1. Generalised fuzzy linear programmingJanez Usenik, Maja Žulj, 2023, izvirni znanstveni članek Opis: Linear programming is one of the widely used methods for optimising business systems, which includes organisational, financial, logistic and control subsystems of energy systems in general. It is possible to express numerous real-world problems in a form of linear program and then solve by simplex method [1]. In the development of linear programming, we are facing a number of upgrades and generalisations, as well as replenishment. Particularly interesting in recent years is an option that decision variables and coefficients are fuzzy numbers. In this case we are dealing with fuzzy linear programming. If we also include in a fuzzy linear program a generalisation with respect to Wolfe’s modified simplex method [1], we obtain a generalised fuzzy linear program (GFLP). Usenik and Žulj introduced methods for solving those programs and proved the existence of the optimal solution in [2]. In the article, the simplex algorithm which enables the determining of an optimal solution for GFLP is described. There is a numerical example at the end of the article that illustrates the algorithm. Ključne besede: linear programming, fuzzy linear programming, generalised linear programming, generalised fuzzy linear programmin Objavljeno v DKUM: 11.10.2023; Ogledov: 134; Prenosov: 4 Celotno besedilo (21,53 MB) Gradivo ima več datotek! Več... |
2. The need for simulation in complex industrial systemsKhalid Aboura, Miroljub Kljajić, Ali Eskandarian, 2012, izvirni znanstveni članek Opis: We discuss the concept of simulation and its application in the resolution of problems in complex industrial systems. Most problems of serious scale, be it an inventory problem, a production and distribution problem, a management of resources or process improvement, all real world problems require a mix of generic, data algorithmic and Ad-hoc solutions making the best of available information. We describe two projects in which analytical solutions were applied or contemplated. The first case study uses linear programming in the optimal allocation of advertising resources by a major internet service provider. The second study, in a series of projects, analyses options for the expansion of the production and distribution network of mining products, as part of a sensitive strategic business review. Using the examples, we make the case for the need of simulation in complex industrial problems where analytical solutions may be attempted but where the size and complexity of the problem forces a Monte Carlo approach. Ključne besede: simulation, linear programming, production process Objavljeno v DKUM: 10.07.2015; Ogledov: 1092; Prenosov: 388 Celotno besedilo (448,62 KB) Gradivo ima več datotek! Več... |
3. On Groebner bases and their use in solving some practical problemsMatej Mencinger, 2013, izvirni znanstveni članek Opis: Groebner basis are an important theoretical building block of modern (polynomial) ring theory. The origin of Groebner basis theory goes back to solving some theoretical problems concerning the ideals in polynomial rings, as well as solving polynomial systems of equations. In this article four practical applications of Groebner basis theory are considered; we use Groebner basis to solve the systems of nonlinear polynomial equations, to solve an integer programming problem, to solve the problem of chromatic number of a graph, and finally we consider an original example from the theory of systems of ordinary (polynomial) differential equations. For practical computations we use systems MATHEMATICA and SINGULAR . Ključne besede: polynomial system of (differential) equations, integer linear programming, chromatic number of a graph, polynomial rings, Groebner basis, CAS systems Objavljeno v DKUM: 10.07.2015; Ogledov: 1421; Prenosov: 94 Povezava na celotno besedilo |
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8. Optimisation of tree path pipe network with nonlinear optimisation methodDanijela Urbancl, Darko Goričanec, 2009, izvirni znanstveni članek Opis: In this paper, the optimisation of pipe network with hot water is presented. The mathematical model, consisting of the nonlinear objective function and system of nonlinear equations for the hydraulics limitations is developed. On its basis, the computer program for determination optimal tree path with the use of simplex method was solved. For economic estimation the capitalised value method, which consider all costs of investment and operation was used. The results are presented for real case study network with 24 nodes and 33 pipe sectors. Ključne besede: district heating, pipe network, optimisation, non-linear programming, simplex method Objavljeno v DKUM: 01.06.2012; Ogledov: 2264; Prenosov: 98 Povezava na celotno besedilo |
9. Optimum design of plane timber trusses considering joint flexibilitySimon Šilih, Miroslav Premrov, Stojan Kravanja, 2005, izvirni znanstveni članek Opis: The paper presents the optimization of metal-plate-connected plane timber trusses with special emphasis on joint flexibility. The optimization was performed by the non-linear programming approach. Since various truss design parameters such as type of truss configuration, span/depth ratio, number and type of diagonal and vertical members and type of joint connections simultaneously affect each other, it is proposed that all of these parameters should be considered simultaneously in a single mathematical model. An optimization model for cost optimization of timber trusses was thus developed. The economic objective function for minimizing the structure's self-manufacturing costs was defined, subjected to the design, stress and deflection (in)equality constraints. The finite element equations were as the equality constraints defined for the calculation of the internal forces and the deflections of the structure. The stiffness matrix of the structure was composed by considering fictitiously decreased cross-section areas of all the flexibly connected elements. Constraints for the dimensioning of the timber members were determined in accordance with Eurocode 5 in order to satisfy the requirements of both the ultimate and the serviceability limit states. The cross-section dimensions and the number of fasteners were defined as independent optimization variables. A numerical example demonstrates the applicability of the optimization approach presented as well as the influence of the fasteners' flexibility on the optimal self-manufacturing costs. Ključne besede: civil engineering, timber structures, trusses, fasteners, flexibility, optimization, non-linear programming Objavljeno v DKUM: 01.06.2012; Ogledov: 2061; Prenosov: 120 Povezava na celotno besedilo |
10. Flow-pressure analysis of loop gas networksJurij Krope, Peter Trop, Darko Goričanec, 2011, izvirni znanstveni članek Opis: This paper proposes a mathematical model underlying a computer program for flow-pressure analysis of loop gas pipe networks. The method is used on a test case with four nodes. The HAPN application for flow-pressure analyses of low pressure gas pipe networks is completely designed in object-oriented programming technology. The equations, which describe the physical flow-pressure conditions through every cross point are assumed to be continuous and the energy of every closed loop of analyzed network conserved. The system of non-linear equations was linearized by LTM (Linear Theory Method). The algorithm for numerical module LTM and the method for solution of sparse matrix are developed at the Faculty of Chemistry and Chemical Engineering, University of Maribor, Slovenia. Ključne besede: fluid mechanics, gas pipe networks, linear method, non-linear programming, pressure losses Objavljeno v DKUM: 01.06.2012; Ogledov: 2216; Prenosov: 33 Povezava na celotno besedilo |