A reliability-and-cost-based fuzzy approach to optimize preventive maintenance scheduling for offshore wind farms

We study the preventive maintenance scheduling problem of wind farms in the offshore wind energy sector which operates under uncertainty due to the state of the ocean and market demand. We formulate a fuzzy multi-objective non-linear chance-constrained programming model with newly-defined reliability and cost criteria and constraints to obtain satisfying schedules for wind turbine maintenance. To solve the optimization model, a 2-phase solution framework integrating the operational law for fuzzy arithmetic and the non-dominated sorting genetic algorithm II for multi-objective programming is developed. Pareto-optimal solutions of the schedules are obtained to form the trade-offs between the reliability maximization and cost minimization objectives. A numerical example is illustrated to validate the model

A reliability-and-cost-based fuzzy approach to optimize preventive maintenance scheduling for offshore wind farms

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordWe study the preventive maintenance scheduling problem of wind farms in the offshore wind energy sector which operates under uncertainty due to the state of the ocean and market demand. We formulate a fuzzy multi-objective non-linear chance-constrained programming model with newly-defined reliability and cost criteria and constraints to obtain satisfying schedules for wind turbine maintenance. To solve the optimization model, a 2-phase solution framework integrating the operational law for fuzzy arithmetic and the non-dominated sorting genetic algorithm II for multi-objective programming is developed. Pareto-optimal solutions of the schedules are obtained to form the trade-offs between the reliability maximization and cost minimization objectives. A numerical example is illustrated to validate the model.Recruitment Program of High-end Foreign Expert

An Experimentally Confirmed Resource Planning Model of Services Under Production Function Uncertainties

The way in which service firms transform inputs into outputs is typically uncertain or unknown. Consequently decision makers, at best, can only make estimates of the underlying production function. The purpose of this study is offer policy recommendations to service providers and to examine experimentally the sensitivity of estimates of production functions. The primary result of this study is a foundation for modeling manpower planning decisions for co-produced services when production functions are mis-estimated and/or mis-specified

Intelligent power system operation in an uncertain environment

This dissertation presents some challenging problems in power system operations. The efficacy of a heuristic method, namely, modified discrete particle swarm optimization (MDPSO) algorithm is illustrated and compared with other methods by solving the reliability based generator maintenance scheduling (GMS) optimization problem of a practical hydrothermal power system. The concept of multiple swarms is incorporated into the MDPSO algorithm to form a robust multiple swarms-modified particle swarm optimization (MS-MDPSO) algorithm and applied to solving the GMS problem on two power systems. Heuristic methods are proposed to circumvent the problems of imposed non-smooth assumptions common with the classical approaches in solving the challenging dynamic economic dispatch problem. The multi-objective combined economic and emission dispatch (MO-CEED) optimization problem for a wind-hydrothermal power system is formulated and solved in this dissertation. This MO-CEED problem formulation becomes a challenging problem because of the presence of uncertainty in wind power. A family of distributed optimal Pareto fronts for the MO-CEED problem has been generated for different scenarios of capacity credit of wind power. A real-time (RT) network stability index is formulated for determining a power system\u27s ability to continue to provide service (electric energy) in a RT manner in case of an unforeseen catastrophic contingency. Cascading stages of fuzzy inference system is applied to combine non real-time (NRT) and RT power system assessments. NRT analysis involves eigenvalue and transient energy analysis. RT analysis involves angle, voltage and frequency stability indices. RT Network status index is implemented in real-time on a practical power system --Abstract, page iv

