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{"work":{"id":92148458,"created_at":"2022-12-04T01:52:35.605-08:00","from_world_paper_id":221943318,"updated_at":"2024-11-25T13:20:09.373-08:00","_data":{"publisher":"IOS Press","grobid_abstract":"The paper presents the solution of a multi objective multi-index generalized assignment problem using Fuzzy Programming Technique which is a new concept. It emphasizes on minimization of the job cost and time at different sites where the jobs are being performed using different machines (medium). Multi objective assignment problem or multi objective generalized assignment problem have been solved in different ways by different mathematicians. But they have considered only two indices (jobs and alternatives). Here we have considered more than two indices and so it becomes a multi-index generalized assignment problem which makes it superior to the previous methods. This type of problem has not been solved earlier by our proposed method. Moreover in this paper Fuzzy Programming Technique has been used considering linear, exponential and hyperbolic (non-linear) membership functions for getting optimal solutions. Finally a real life application has been presented.","publication_date":"2017,,","publication_name":"Journal of Intelligent \u0026 Fuzzy Systems","grobid_abstract_attachment_id":"95235263"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Solution of a class of generalized assignment problem","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [227760845]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":95235263,"attachmentType":"pdf"}"><img alt="First page of “Solution of a class of generalized assignment problem”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/95235263/mini_magick20221204-1-16bdwt5.png?1670147651" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Solution of a class of generalized assignment problem</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="227760845" href="https://independent.academia.edu/DrKajlaBasu"><img alt="Profile image of Dr.Kajla Basu" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/227760845/84634117/73270097/s65_dr.kajla.basu.jpeg" />Dr.Kajla Basu</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2017, Journal of Intelligent & Fuzzy Systems</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">11 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 92148458; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">The paper presents the solution of a multi objective multi-index generalized assignment problem using Fuzzy Programming Technique which is a new concept. It emphasizes on minimization of the job cost and time at different sites where the jobs are being performed using different machines (medium). Multi objective assignment problem or multi objective generalized assignment problem have been solved in different ways by different mathematicians. But they have considered only two indices (jobs and alternatives). Here we have considered more than two indices and so it becomes a multi-index generalized assignment problem which makes it superior to the previous methods. This type of problem has not been solved earlier by our proposed method. Moreover in this paper Fuzzy Programming Technique has been used considering linear, exponential and hyperbolic (non-linear) membership functions for getting optimal solutions. 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This method gives an optimum solution is more or less same solution when compared to currently used method&lt;strong&gt;. &lt;/strong&gt;To check its feasibility numerical examples are illustrated.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"An Algorithm To Solve Multi Objective Assignment Problem Using Fuzzy Programming Technique","attachmentId":82105408,"attachmentType":"pdf","work_url":"https://www.academia.edu/73677622/An_Algorithm_To_Solve_Multi_Objective_Assignment_Problem_Using_Fuzzy_Programming_Technique","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/73677622/An_Algorithm_To_Solve_Multi_Objective_Assignment_Problem_Using_Fuzzy_Programming_Technique"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="87320002" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/87320002/Solution_of_Generalized_Fuzzy_Assignment_Problem_with_Restriction_on_Costs_under_Fuzzy_Environment">Solution of Generalized Fuzzy Assignment Problem with Restriction on Costs under Fuzzy Environment</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="29526827" href="https://independent.academia.edu/SupriyaKar">Supriya Kar</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2014</p><p class="ds-related-work--abstract ds2-5-body-sm">To solve the problems of Engineering and Management Science Generalized Assignment Problem (GAP) plays a very important role. The GAP is a classical example of a difficult combinatorial optimization problem that has received considerable attention over the years due to its widespread applications. In many instances it appears as a substructure in more complicated models, including routing problems, facility location models, knapsack problems, computer networking applications etc. Recently, Fuzzy Generalized Assignment Problem (FGAP) became very popular because in real life, data may not be known with certainty. So, to consider uncertainty in real life situations fuzzy data instead of crisp data is more advantageous. In this paper, cost for assigning the j-th job to the i-th person is taken as triangular fuzzy numbers. Further we have put a restriction on the total available cost which makes the problem more realistic and general. The problem is solved by modified Fuzzy Extremum Diff...