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    Wyświetlanie 1-14 z 14
    Tytuł:
    Software tools in didactics of mathematics
    Autorzy:
    Dudzińska-Baryła, Renata
    Kopańska-Bródka, Donata
    Michalska, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/421290.pdf
    Data publikacji:
    2015
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    visualisations
    GeoGebra
    multi-objective programming
    fuzzy sets
    derivative
    Opis:
    The use of software tools in the teaching process allows us to enrich the traditional methods. Graphics and animation complement the text and create positive associations related to the presented content. Recent research shows that using the visual methods in teaching leads to better scores obtained by students. The aim of the paper is to present the dynamic visualisations of selected concepts taught in mathematics and other “quantitative” subjects at university. Our dynamic visualisations can be used during lectures to help students to better understand difficult ideas and dependencies, for example the derivate of a function, the concept of fuzzy sets and the operations on these sets as well as the concept of the best solution in multi-objective programming problems. Visualisations of these issues are prepared in GeoGebra, which combines algebra and geometry and allows for the dynamic visualisation of concepts with a mathematical background.
    Źródło:
    Didactics of Mathematics; 2015, 12(16); 35-46
    1733-7941
    Pojawia się w:
    Didactics of Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generating a set of compromise solutions of a multi objective linear programming problem through game theory
    Autorzy:
    Sivri, Mustafa
    Kocken, Hale Gonce
    Albayrak, Inci
    Akin, Sema
    Powiązania:
    https://bibliotekanauki.pl/articles/406253.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    multi-objective programming problem
    game theory
    compromise solution
    Opis:
    Most of real-life problems, including design, optimization, scheduling and control, etc., are inherently characterized by multiple conflicting objectives, and thus multi-objective linear programming (MOLP) problems are frequently encountered in the literature. One of the biggest difficulties in solving MOLP problems lies in the trade-off among objectives. Since the optimal solution of one objective may lead other objective(s) to bad results, all objectives must be optimized simultaneously. Additionally, the obtained solution will not satisfy all the objectives in the same satisfaction degree. Thus, it will be useful to generate a set of compromise solutions in order to present it to the decision maker (DM). With this motivation, after determining a modified payoff matrix for MOLP, all possible ratios are formed between all rows. These ratio matrices are considered a two person zero-sum game and solved by linear programming (LP) approach. Taking into consideration the results of the related game, the original MOLP problem is converted to a single objective LP problem. Since there exist numerous ratio matrices, a set of compromise solutions is obtained for MOLP problem. Numerical examples are used to demonstrate this approach.
    Źródło:
    Operations Research and Decisions; 2019, 29, 2; 77-88
    2081-8858
    2391-6060
    Pojawia się w:
    Operations Research and Decisions
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    MOLPTOL – a software package for sensitivity analysis in MOLP
    Autorzy:
    Sitarz, Sebastian
    Botor, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2027992.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Ekonomiczny w Katowicach
    Tematy:
    Computer software
    Multi-objective linear programming
    Sensitivity analysis
    Opis:
    The paper introduces a new software package, MOLPTOL, for sensitivity analysis in multi-objective linear programming. In this application, which is available for free of charge on the web page (https:// sites.google.com/view/molptol), the tolerance approach as a measure of sensitivity is used. The motivation for creating MOLPTOL is the lack of such tools to date. MOLPTOL is novel for multi-criteria decision-making methods based on sensitivity analysis. The paper presents some new computational methods for obtaining the supremal tolerances as well.
    Źródło:
    Multiple Criteria Decision Making; 2021, 16; 140-152
    2084-1531
    Pojawia się w:
    Multiple Criteria Decision Making
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem
    Autorzy:
    Arora, R.
    Gupta, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1403683.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    bilevel programming
    indefinite quadratic programming
    multi-objective programming
    pay-off matrix
    Taylor series approximation
    LINGO 17.0
    Opis:
    Bilevel programming problem is a non-convex two stage decision making process in which the constraint region of upper level is determined by the lower level problem. In this paper, a multi-objective indefinite quadratic bilevel programming problem (MOIQBP) is presented. The defined problem (MOIQBP) has multi-objective functions at both the levels. The followers are independent at the lower level. A fuzzy goal programming methodology is employed which minimizes the sum of the negative deviational variables of both the levels to obtain highest membership value of each of the fuzzy goal. The membership function for the objective functions at each level is defined. As these membership functions are quadratic they are linearized by Taylor series approximation. The membership function for the decision variables at both levels is also determined. The individual optimal solution of objective functions at each level is used for formulating an integrated pay-off matrix. The aspiration levels for the decision makers are ascertained from this matrix. An algorithm is developed to obtain a compromise optimal solution for (MOIQBP). A numerical example is exhibited to evince the algorithm. The computing software LINGO 17.0 has been used for solving this problem.