Integrated management of chemical processes in a competitive environment

El objetivo general de esta Tesis es mejorar el proceso de la toma de decisiones en la gestión de cadenas de suministro, tomando en cuenta principalmente dos diferencias: ser competitivo considerando las decisiones propias de la cadena de suministro, y ser competitivo dentro de un entorno global. La estructura de ésta tesis se divide en 4 partes principales: La Parte I consiste en una introducción general de los temas cubiertos en esta Tesis (Capítulo 1). Una revisión de la literatura, que nos permite identificar las problemáticas asociadas al proceso de toma de decisiones (Capítulo 2). El Capítulo 3 presenta una introducción de las técnicas y métodos de optimización utilizados para resolver los problemas propuestos en esta Tesis. La Parte II se enfoca en la integración de los niveles de decisión, buscando mejorar la toma de decisiones de la propia cadena de suministro. El Capítulo 4 presenta una formulación matemática que integra las decisiones de síntesis de procesos y las decisiones operacionales. Además, este capítulo presenta un modelo integrado para la toma de decisiones operacionales incluyendo las características del control de procesos. El Capítulo 5 muestra la integración de las decisiones del nivel táctico y el operacional, dicha propuesta está basada en el conocimiento adquirido capturando la información relacionada al nivel operacional. Una vez obtenida esta información se incluye en la toma de decisiones a nivel táctico. Finalmente en el capítulo 6 se desarrolla un modelo simplificado para integrar múltiples cadenas de suministro. El modelo propuesto incluye la información detallada de las entidades presentes en una cadena de suministro (suministradores, plantas de producción, distribuidores y mercados) introduciéndola en un modelo matemático para su coordinación. La Parte III propone la integración explicita de múltiples cadenas de suministro que tienen que enfrentar numerosas situaciones propias de un mercado global. Asimismo, esta parte presenta una nueva herramienta de optimización basada en el uso integrado de métodos de programación matemática y conceptos relacionados a la Teoría de Juegos. En el Capítulo 7 analiza múltiples cadenas de suministro que cooperan o compiten por la demanda global del mercado. El Capítulo 8 incluye una comparación entre el problema resuelto en el Capítulo anterior y un modelo estocástico, los resultados obtenidos nos permiten situar el comportamiento de los competidores como fuente exógena de la incertidumbre típicamente asociada la demanda del mercado. Además, los resultados de ambos Capítulos muestran una mejora sustancial en el coste total de las cadenas de suministro asociada al hecho de cooperar para atender de forma conjunta la demanda disponible. Es por esto, que el Capítulo 9 presenta una nueva herramienta de negociación, basada en la resolución del mismo problema (Capítulo 7) bajo un análisis multiobjetivo. Finalmente, la parte IV presenta las conclusiones finales y una descripción general del trabajo futuro.This Thesis aims to enhance the decision making process in the SCM, remarking the difference between optimizing the SC to be competitive by its own, and to be competitive in a global market in cooperative and competitive environments. The structure of this work has been divided in four main parts: Part I: consists in a general introduction of the main topics covered in this manuscript (Chapter I); a review of the State of the Art that allows us to identify new open issues in the PSE (Chapter 2). Finally, Chapter 3 introduces the main optimization techniques and methods used in this contribution. Part II focuses on the integration of decision making levels in order to improve the decision making of a single SC: Chapter 4 presents a novel formulation to integrate synthesis and scheduling decision making models, additionally, this chapter also shows an integrated operational and control decision making model for distributed generations systems (EGS). Chapter 5 shows the integration of tactical and operational decision making levels. In this chapter a knowledge based approach has been developed capturing the information related to the operational decision making level. Then, this information has been included in the tactical decision making model. In Chapter 6 a simplified approach for integrated SCs is developed, the detailed information of the typical production‐distribution SC echelons has been introduced in a coordinated SC model. Part III proposes the explicit integration of several SC’s decision making in order to face several real market situations. As well, a novel formulation is developed using an MILP model and Game Theory (GT) as a decision making tool. Chapter 7 includes the tactical and operational analysis of several SC’s cooperating or competing for the global market demand. Moreover, Chapter 8 includes a comparison, based on the previous results (MILP‐GT optimization tool) and a two stage stochastic optimization model. Results from both Chapters show how cooperating for the global demand represent an improvement of the overall total cost. Consequently, Chapter 9 presents a bargaining tool obtained by the Multiobjective (MO) resolution of the model presented in Chapter 7. Finally, final conclusions and further work have been provided in Part IV.Postprint (published version

