Fuzzy Mathematical Programming Model Research Articles

Optimisasi Portofolio Saham Syariah dengan Pendekatan Fuzzy Goal Programming

This study discusses about solving the problem of stock portfolio optimization. The portfolio optimization problem can be modeled as a multiobjective model with two objective functions, they are maximizing return and minimizing risk. This study uses the mean-variance Markowitz model to model the portfolio. The fuzzy goal programming approach is used to solve stock portfolio problems by converting a multi-objective model into a fuzzy mathematical programming model which is solved using a nonlinear programming method. The results of implementing the model on stocks listed on the Jakarta Islamic Index show that the best investment proportion forms an optimal portfolio according to the level of aspirations. Several different optimal portfolios can be formed using the fuzzy goal programming approach. The difference in the results of these portfolios depends on the level of aspiration of investors.

A novel integrated approach based on best–worst and VIKOR methods for green supplier selection under multi-granularity extended probabilistic linguistic environment

With consideration for the extensive resources consumption and environmental degradation being on the rise today, implementing green development strategy to pursue both socioeconomic growth and the coordinated of environment sustainability, has become an increasingly important issue in modern enterprise supply chain operations management. Hence, the appropriate green supplier selection (GSS), viewed as a core issue in green supply chain management (GSCM), requires continuous research in this field to obtain a complete perception on GSS practices. It can be regarded as a multi-attribute group decision-making (MAGDM) problem that involves many conflict and unmeasurable evaluation criteria. In view of the superiority of multi-granularity extended probabilistic linguistic term sets (MGEPLTSs) in modeling such issues on potential ambiguity, complexity and uncertainty in actual GSS practices, we propose a novel integrated MAGDM methodology for GSS problems, by integrating the BWM (best–worst method) with the VIKOR (VIšekriterijumsko KOmpromisno Rangiranje) technique under the MGEPLTSs environment. First, by introducing the multi-granularity and probabilistic linguistic term sets, the MGEPLTSs are proposed to represent and quantify the decision information of GSCM practitioners. Then, the BWM is introduced to the MGEPLTSs environment to compute the weights of decision-making panels and evaluation attributes in GSS problems, by building the fuzzy mathematical programming model, respectively. Finally, we extend a multi-granularity extended probabilistic linguistic VIKOR method to calculate the compromise measure of alternatives considering the group utility maximization and the individual regret minimization, thereby achieving the full ranking of alternatives. A GSS case is conducted to illustrate the feasibility of the proposed approach, and the sensitivity analysis and comparative analysis with other similar approaches are presented to demonstrate its effectiveness and advantages.

Collaborative emergency decision-making for public health events: An integrated BWM-TODIM approach with multi-granularity extended probabilistic linguistic term sets

Carrying out emergency rescue in coordination with multiple organizations, is of great significance for the effectiveness and timeliness of emergency response. Therefore, this study aims to extend a novel practical tool for distinguishing the optimal combination of different emergency plans in multiple organizations. In a multi-granularity extended probabilistic linguistic term sets (MGEPLTSs) environment, we propose a new collaborative emergency decision-making (CEDM) approach in the inspiration of the best–worst method (BWM) and TOmada de Decisão Iterativa Multicritério (TODIM) method. Firstly, a combined multi-granularity and extended probabilistic linguistic term sets, namely MGEPLTSs, are proposed to quantify the preferences given by decision makers (DMs) to address the issues on potential ambiguity and uncertainty in actual CEDM. Then, the BWM is introduced to the MGEPLTSs environment to compute the index weights of the individual and collaborative performance evaluation for multi-plan combinations, by building the fuzzy mathematical programming model respectively. Finally, we develop the multi-granularity extended probabilistic linguistic TODIM method to calculate the overall dominance of indexes considering the psychological behavior of DMs, thereby achieving the ranking of multi-plan combinations. A CEDM case on COVID-19 epidemic is used to illustrate the feasibility of the proposed approach, and the sensitivity analysis and comparative analysis with other similar approaches are presented to demonstrate its effectiveness and superiority.

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.