    Źródło:
    Archives of Control Sciences; 2020, 30, 4; 683-699
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multicriterial optimization
    Autorzy:
    Khan, Phan Quoc
    Powiązania:
    https://bibliotekanauki.pl/articles/747912.pdf
    Data publikacji:
    1990
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Research exposition
    Multi-objective and goal programming
    Opis:
    .
    This work is a survey. Basic notions, a few words on the history and a classification of problems in multicriterial optimization are presented. Optimality conditions of various types are discussed in more detail.
    Źródło:
    Mathematica Applicanda; 1990, 18, 32
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multi-objective data envelopment analysis: A game of multiple attribute decision-making
    Autorzy:
    Chen, Yuh Wen
    Powiązania:
    https://bibliotekanauki.pl/articles/522074.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Ekonomiczny w Katowicach
    Tematy:
    Data Envelopment Analysis (DEA)
    Multi-Objective Linear Programming (MOLP)
    Multiple Attribute Decision Making (MADM)
    Research and Development (R&D) efficiency
    Opis:
    Aim/purpose ‒ The traditional data envelopment analysis (DEA) is popularly used to evaluate the relative efficiency among public or private firms by maximising each firm’s efficiency: the decision maker only considers one decision-making unit (DMU) at one time; thus, if there are n firms for computing efficiency scores, the resolution of n similar problems is necessary. Therefore, the multi-objective linear programming (MOLP) problem is used to simplify the complexity. Design/methodology/approach ‒ According to the similarity between the DEA and the multiple attribute decision making (MADM), a game of MADM is proposed to solve the DEA problem. Related definitions and proofs are provided to clarify this particular approach. Findings ‒ The multi-objective DEA is validated to be a unique MADM problem in this study: the MADM game for DEA is eventually identical to the weighting multi-objective DEA. This MADM game for DEA is used to rank ten LCD companies in Taiwan for their research and development (R&D) efficiencies to show its practical application. Research implications/limitations ‒ The main advantage of using an MADM game on the weighting multi-objective DEA is that the decision maker does not need to worry how to set these weights among DMUs/objectives, this MADM game will decide the weights among DMUs by the game theory. However, various DEA models are eventually evaluation tools. No one can guarantee us with 100% confidence that their evaluated results of DEA could be the absolute standard. Readers should analyse the results with care. Originality/value/contribution ‒ A unique link between the multi-objective CCR DEA and the MADM game for DEA is established and validated in this study. Previous scholars seldom explored and developed this breathtaking view before.
    Źródło:
    Journal of Economics and Management; 2019, 37; 156-177
    1732-1948
    Pojawia się w:
    Journal of Economics and Management
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers
    Autorzy:
    Goyal, Vandana
    Rani, Namrata
    Gupta, Deepak
    Powiązania:
    https://bibliotekanauki.pl/articles/2175831.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    multi-objective quadratic fractional programming model
    MOQFPM
    pentagonal fuzzy number
    PFN
    mean method of α-cut
    parametric approach
    ε-constraint method
    Opis:
    This study proposes a methodology to obtain an efficient solution for a programming model which is multi-objective quadratic fractional with pentagonal fuzzy numbers as coefficients in all the objective functions and constraints. The proposed approach consists of three stages. In the first stage, defuzzification of the coefficients is carried out using the mean method of α-cut. Then, in the second stage, a crisp multi-objective quadratic fractional programming model (MOQFP) is constructed to obtain a non-fractional model based on an iterative parametric approach. In the final stage, this multi- -objective non-fractional model is transformed to obtain a model with a single objective by applying the ε-constraint method. This final model is then solved to get desired solution. Also, an algorithm and flowchart expressing the methodology are given to present a clear picture of the approach. Finally, a numerical example illustrating the complete approach is given.