Integrating the fleet assignment model with uncertain demand

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.One of the main challenges facing the airline industry is planning under uncertainty, especially in the context of schedule disruptions. The robust models and solution algorithms that have been proposed and developed to handle the uncertain parameters will be discussed. Fleet assignment models (FAM) are used by many airlines to assign aircraft to fights in a schedule to maximize profit. In the context of FAM, the goal of robustness is to produce solutions that perform well relative to uncertainties in demand and operation. In this thesis, we introduce new FAMs (i.e. DFAM1 and DFAM2) that tackles the common problem associated with aircraft utilization. Subsequently, stochastic programming (SP) is presented as a method of choice for the research. Through the use of a two-stage SP with recourse technique, the DFAMs are extended to SP-FAMs (SP-FAM1 and SP-FAM2). The main distinction of the SP-FAM compared with other FAMs is that, given a stochastic passenger demand, it gives a strategic fleet assignment solution that hedges against all possible tactical solutions. In addition, we have a tactical solution for every scenario. In generating the demand scenarios, we use a network-simulation model embedded with a time-series engine that gives a snapshot of one week that is representative of any other week of the scheduling season. We later outline the approach of solving the SP-FAMs where the schedule is compacted through several preprocessing steps before inputting it into SAS-AMPL converter. The SAS-AMPL converter prepares all the data into readable AMPL format. Finally, we execute the optimizer using a FortMP solver (integrated in AMPL) that invokes branch-and-bound algorithm. We give a proof of concept using real data from a Middle East airline. Our investigations establish clear benefits of the recourse FAM compared to alternative models. Finally, we propose areas of future research to improve SP-FAM robustness through solution algorithms, revenue management (RM) effects, calibration of network-simulation models and system integration

Application of nature-inspired optimization algorithms to improve the production efficiency of small and medium-sized bakeries