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Solution of Generalized Fuzzy Assignment Problem with Restriction on Costs under Fuzzy Environment","attachmentId":91562385,"attachmentType":"pdf","work_url":"https://www.academia.edu/87320002/Solution_of_Generalized_Fuzzy_Assignment_Problem_with_Restriction_on_Costs_under_Fuzzy_Environment","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/87320002/Solution_of_Generalized_Fuzzy_Assignment_Problem_with_Restriction_on_Costs_under_Fuzzy_Environment"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="4752358" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/4752358/SOLUTION_OF_GENERALIZED_FUZZY_ASSIGNMENT_PROBLEM_WITH_RESTRICTION_ON_THE_COST_OF_BOTH_JOB_AND_PERSON_UNDER_FUZZY_ENVIRONMENT">SOLUTION OF GENERALIZED FUZZY ASSIGNMENT PROBLEM WITH RESTRICTION ON THE COST OF BOTH JOB AND PERSON UNDER FUZZY ENVIRONMENT</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3194628" href="https://iaeme.academia.edu/iaeme">iaeme iaeme</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Generalized Assignment Problem is a very popular topic which is used to solve different engineering and management problems. It becomes more realistic when used under fuzzy environment since in practical situation it is difficult to get precise data. In this paper cost for assigning the j-th job to the i-th person is taken as trapezoidal fuzzy numbers (TrFNs) which are more realistic and general in nature. To solve the real life problems restrictions have been put on both job cost and person cost depending on his/her efficiency/qualification. Yager's Ranking Method[1] has been used for ranking the fuzzy numbers. The fuzzy generalized assignment problem (FGAP) has been solved by Modified Extremum Difference Method (EDM) for initial Basic Feasible Solution (BFS). To test the optimality MODI method is used. Again the solution by the proposed method has been verified by LINGO 9.0.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"SOLUTION OF GENERALIZED FUZZY ASSIGNMENT PROBLEM WITH RESTRICTION ON THE COST OF BOTH JOB AND PERSON UNDER FUZZY ENVIRONMENT","attachmentId":32063542,"attachmentType":"pdf","work_url":"https://www.academia.edu/4752358/SOLUTION_OF_GENERALIZED_FUZZY_ASSIGNMENT_PROBLEM_WITH_RESTRICTION_ON_THE_COST_OF_BOTH_JOB_AND_PERSON_UNDER_FUZZY_ENVIRONMENT","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/4752358/SOLUTION_OF_GENERALIZED_FUZZY_ASSIGNMENT_PROBLEM_WITH_RESTRICTION_ON_THE_COST_OF_BOTH_JOB_AND_PERSON_UNDER_FUZZY_ENVIRONMENT"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="103130624" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/103130624/Multi_objective_Assignment_Problem_with_Generalized">Multi-objective Assignment Problem with Generalized</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="169059648" href="https://independent.academia.edu/PranabBiswas13">Pranab Biswas</a></div><p class="ds-related-work--abstract ds2-5-body-sm">The aim of this paper is to study multi-objective assignment problem with imprecise costs, time and ineffectiveness instead of its precise information. Here, elements of cost matrix, consumed time matrix and ineffectiveness level matrix have been represented by generalized trapezoidal fuzzy numbers as it is suitable way to represent the impreciseness of values provided by the decision makers due to time pressure or limited information and poor information processing capabilities. A priority based fuzzy goal programming method has been developed for generalized trapezoidal fuzzy numbers and it is applied for multi-objective assignment problem. Euclidean distance function is used to identify the most appropriate priority structure of fuzzy goals among the different priorities of the fuzzy goals. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multi-objective Assignment Problem with Generalized","attachmentId":103219887,"attachmentType":"pdf","work_url":"https://www.academia.edu/103130624/Multi_objective_Assignment_Problem_with_Generalized","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/103130624/Multi_objective_Assignment_Problem_with_Generalized"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="27813780" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27813780/Fuzzy_weighted_equilibrium_multi_job_assignment_problem_and_genetic_algorithm">Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="52130121" href="https://independent.academia.edu/CindyGao3">Cindy Gao</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Applied Mathematical Modelling, 2009</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, the equilibrium optimization problem is proposed and the assignment problem is extended to the equilibrium multi-job assignment problem, equilibrium multi-job quadratic assignment problem and the minimum cost and equilibrium multi-job assignment problem. Furthermore, the mathematical models of the equilibrium multi-job assignment problem and the equilibrium multi-job quadratic assignment problem with fuzzy parameters are formulated. Finally, a genetic algorithm is designed for solving the proposed programming models and some numerical examples are given to verify the efficiency of the designed algorithm.