    Źródło:
    Operations Research and Decisions; 2022, 32, 1; 49--71
    2081-8858
    2391-6060
    Pojawia się w:
    Operations Research and Decisions
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fuzzy multi-objective supplier selection problem in a supply chain
    Autorzy:
    Kamal, Murshid
    Gupta, Srikant
    Raina, Ather Aziz
    Powiązania:
    https://bibliotekanauki.pl/articles/1177774.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Fuzzy Goal Programming
    Multi-objective Optimization
    Supplier Selection Problem
    Opis:
    The decision making of supplier selection and their allocation is one of the main concerns in supply chain management. In this paper, an attempt has been made to obtain an optimal allocation for supplier based on minimizing the net cost, minimizing the net rejections, and minimizing the net late deliveries subject to realistic constraints regarding buyer’s demand, vendors’ capacity, vendors’ quota flexibility, purchase value of items, budget allocation to individual vendor, etc. We convert the problem into single objective fuzzy goal programming problem by using weighted root power mean the method of aggregation with linear, exponential and hyperbolic membership functions. The comparison has been made by assigning different weights to the objective functions. A numerical illustration is provided for the verification of applicability of the approach.
    Źródło:
    World Scientific News; 2018, 100; 165-183
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bi-objective routing in a dynamic network: An application to maritime logistics
    Autorzy:
    Maskooki, Alaleh
    Nikulin, Yury
    Powiązania:
    https://bibliotekanauki.pl/articles/2050033.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    travelling salesman
    time dependent network
    multi-objective optimization
    integer programming
    Opis:
    A bi-objectiveMILP model for optimal routing in a dynamic network with moving targets (nodes) is developed, where all targets are not necessarily visited. Hence, our problem extends the moving target travelling salesman problem. The two objectives aim at finding the sequence of targets visited in a given time horizon by minimizing the total travel distance and maximizing the number of targets visited. Due to a huge number of binary variables, such a problem often becomes intractable in the real life cases. To reduce the computational burden, we introduce a measure of traffic density, based on which we propose a time horizon splitting heuristics. In a real-world case study of greenhouse gas emissions control, using Automatic Identification System data related to the locations of ships navigating in the Gulf of Finland, we evaluate the performance of the proposed method. Different splitting scenarios are analysed numerically. Even in the cases of a moderate scale, the results show that near-efficient values for the two objectives can be obtained by our splitting approach with a drastic decrease in computational time compared to the exact MILP method. A linear value function is introduced to compare the Pareto solutions obtained by different splitting scenarios. Given our results, we expect that the present study is valuable in logistic applications, specifically maritime management services and autonomous navigation.
    Źródło:
    Control and Cybernetics; 2020, 49, 2; 211--232
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The airport gate assignment problem – multi-objective optimization versus evolutionary multi-objective optimization
    Autorzy:
    Kaliszewski, I.
    Miroforidis, J.
    Stańczak, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/305661.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    airport gate assignment problem
    Evolutionary Multi-objective Optimization
    mixed-integer programming
    Opis:
    In this paper, we approach the Airport Gate Assignment Problem by Multi-objective Optimization as well as Evolutionary Multi-objective Optimization. We solve a bi-criteria formulation of this problem by the commercial mixed-integer programming solver CPLEX and a dedicated Evolutionary Multi-objective Optimization algorithm. To deal with multiple objectives, we apply a methodology that we developed earlier to capture decision-maker preferences in multi-objective environments. We present the results of numerical tests for these two approaches.
    Źródło:
    Computer Science; 2017, 18 (1); 41-52
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A New Mathematical Model for Multisession Exams-Building Assignment
    Autorzy:
    Ergul, Z.
    Kamisli Ozturk, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/1031701.pdf
    Data publikacji:
    2017-09
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    Educational timetabling
    Examination-building assignment
    Multi objective nonlinear optimization
    Mixed Integer Programming
    Opis:
    The educational timetabling problem has been extensively investigated in timetabling literature. However, the problem of assigning exams to examination buildings has not been studied intensively by researchers. We were inspired by Open and Distance Education System exams of Anadolu University. Anadolu University Open and Distance Education System, which is used by approximately two millions of students and has more than two millions of graduates, is a well-known institution in Turkey. In this study, we propose a multi-objective mathematical model for multisession exam-building assignment problem. Objective functions of this model are to minimize the distance between consecutive session buildings for a given student, to maximize the number of occupants of buildings in every session and to minimize the variety of booklets for building in every session. Mathematical model has been found inadequate because students-examination building assignment in the Anadolu University Open Education system is a large size real life problem. Starting from this point of view, an order-based multi-objective heuristic algorithm is developed to solve this problem. The solutions obtained by the proposed algorithm are compared with the solution obtained by the mathematical modelling and the current state of the existing system.