Increasing production efficiency through schedule optimization is one of the most influential topics in operations research that contributes to decision-making process. It is the concept of allocating tasks among available resources within the constraints of any manufacturing facility in order to minimize costs. It is carried out by a model that resembles real-world task distribution with variables and relevant constraints in order to complete a planned production. In addition to a model, an optimizer is required to assist in evaluating and improving the task allocation procedure in order to maximize overall production efficiency. The entire procedure is usually carried out on a computer, where these two distinct segments combine to form a solution framework for production planning and support decision-making in various manufacturing industries. Small and medium-sized bakeries lack access to cutting-edge tools, and most of their production schedules are based on personal experience. This makes a significant difference in production costs when compared to the large bakeries, as evidenced by their market dominance. In this study, a hybrid no-wait flow shop model is proposed to produce a production schedule based on actual data, featuring the constraints of the production environment in small and medium-sized bakeries. Several single-objective and multi-objective nature-inspired optimization algorithms were implemented to find efficient production schedules. While makespan is the most widely used quality criterion of production efficiency because it dominates production costs, high oven idle time in bakeries also wastes energy. Combining these quality criteria allows for additional cost reduction due to energy savings as well as shorter production time. Therefore, to obtain the efficient production plan, makespan and oven idle time were included in the objectives of optimization. To find the optimal production planning for an existing production line, particle swarm optimization, simulated annealing, and the Nawaz-Enscore-Ham algorithms were used. The weighting factor method was used to combine two objectives into a single objective. The classical optimization algorithms were found to be good enough at finding optimal schedules in a reasonable amount of time, reducing makespan by 29 % and oven idle time by 8 % of one of the analyzed production datasets. Nonetheless, the algorithms convergence was found to be poor, with a lower probability of obtaining the best or nearly the best result. In contrast, a modified particle swarm optimization (MPSO) proposed in this study demonstrated significant improvement in convergence with a higher probability of obtaining better results. To obtain trade-offs between two objectives, state-of-the-art multi-objective optimization algorithms, non-dominated sorting genetic algorithm (NSGA-II), strength Pareto evolutionary algorithm, generalized differential evolution, improved multi-objective particle swarm optimization (OMOPSO) and speed-constrained multi-objective particle swarm optimization (SMPSO) were implemented. Optimization algorithms provided efficient production planning with up to a 12 % reduction in makespan and a 26 % reduction in oven idle time based on data from different production days. The performance comparison revealed a significant difference between these multi-objective optimization algorithms, with NSGA-II performing best and OMOPSO and SMPSO performing worst. Proofing is a key processing stage that contributes to the quality of the final product by developing flavor and fluffiness texture in bread. However, the duration of proofing is uncertain due to the complex interaction of multiple parameters: yeast condition, temperature in the proofing chamber, and chemical composition of flour. Due to the uncertainty of proofing time, a production plan optimized with the shortest makespan can be significantly inefficient. The computational results show that the schedules with the shortest and nearly shortest makespan have a significant (up to 18 %) increase in makespan due to proofing time deviation from expected duration. In this thesis, a method for developing resilient production planning that takes into account uncertain proofing time is proposed, so that even if the deviation in proofing time is extreme, the fluctuation in makespan is minimal. The experimental results with a production dataset revealed a proactive production plan, with only 5 minutes longer than the shortest makespan, but only 21 min fluctuating in makespan due to varying the proofing time from -10 % to +10 % of actual proofing time. This study proposed a common framework for small and medium-sized bakeries to improve their production efficiency in three steps: collecting production data, simulating production planning with the hybrid no-wait flow shop model, and running the optimization algorithm. The study suggests to use MPSO for solving single objective optimization problem and NSGA-II for multi-objective optimization problem. Based on real bakery production data, the results revealed that existing plans were significantly inefficient and could be optimized in a reasonable computational time using a robust optimization algorithm. Implementing such a framework in small and medium-sized bakery manufacturing operations could help to achieve an efficient and resilient production system.Die Steigerung der Produktionseffizienz durch die Optimierung von Arbeitsplänen ist eines der am meisten erforschten Themen im Bereich der Unternehmensplanung, die zur Entscheidungsfindung beiträgt. Es handelt sich dabei um die Aufteilung von Aufgaben auf die verfügbaren Ressourcen innerhalb der Beschränkungen einer Produktionsanlage mit dem Ziel der Kostenminimierung. Diese Optimierung von Arbeitsplänen wird mit Hilfe eines Modells durchgeführt, das die Aufgabenverteilung in der realen Welt mit Variablen und