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm","attachmentId":48095777,"attachmentType":"pdf","work_url":"https://www.academia.edu/27813780/Fuzzy_weighted_equilibrium_multi_job_assignment_problem_and_genetic_algorithm","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/27813780/Fuzzy_weighted_equilibrium_multi_job_assignment_problem_and_genetic_algorithm"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="126706650" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/126706650/An_Algorithm_to_Solve_Multi_Objective_Assignment_Problem_Using_Interactive_Fuzzy_Goal_Programming_Approach">An Algorithm to Solve Multi-Objective Assignment Problem Using Interactive Fuzzy Goal Programming Approach</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="25243827" href="https://nitsilchar.academia.edu/PijusKantiDe">Pijus Kanti De</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2011</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper proposes an algorithm for solving multi-objective assignment problem (MOAP) through interactive fuzzy goal programming approach. A mathematical model has been established to discuss about multi-objective assignment problem which is characterized by non-linear(exponential) membership function. The approach emphasizes on optimal solution of each objective function by minimizing the worst upper bound, which is close to the best lower bound. To illustrate the algorithm a numerical example is presented.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"An Algorithm to Solve Multi-Objective Assignment Problem Using Interactive Fuzzy Goal Programming Approach","attachmentId":120543919,"attachmentType":"pdf","work_url":"https://www.academia.edu/126706650/An_Algorithm_to_Solve_Multi_Objective_Assignment_Problem_Using_Interactive_Fuzzy_Goal_Programming_Approach","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/126706650/An_Algorithm_to_Solve_Multi_Objective_Assignment_Problem_Using_Interactive_Fuzzy_Goal_Programming_Approach"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="34295202" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/34295202/An_alternative_formulation_for_the_fuzzy_assignment_problem">An alternative formulation for the fuzzy assignment problem</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="39724225" href="https://independent.academia.edu/WilliamHo16">Bill Chan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of the Operational Research Society, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit measured as crisp. However, in many real applications, costs are not deterministic numbers. This paper develops a procedure based on Data Envelopment Analysis method to solve the assignment problems with fuzzy costs or fuzzy profits for each possible assignment. It aims to obtain the points with maximum membership values for the fuzzy parameters while maximizing the profit or minimizing the assignment cost. In this method, a discrete approach is presented to rank the fuzzy numbers first. Then, corresponding to each fuzzy number, we introduce a crisp number using the efficiency concept. A numerical example is used to illustrate the usefulness of this new method.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"An alternative formulation for the fuzzy assignment problem","attachmentId":54199492,"attachmentType":"pdf","work_url":"https://www.academia.edu/34295202/An_alternative_formulation_for_the_fuzzy_assignment_problem","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/34295202/An_alternative_formulation_for_the_fuzzy_assignment_problem"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="96052429" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/96052429/Proposal_of_an_Algorithm_for_Solving_Multi_Objective_Assignment_Problem_Moap_with_Linear_and_Nonlinear_Membership_Functions">Proposal of an Algorithm for Solving Multi-Objective Assignment Problem (Moap) with Linear and Nonlinear Membership Functions</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="255562043" href="https://independent.academia.edu/72UmangKumarPandey">72Umang Kumar Pandey</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Assignment Problem (AP), as extensively discussed in operations research, industrial engineering and computational mathematics has been addressed under different headings and using different approaches. One of the approaches to solve an AP under uncertainty and in real world scenarios is using fuzzy theory. Fuzzy multi-objective linear programming usually deals with flexible aspiration levels that are indicative of optimality when considering all objectives or goals simultaneously with possible deviation in objectives or constraints in vague, imprecise and uncertain environment. Therefore in this study we propose an algorithm for solving multi-objective assignment problem (MOAP) with linear and nonlinear membership functions. The proposed model will give a compromised solution for best optimality and higher satisfaction level for parameters being considered in uncertain environment. The result obtained by using a linear membership function has been compared with the solution obtaine...