Green Design of Regional Wheat Supply Chains under Uncertainty

This study presents a fuzzy mathematical programming model to optimize regional wheat hub center in Iran with the aim of achieving sustainable self-sufficiency, swap and export of wheat to neighboring countries. The proposed model is developed for a 10-year planning horizon with real-world assumptions under uncertainty. By the proposed model, the optimal decisions are made on the amount of wheat cultivation areas in different provinces, capacity of silos, amount of import, swap and export of wheat, transportation mode and storage amount of wheat in different periods. Two objective functions including economic and environmental goals are optimized by the proposed model. The proposed model is examined under uncertainty conditions and the possibilistic programming approach is used to deal with the uncertainty of parameters. Finally, the presented model is validated through investigating a real case study in Iran. The results show the efficiency of the model for making optimal strategic and tactical decisions in wheat supply chains.

A Fuzzy Multi-Objective Mixed Integer Linear Programming Model for End of Life Use

One of the main challenges of designing the effective reverse logistic network is to predict the amount of product which reach end of their useful life. Thus, in this study, we propose fuzzy multi-objective mixed integer linear programming (Fuzzy-MOMILP) model which the amount of returned product is considered as an uncertain parameter. In order to solve the proposed multi objective fuzzy mathematical programming model, a fuzzy solution approach is applied. The proposed Fuzzy-MOMILP model seeks to minimize the total reverse logistic network cost and minimize the total carbon emissions related to the transportation and processing of used products. To validate the model, a case study is examined. The results of this study indicate that the proposed model can be used to design a sustainable reverse logistic network for end-of-life (EOL) products.

The impact of petrochemical industry economic activities on environmental factors using a fuzzy mathematical programming model

Due to the nature of activities and processes, the petrochemical industry causes the production of industrial effluents, emissions and wastes that have adverse effects on the environment. The purpose of this study is to investigate the effect of petrochemical economic activities on environmental factors. In this paper, in order to minimize the costs and the amount of pollution caused by the emission of harmful gases, the closed-loop green supply chain model has been used, in which direct and reverse logistics networks have been considered. As a result, a fuzzy mathematical programming model has been developed for when the data are not definitively known. After the demand parameters and the amount of pollution are considered fuzzy, the maximum and bisector mean methods of the area are considered as methods (diffusion) of comparison and ranking of fuzzy definite numbers, and by adding Limitations of these two methods, the model was developed. To solve the model with real data, a plant from the petrochemical industry was selected and the data were prepared for a solution with very good estimates. Finally, the colonial competition algorithm was used to solve it. According to the model, its applicability was shown to reduce the number of environmental pollutants along with the reduction of transportation and waste, and the model for the closed-loop supply chain, which simultaneously considers two direct and inverse logistics networks. It is appropriate.

A fuzzy mathematical programming model for sustainable supply chain under competition and uncertainty environment

A fuzzy mathematical programming model for sustainable supply chain under competition and uncertainty environment

A possibilistic programming approach for biomass supply chain network design under hesitant fuzzy membership function estimation

The recognition of membership function by knowledge acquisition from experts is an important factor for many fuzzy mathematical programming models. Thus, the hesitant fuzzy membership function (HFMF) estimation could help users of the mathematical programming approaches to provide a powerful solution in continuous space problems. Therefore, this study proposes a possibilistic programming approach based on Bezier curve mechanism for estimating the HFMF. In the process of possibilistic programming approach, an optimization model is presented to tune the primary parameters of Bezier curve by the goal of minimizing the sum of the squared errors (SSE) between the empirical data and fitted HFMF. After that, the efficiency and applicability of the proposed approach is checked by proposing a novel mathematical model for biomass supply chain network design problem. In this case, the bio-products demand is declared as an imprecise parameter that follows from the estimated HFMF to increase the accuracy of the obtained results by addressing the uncertainty and unreliability of the information. Finally, a computational experiment and validation procedure about the biomass supply chain network design is provided to peruse the verification and validation of the proposed approaches.