relevanten Einschränkungen nachbildet, um die Produktion zu simulieren. Zusätzlich zu einem Modell sind Optimierungsverfahren erforderlich, die bei der Bewertung und Verbesserung der Aufgabenverteilung helfen, um eine effiziente Gesamtproduktion zu erzielen. Das gesamte Verfahren wird in der Regel auf einem Computer durchgeführt, wobei diese beiden unterschiedlichen Komponenten (Modell und Optimierungsverfahren) zusammen einen Lösungsrahmen für die Produktionsplanung bilden und die Entscheidungsfindung in verschiedenen Fertigungsindustrien unterstützen. Kleine und mittelgroße Bäckereien haben zumeist keinen Zugang zu den modernsten Werkzeugen und die meisten ihrer Produktionspläne beruhen auf persönlichen Erfahrungen. Dies macht einen erheblichen Unterschied bei den Produktionskosten im Vergleich zu den großen Bäckereien aus, was sich in deren Marktdominanz widerspiegelt. In dieser Studie wird ein hybrides No-Wait-Flow-Shop-Modell vorgeschlagen, um einen Produktionsplan auf der Grundlage tatsächlicher Daten zu erstellen, der die Beschränkungen der Produktionsumgebung in kleinen und mittleren Bäckereien berücksichtigt. Mehrere einzel- und mehrzielorientierte, von der Natur inspirierte Optimierungsalgorithmen wurden implementiert, um effiziente Produktionspläne zu berechnen. Die Minimierung der Produktionsdauer ist das am häufigsten verwendete Qualitätskriterium für die Produktionseffizienz, da sie die Produktionskosten dominiert. Jedoch wird in Bäckereien durch hohe Leerlaufzeiten der Öfen Energie verschwendet was wiederum die Produktionskosten erhöht. Die Kombination beider Qualitätskriterien (minimale Produktionskosten, minimale Leerlaufzeiten der Öfen) ermöglicht eine zusätzliche Kostenreduzierung durch Energieeinsparungen und kurze Produktionszeiten. Um einen effizienten Produktionsplan zu erhalten, wurden daher die Minimierung der Produktionsdauer und der Ofenleerlaufzeit in die Optimierungsziele einbezogen. Um optimale Produktionspläne für bestehende Produktionsprozesse von Bäckereien zu ermitteln, wurden folgende Algorithmen untersucht: Particle Swarm Optimization, Simulated Annealing und Nawaz-Enscore-Ham. Die Methode der Gewichtung wurde verwendet, um zwei Ziele zu einem einzigen Ziel zu kombinieren. Die Optimierungsalgorithmen erwiesen sich als gut genug, um in angemessener Zeit optimale Pläne zu berechnen, wobei bei einem untersuchten Datensatz die Produktionsdauer um 29 % und die Leerlaufzeit des Ofens um 8 % reduziert wurde. Allerdings erwies sich die Konvergenz der Algorithmen als unzureichend, da nur mit einer geringen Wahrscheinlichkeit das beste oder nahezu beste Ergebnis berechnet wurde. Im Gegensatz dazu zeigte der in dieser Studie ebenfalls untersuchte modifizierte Particle-swarm-Optimierungsalgorithmus (mPSO) eine deutliche Verbesserung der Konvergenz mit einer höheren Wahrscheinlichkeit, bessere Ergebnisse zu erzielen im Vergleich zu den anderen Algorithmen. Um Kompromisse zwischen zwei Zielen zu erzielen, wurden moderne Algorithmen zur Mehrzieloptimierung implementiert: Non-dominated Sorting Genetic Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm, Generalized Differential Evolution, Improved Multi-objective Particle Swarm Optimization (OMOPSO), and Speed-constrained Multi-objective Particle Swarm Optimization (SMPSO). Die Optimierungsalgorithmen ermöglichten eine effiziente Produktionsplanung mit einer Verringerung der Produktionsdauer um bis zu 12 % und einer Verringerung der Leerlaufzeit der Öfen um 26 % auf der Grundlage von Daten aus unterschiedlichen Produktionsprozessen. Der Leistungsvergleich zeigte signifikante Unterschiede zwischen diesen Mehrziel-Optimierungsalgorithmen, wobei NSGA-II am besten und OMOPSO und SMPSO am schlechtesten abschnitten. Die Gärung ist ein wichtiger Verarbeitungsschritt, der zur Qualität des Endprodukts beiträgt, indem der Geschmack und die Textur des Brotes positiv beeinflusst werden kann. Die Dauer der Gärung ist jedoch aufgrund der komplexen Interaktion von mehreren Größen abhängig wie der Hefezustand, der Temperatur in der Gärkammer und der chemischen Zusammensetzung des Mehls. Aufgrund der Variabilität der Gärzeit kann jedoch ein Produktionsplan, der auf die kürzeste Produktionszeit optimiert ist, sehr ineffizient sein. Die Berechnungsergebnisse zeigen, dass die Pläne mit der kürzesten und nahezu kürzesten Produktionsdauer eine erhebliche (bis zu 18 %) Erhöhung der Produktionsdauer aufgrund der Abweichung der Gärzeit von der erwarteten Dauer aufweisen. In dieser Arbeit wird eine Methode zur Entwicklung einer robusten Produktionsplanung vorgeschlagen, die Veränderungen in den Gärzeiten berücksichtigt, so dass selbst bei einer extremen Abweichung der Gärzeit die Schwankung der Produktionsdauer minimal ist. Die experimentellen Ergebnisse für einen Produktionsprozess ergaben einen robusten Produktionsplan, der nur 5 Minuten länger ist als die kürzeste Produktionsdauer, aber nur 21 Minuten in der Produktionsdauer schwankt, wenn die Gärzeit von -10 % bis +10 % der ermittelten Gärzeit variiert. In dieser Studie wird ein Vorgehen für kleine und mittlere Bäckereien vorgeschlagen, um ihre Produktionseffizienz in drei Schritten zu verbessern: Erfassung von Produktionsdaten, Simulation von Produktionsplänen mit dem hybrid No-Wait Flow Shop Modell und Ausführung der Optimierung. Für die Einzieloptimierung wird der mPSO-Algorithmus und für die Mehrzieloptimierung NSGA-II-Algorithmus empfohlen. Auf der Grundlage realer Bäckereiproduktionsdaten zeigten die Ergebnisse, dass die in den Bäckereien verwendeten Pläne ineffizient waren und mit Hilfe eines effizienten Optimierungsalgorithmus in einer angemessenen Rechenzeit optimiert werden konnten. Die Umsetzung eines solchen Vorgehens in kleinen und mittelgroßen Bäckereibetrieben trägt dazu bei effiziente und robuste Produktionspläne zu erstellen und somit die Wettbewerbsfähigkeit dieser Bäckereien zu erhöhen

