is proposed to support the sustainable crop planning definition for a region that jointly optimize three objectives aligned to the sustainability aspects: supply chain profits maximization (economic objective), waste minimization (environmental objective) and unfairness among farmers minimization (social objective), being the last two objectives novel in the crop planning literature. It has also shown the conflicting nature of the three objectives finding trade-offs among them. Other novelties of this proposal are: (1) anticipation of operative decisions (such as harvest, transport, sale, clearance sale, waste and unmet demand) when defining the crop planning, (2) possibility of clearing the oversupply of crops as a means of increasing the farmers’ profits and reducing waste, and (3) the modelling of a agri-food supply chain characterized by the lack of intermediaries between farmers and retailers, fostering the freshest product delivery and farmers’ power position. The model is solved by applying the weighted sum method concluding that the crop waste generated along the chain and the unfairness among farmers can be considerably reduced by little decreasing the optimal SC profits.

Exploiting the Chain Convenience Store Supplier Selection Based on ANP-MOP Model

The purchase cost of chain convenience stores accounts for a large proportion of the total cost. Enterprises are facing the problem of how to reasonably reduce the purchase cost while ensuring the quality of service. This paper first considers the uniqueness of chain convenience stores, draws on existing research results, and establishes an evaluation index system for chain convenience store suppliers through field research. Then, we use the principal component analysis method of selection to determine the weight of each index and make a preliminary ranking of the importance of chain convenience store suppliers. Secondly, according to the relevant weights determined by the network hierarchy method, the collected data are substituted into the multiobjective mathematical programming model to analyze the distribution of supplier procurement and calculate the procurement cost. The level of procurement expenditures accounted for by suppliers confirms the importance of suppliers. The results show that through the evaluation and ranking of suppliers and the effective management of suppliers according to the ranking results, not only the goal of cost minimization is achieved but also the reasonable service level is guaranteed, which is scientific.