Multi-mode project portfolio selection and scheduling in a build-operate-transfer environment

Integrated decision-making about selecting and scheduling a project portfolio can lead to a more desirable performance. This paper considers the problem of selecting a portfolio among a set of possible projects which should be scheduled from vantage point of contractor simultaneously. Each project can be implemented in several modes, each of which has potential cash flows over the time horizon. Therefore, an NPV can be calculated for each project in a particular implementation mode. In this contribution, a structure composed of a fuzzy hybrid multi-criteria method and a fuzzy bi-objective mathematical programming model are presented to deal with quantitative and qualitative dimensions of the project portfolio selection and scheduling problem. To solve the problem, first the qualitative criteria are weighted by the fuzzy AHP, the obtained weights are applied to evaluate the projects in the fuzzy TOPSIS. Then, the fuzzy mathematical model is formulated with two objectives, including maximizing NPV of profit and portfolio score based on assumptions close to real conditions of build-operate-transfer (BOT) contract. According to the assumptions, projects have multi-period implementation and operation phases; there are a penalty and reward system to meet the deadlines. Also, the company is able to attract external capital. The fuzzy model is converted to its crisp counterpart, and then the model is solved using the augmented epsilon constraint method with the data of an Iranian company as a case-study. The results show that considering multiple modes for project implementation has better results in comparison with confining the implementation of each project to only one mode (the mode with the maximum NPV).

A collaborative emergency decision making approach based on BWM and TODIM under interval 2-tuple linguistic environment.

Emergencies require various emergency departments to collaborate to achieve timely and effective emergency responses. Thus, the overall performance of emergency response is influenced not only by the efficiency of each department alternative but also by the coordination effect among different department alternatives. This paper proposes a collaborative emergency decision making (CEDM) approach considering the synergy among different department alternatives based on the best–worst method (BWM) and TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method within an interval 2-tuple linguistic environment. First, the evaluation information provided by decision makers (DMs) is represented by interval 2-tuple linguistic variables to reflect and model the underlying diversity and uncertainty. On the basis of the DMs’ evaluations, the individual and collaborative performance evaluations of multi-alternative combinations composed of different department alternatives are constructed. Then, the BWM is extended into interval 2-tuple linguistic environment to obtain the weights of evaluation criteria, where the group decision making is taken into account in an interval fuzzy mathematical programming model. Furthermore, to derive more practical and accurate decision results, an interval 2-tuple linguistic TODIM (ITL-TODIM) method is proposed by considering the DMs’ psychological behaviours. In the developed ITL-TODIM method, both the gain and loss degrees of one alternative relative to another are simultaneously computed. Finally, a numerical example is presented to illustrate the applicability of the proposed method. Sensitivity and comparative analyses are also provided to demonstrate the effectiveness and advantages of the proposed approach.

Green- Closed Loop Supply Chain Network Design by Considering Customer Relationship Management and solving it using Multi-Objective Genetic Algorithm

Background and Objective: Increasing greenhouse gas emissions and pollutants has led organizers and researchers to seek to design and set up networks that focus on environmental factors and reduce pollutants in all sectors. Therefore, the main objective of this paper is to present a fuzzy mathematical programming model for the green closed loop supply chain network, taking into account customer relationship management.Method: This is an applied-development study implemented in Saba Battery Company. In this study, a mixed integer linear programming model is proposed for designing a closed loop supply chain network that seeks to minimize costs and minimize environmental impacts. Also, the concept of customer relationship management in the form of the third objective function has been added to maximize the amount of worn-out product collected to this model.Results: Given that the proposed model belongs to the NP-hard category, a multi-objective genetic algorithm is used to solve the model, and finally, the Pareto's solutions are determined. Based on the results, the two objectives of the economic and environmental objectives are contradictory. That is, moving each one toward the desired one requires movement of the other objective function to the undesirable.Conclusion: In this research, the proposed mathematical programming model has been solved with a multi-objective genetic algorithm, which results indicate the location and capacity of the facility, the amount of production, the amount of inventory and the amount of transportation of the products.

Resilience cloud-based global supply chain network design under uncertainty: Resource-based approach

This study presents a fuzzy multi-objective mathematical programming model to design an efficient and resilience global supply chain network structure based on the service-oriented approach. Service composition and transportation within globally scattered resources are considered under the cloud manufacturing paradigm. The proposed comprehensive model is adapted to a global electrical medical device manufacturing system. Key performance measures include robustness, agility, leanness, and flexibility as resiliency pillars are considered in designing the network under uncertainty. To efficiently deal with the computational tractability of this non-linear and multi-objective optimization problem, a new hybrid solution algorithm is developed that incorporates fuzzy multi-criteria decision-making methods and augmented ε-constraint method. Obtained computational results of a real case study present that the proposed service-oriented global supply chain network design can respond to its global customers’ demands in a resilient as well as efficient manner.