Model Development Of Single Unit Machine Capacity Measure For Production Planning And Control

Perancangan dan Kawalan Pengeluaran (PPC) adalah berkaitan dengan perancangan dan kawalan seluruh aspek pengeluaran termasuk mengurus bahan-bahan, menjadualkan mesin-mesin dan tenaga peketja, dan menyelaras pembekal-pembekal dan pelanggan-pelanggan utama, Pihak pengurusan mempunyai tanggungjawab yang asas dalam mewujudkan keupayaan memenuhi permintaan semasa dan masa akan datang, Ciri-ciri penting bagi PPC adalah berhubung kait dalam menentukan takat kapasiti jangka masa pendek dan sederhana secara aggregat. Penyelidikan ini menumpu kepada pembangunan satu Model Kapasiti Mesin untuk mengukur kapasiti sesebuah mesin, Production Planning and Control (PPC) is concerned with planning and controlling all aspects of manufacturing, including managing materials, scheduling machines and people, and coordinating suppliers' and key customers. Providing the capability to satisfy current and future demand is a fundamental responsibility of operations management. The important characteristic of PPC is concerned with to detennine capacity levels over short and medium tenns in aggregated tenns. This research focuses on developing a Machine Capacity Model for single unit machine capacity measure

Cost Optimization Modeling for Airport Capacity Expansion Problems in Metropolitan Areas

The purpose of this research was to develop a cost optimization model to identify an optimal solution to expand airport capacity in metropolitan areas in consideration of demand uncertainties. The study first analyzed four airport capacity expansion cases from different regions of the world to identify possible solutions to expand airport capacity and key cost functions which are highly related to airport capacity problems. Using mixedinteger nonlinear programming (MINLP), a deterministic optimization model was developed with the inclusion of six cost functions: capital cost, operation cost, delay cost, noise cost, operation readiness, and airport transfer (ORAT) cost, and passenger access cost. These six cost functions can be used to consider a possible trade-off between airport capacity and congestion and address multiple stakeholders’ cost concerns. This deterministic model was validated using an example case of the Sydney metropolitan area in Australia, which presented an optimal solution of a dual airport system along with scalable outcomes for a 50-year timeline. The study also tested alternative input values to the discount rate, operation cost, and passenger access costs to review the reliability of the deterministic model. Six additional experimental models were tested, and all models successfully yielded optimal solutions. The moderating effects of financial discount rate, airport operation cost, and passenger access costs on the optimal solution were quantitatively the same in presence of a deterministic demand profile. This deterministic model was then transformed into a stochastic optimization model to address concerns with the uncertainty of future traffic demand, which was further reviewed with three what-if demand scenarios of the Sydney Model: random and positive growth of traffic demand, normal distribution of traffic demand changes based on the historical traffic record of the Sydney region, and reflection of the current COVID- 19 pandemic situation. This study used a Monte Carlo simulation to address the uncertainty of future traffic demand as an uncontrollable input. The Sydney Model and three What-if Models successfully presented objective model outcomes and identified the optimal solutions to expand airport capacity while minimizing overall costs. The results of this work indicated that the moderating effect of traffic uncertainties can make a difference with an optimal solution. Therefore, airport decision-makers and airport planners should carefully consider the uncertainty factors that would influence the airport capacity expansion solution. This research demonstrated the effectiveness of combining MINLP and the Monte Carlo simulation to support a long-term strategic decision for airport capacity problems in metropolitan areas at the early stages of the planning process while addressing future traffic demand uncertainty. Other uncertainty factors, such as political events, new technologies, alternative modes of transport, financial crisis, technological innovation, and demographic changes might also be treated as uncontrollable variables to augment this optimization model

A Redundancy Detection Algorithm for Fuzzy Stochastic Multi-Objective Linear Fractional Programming Problems

The computational complexity of linear and nonlinear programming problems depends on the number of objective functions and constraints involved and solving a large problem often becomes a difficult task. Redundancy detection and elimination provides a suitable tool for reducing this complexity and simplifying a linear or nonlinear programming problem while maintaining the essential properties of the original system. Although a large number of redundancy detection methods have been proposed to simplify linear and nonlinear stochastic programming problems, very little research has been developed for fuzzy stochastic (FS) fractional programming problems. We propose an algorithm that allows to simultaneously detect both redundant objective function(s) and redundant constraint(s) in FS multi-objective linear fractional programming problems. More precisely, our algorithm reduces the number of linear fuzzy fractional objective functions by transforming them in probabilistic-possibilistic constraints characterized by predetermined confidence levels. We present two numerical examples to demonstrate the applicability of the proposed algorithm and exhibit its efficacy