    Źródło:
    Acta Physica Polonica A; 2017, 132, 3; 1207-1210
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Milk runs model with overtime: application to cluster supply chain
    Autorzy:
    Tomczak, M.
    Bucoń, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/390975.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
    Tematy:
    cluster supply chain
    mathematical programming
    multi-objective optimization
    small and medium enterprises
    Opis:
    Paper identifies obstacles limiting functioning and development of small and medium construction enterprises. It also includes a description of cluster supply chain (CSC) idea as a suggested solution to some of the problems resulting from the small scale of company activities. One of more important issues of every distribution centre, i.e. portions of deliveries smaller than truck capacity for particular consumers, is also discussed. This problem was formulated for the first time in dairy industry, therefore, it was called milk runs. Moreover, the authors of this paper presented the outcome analysis of survey carried out among construction engineers and managers. This study aimed at determining organizational principles for logistic centre working with CSC framework. The mathematical model depicting milk runs deliveries with overtime consideration, done for many construction sites within a distribution centre is presented hereunder. This model may be potentially used to optimize distribution centres working within cluster supply chain framework.
    Źródło:
    Budownictwo i Architektura; 2015, 14, 4; 139-147
    1899-0665
    Pojawia się w:
    Budownictwo i Architektura
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of goal programming in the textile apparel industry to resolve production planning problems : a meta-goal programming technique using weights
    Autorzy:
    Malik, Zahid Amin
    Kumar, Rakesh
    Pathak, Govind
    Roy, Haridas
    Powiązania:
    https://bibliotekanauki.pl/articles/2175839.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    meta-goal programming
    weighted goal programming
    multi-objective decision making
    asset allocation
    textile sector
    sensitivity analysis
    Opis:
    In the present business environment, rapidly developing technology and the competitive world market pose challenges to the available assets of industries. Hence, industries need to allocate and use available assets at the optimum level. Thus, industrialists must create a good decision plan to guide their performance in the production sector. As a result, the present study applies the Meta-Goal Programming technique to attain several objectives simultaneously in the textile production sector. The importance of this study lies in pursuing different objectives simultaneously, which has been almost ignored till now. The production scheduling problem in a textile firm is used to illustrate the practicability and mathematical validity of the suggested approach. Analysis of the results obtained demonstrates that the solution met all three meta-goals with some original goals being met partially. An analysis of the sensitivity of the approach to the weights of the preferences was conducted.
    Źródło:
    Operations Research and Decisions; 2022, 32, 2; 74--88
    2081-8858
    2391-6060
    Pojawia się w:
    Operations Research and Decisions
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A fuzzy approach to multi-objective mixed integer linear programming model for multi-echelon closed-loop supply chain with multi-product multi-time-period
    Autorzy:
    Akin Bas, Sema
    Ahlatcioglu Ozkok, Beyza
    Powiązania:
    https://bibliotekanauki.pl/articles/406583.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    closed-loop supply chain management
    multi-objective optimization
    fuzzy mixed-integerlinear programming
    inventory decision
    Opis:
    By the green point of view, supply chain management (SCM), which contains supplier and location selection, production, distribution, and inventory decisions, is an important subject being examined in recent years by both practitioners and academicians. In this paper, the closed-loop supply chain (CLSC) network that can be mutually agreed by meeting at the level of common satisfaction of conflicting objectives is designed. We construct a multi-objective mixed-integer linear programming (MOMILP) model that allows decision-makers to more effectively manage firms’ closed-loop green supply chain (SC). An ecological perspective is brought by carrying out the recycling, remanufacturing and destruction to SCM in our proposed model. Maximize the rating of the regions in which they are located, minimize total cost and carbon footprint are considered as the objectives of the model. By constructing our model, the focus of customer satisfaction is met, as well as the production, location of facilities and order allocation are decided, and we also carry out the inventory control of warehouses. In our multi-product multi-component multi-time-period model, the solution is obtained with a fuzzy approach by using the min operator of Zimmermann. To illustrate the model, we provide a practical case study, and an optimal result containing a preferable level of satisfaction to the decision-maker is obtained.
    Źródło:
    Operations Research and Decisions; 2020, 30, 1; 25-46
    2081-8858
    2391-6060
    Pojawia się w:
    Operations Research and Decisions
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-14 z 14

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