A Fuzzy Multi-objective Mathematical Programming Model for Project Management Decisions Considering Quality and Contractual Reward and Penalty Costs in a Project Network

Project management is a process that schemes and controls the project life cycle via the easiest and the best way to achieve project goals. Project managers always aim to simultaneously handle conflicting goals in the organization. In this paper, a new mathematical model is proposed that simultaneously minimizes total cost and completion time and maximizes the quality in the project management decision problem. Contractual penalty cost and contractual reward cost with a new method are the other consideration in the proposed model. In the projects, the relation between time and direct cost is a nonlinear function. Hence, a linearization technique is presented with attention to variable change and piecewise linearization, in which nonlinear function is converted to the linear programming model. On the other hand, in real conditions according to uncertainty in environmental situations and incomplete information, there can be ambiguity in parameters and variables of the problem. The uncertainty of the parameters and variables is expressed with fuzzy sets theory and fuzzy mathematical programming. The other aim of this paper is to introduce a modified version of fully fuzzy multi-objective linear programming for the problem. For analyzing a fully fuzzy time–cost–quality project management model, a practical example of the literature is provided. By examining the results of the model with conflicting objectives, two scenarios are presented to explore the interactions of conflicting objectives on the project, and the results are reported.

A Fuzzy Mathematical Programming Model for Sustainable Supply Chain under Competition and Uncertainty Environment

In this paper, a fuzzy mathematical programming model based on the nested model is proposed to design a sustainable multi-product, multi-period supply chain network (including three parts of the procurement, production and distribution) under the competition and uncertainty conditions. Sustainability measures are carried out using previous studies and the supply chain operations reference (SCOR) model is extracted in each of the sustainability dimensions and then localised using the fuzzy Delphi method. In order to determine the relationship between indicators and the importance of each index, DEMATEL method is used and then the obtained fuzzy model is converted into a crisp one. To demonstrate the efficiency of the model, a real example is presented in the refractory industry. Finally, the results are analysed and suggestions are presented.

A multiobjective integrated multiproject scheduling and multiskilled workforce assignment model considering learning effect under uncertainty

AbstractToday, organizations try to decline academically expenses using humans and resources in addition to rising managers and operators' satisfaction. Meantime, a very important step in the process of decision is the assignment of human resources, particularly in connection with research and development (R&D) projects in which the system is highly dependent on the capabilities of human resources. In this study, we tried all the assumptions that come true in the real world, considered a model for applied R&D projects to reduce costs and increase the efficiency of projects. Therefore, an integrated multiproject scheduling and multiskill human resource assignment model under uncertainty has developed for R&D projects. Furthermore, it is assumed that the activity processing time is related to human resources assignment that means the learning effect is considered. To demonstrate the proposed model efficiency, the various dimensions instance problem was solved accurately and efficiently in GAMS software, and the results have been reported. In addition, the proposed model is validated through the input parameter sensitivity analysis. The results indicate a suitable performance of the proposed fuzzy mathematical programming model is due to the complexity of the problem.

Hybrid fuzzy multi-criteria decision making to solve the irrigation water allocation problem in the Tunisian case

Modernization and optimization of irrigated agriculture management can involve substantial conflicting factors using the opinions of experts. A combined approach based on concepts of Fuzzy Multi-Criteria Decision-Making (FMCDM) methods and Mathematical Optimization Programming (MOP) model for water allocation problem has been developed. In the first phase, we calculate the criteria weights using fuzzy AHP with water expert opinions. Then, we determine the performance of various water resources performed through the application of the fuzzy TOPSIS method. In the second phase, we solve the water resource allocation using the MOP model with the Multi-Criteria Decision-Making (MCDM) results. The allocation of irrigation water resources using the proposed approach was tested on Sfax irrigation district, southern Tunisia. The achieved results indicate that the combination of the fuzzy MCDM model and the MOP methods provide effective linkages between irrigation expert opinions, economic return, and performance of water resource objectives.