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Proposal of an Algorithm for Solving Multi-Objective Assignment Problem (Moap) with Linear and Nonlinear Membership Functions","attachmentId":98058303,"attachmentType":"pdf","work_url":"https://www.academia.edu/96052429/Proposal_of_an_Algorithm_for_Solving_Multi_Objective_Assignment_Problem_Moap_with_Linear_and_Nonlinear_Membership_Functions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/96052429/Proposal_of_an_Algorithm_for_Solving_Multi_Objective_Assignment_Problem_Moap_with_Linear_and_Nonlinear_Membership_Functions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="50776512" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/50776512/Genetic_algorithm_based_hybrid_approach_to_solve_fuzzy_multi_objective_assignment_problem_using_exponential_membership_function">Genetic algorithm based hybrid approach to solve fuzzy multi-objective assignment problem using exponential membership function</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="52246454" href="https://independent.academia.edu/AnitaTailor1">Anita Tailor</a></div><p class="ds-related-work--metadata ds2-5-body-xs">SpringerPlus</p><p class="ds-related-work--abstract ds2-5-body-sm">Background The assignment problem (AP) has been extensively used in manufacturing and developing service systems, to optimally resolve the problem of assigning N duties to N employees to optimize the total resources. Furthermore, in AP, N employees must be assigned N number of duties, where in each employee must complete their individual assigned duty. However, because of personal ability or other reasons, each employee may spend a different amount of resources to complete various duties. The objective is to assign each duty to the appropriate employee to optimize the total utilization of resources and to complete all duties. Two types of objectives are generally measured in AP: maximization and minimization. Minimization refers to minimizing aspects such as duty cost and total duration, whereas maximization refers to maximizing aspects such as the overall manufacturing profit and overall sale of manufacture. Responsible parameters that are considered for determining the assignment plan in a real-world scenario should not be precise but should be exaggerated by indistinctness and imprecision represented by linguistic terms which expressed by the DM. In such a scenario, the AP is converted into a fuzzy assignment problem (FAP). The concept Abstract This paper presents a genetic algorithm based hybrid approach for solving a fuzzy multi-objective assignment problem (FMOAP) by using an exponential membership function in which the coefficient of the objective function is described by a triangular possibility distribution. Moreover, in this study, fuzzy judgment was classified using α-level sets for the decision maker (DM) to simultaneously optimize the optimistic, most likely, and pessimistic scenarios of fuzzy objective functions. To demonstrate the effectiveness of the proposed approach, a numerical example is provided with a data set from a realistic situation. This paper concludes that the developed hybrid approach can manage FMOAP efficiently and effectively with an effective output to enable the DM to take a decision.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Genetic algorithm based hybrid approach to solve fuzzy multi-objective assignment problem using exponential membership function","attachmentId":68644639,"attachmentType":"pdf","work_url":"https://www.academia.edu/50776512/Genetic_algorithm_based_hybrid_approach_to_solve_fuzzy_multi_objective_assignment_problem_using_exponential_membership_function","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/50776512/Genetic_algorithm_based_hybrid_approach_to_solve_fuzzy_multi_objective_assignment_problem_using_exponential_membership_function"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="1261874" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/1261874/Article_Multi_objective_Assignment_Problem_with_Generalized_Trapezoidal_Fuzzy_Numbers_">Article: Multi-objective Assignment Problem with Generalized Trapezoidal Fuzzy Numbers}</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2018023" href="https://ngbtc.academia.edu/SurapatiPramanik">Surapati Pramanik</a></div><p class="ds-related-work--metadata ds2-5-body-xs">research.ijais.org</p><p class="ds-related-work--abstract ds2-5-body-sm">The aim of this paper is to study multi-objective assignment problem with imprecise costs, time and ineffectiveness instead of its precise information. Here, elements of cost matrix, consumed time matrix and ineffectiveness level matrix have been represented by generalized trapezoidal fuzzy numbers as it is suitable way to represent the impreciseness of values provided by the decision makers due to time pressure or limited information and poor information processing capabilities. A priority based fuzzy goal programming method has been developed for generalized trapezoidal fuzzy numbers and it is applied for multi-objective assignment problem. Euclidean distance function is used to identify the most appropriate priority structure of fuzzy goals among the different priorities of the fuzzy goals. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Article: Multi-objective Assignment Problem with Generalized Trapezoidal Fuzzy Numbers}","attachmentId":21361060,"attachmentType":"pdf","work_url":"https://www.academia.edu/1261874/Article_Multi_objective_Assignment_Problem_with_Generalized_Trapezoidal_Fuzzy_Numbers_","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/1261874/Article_Multi_objective_Assignment_Problem_with_Generalized_Trapezoidal_Fuzzy_Numbers_"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":95235263,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":95235263,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_95235263" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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