A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm

The closed-loop supply chain (CLSC) management as one of the most significant management issues has been increasingly spotlighted by the government, companies and customers, over the past years. The primary reasons for this growing attention mainly down to the governments-driven and environmental-related regulations which has caused the overall supply cost to reduce while enhancing the customer satisfaction. Thereby, in the present study, efforts have been made to propose a facility location/allocation model for a multi-echelon multi-product multi-period CLSC network under shortage, uncertainty, and discount on the purchase of raw materials. To design the network, a mixed-integer nonlinear programming (MINLP) model capable of reducing total costs of network is proposed. Moreover, the model is developed using a robust fuzzy programming (RFP) to investigate the effects of uncertainty parameters including customer demand, fraction of returned products, transportation costs, the price of raw materials, and shortage costs. As the developed model was NP-hard, a novel whale optimization algorithm (WOA) aimed at minimizing the network total costs with application of a modified priority-based encoding procedure is proposed. To validate the model and effectiveness of the proposed algorithm, some quantitative experiments were designed and solved by an optimization solver package and the proposed algorithm. Comparison of the outcomes provided by the proposed algorithm and exact solution is indicative of high quality performance of the applied algorithm to find a near-optimal solution within the reasonable computational time.

Network Design for Allied Supply Chains under Uncertain Conditions: A Possibilistic Programming Approach

The complex relationships between firms in today’s competitive business world affect supply chain (SC) structures so that managers have to consider SC versus SC relations instead of firm versus firm ones. In the corporate or multi-business companies, it is possible to share a number of resources between different SCs to achieve synergy and reduce costs. This paper addresses the strategic–tactical SC planning decisions (i.e., SC network design and master planning) in an uncertain environment for allied SCs belong to a single corporate. First, a fuzzy mixed-integer mathematical programming model that considers the imprecise nature of critical parameters such as cost coefficients, capacity levels, market demands is developed for integrated design of two SCs. Then, a robust possibilistic programming model is proposed to cope with the inherent uncertainty in the model parameters. The proposed model is able to achieve significant cost synergies via integrating the design of corporate SCs. Using hypothetical data inspired by an industrial case, the performance and applicability of the proposed models are investigated via experimental evaluations. Computational results indicate that our proposed model and solution approach can effectively be used to solve the allied SCs under uncertain condition.

Double Hierarchy Hesitant Fuzzy Linguistic Mathematical Programming Method for MAGDM Based on Shapley Values and Incomplete Preference Information

This paper investigates a double-hierarchy hesitant fuzzy linguistic mathematical programming method to multiple attribute group decision making (MAGDM) problems, where the assessment values of alternatives and the truth degrees of pairwise comparisons between alternatives are denoted by double-hierarchy hesitant fuzzy linguistic elements (DHHFLEs) and the inter-dependent or interactive characteristics among attributes and the incomplete preference information are taken into account. First, based on the distance measure between DHHFLEs, the double-hierarchy hesitant fuzzy linguistic positive ideal group consistency index (DHHFLPIGCI), double-hierarchy hesitant fuzzy linguistic positive ideal group inconsistency index (DHHFLPIGII), double-hierarchy hesitant fuzzy linguistic negative ideal group consistency index (DHHFLNIGCI), and double-hierarchy hesitant fuzzy linguistic negative ideal group inconsistency index (DHHFLNIGII) are defined, respectively. Then, to determine the positive ideal solution (PIS), negative ideal solution (NIS), and Shapley values of attributes simultaneously, a four-objective double-hierarchy hesitant fuzzy linguistic mathematical programming model is constructed by minimizing the DHHFLPIGII and DHHFLNIGII as well as maximizing the DHHFLPIGCI and DHHFLNIGCI. Subsequently, the relative closeness degrees (RCDs) of all feasible alternatives for each decision maker (DM) are obtained and the individual ranking order of alternatives for each DM is derived according to the descending order of RCDs, and thus a single-objective assignment model is established to generate the group ranking order of alternatives. Finally, a numerical example is given to illustrate the application of the proposed method and its effectiveness is demonstrated by comparison analysis.