Solver

Na rynku można odnaleźć wiele podręczników pomocnych w rozwijaniu kompetencji związanych z posługiwaniem się arkuszem kalkulacyjnym w praktyce menedżerskiej. Niewiele jest natomiast pozycji literaturowych pokazujących możliwości wykorzystania MS Solver do wspomagania decyzji. Niniejsza książka ma za zadanie wypełnić tę lukę. Jej celem jest przedstawienie możliwości dodatku Solver w procesie podejmowania decyzji optymalnych. Intencją Autorki było stworzenie podręcznika dla osób zainteresowanych samodzielną nauką pracy z MS Excel Solver.
Niniejsze opracowanie składa się z trzech rozdziałów. Rozdział pierwszy zawiera teoretyczne podstawy wprowadzające do zagadnień podejmowania decyzji optymalnych. Przedstawiono w nim podstawowe pojęcia z tego zakresu, omówiono czym jest proces rozwiązywania problemów decyzyjnych ze szczególnym rozróżnieniem pomiędzy rozwiązywaniem problemów decyzyjnych a ich podejmowaniem.
Drugi rozdział został dedykowany przedstawieniu funkcjonalności dodatku Solver wraz z omówieniem opcji ustawień i metod rozwiązań dostępnych w programie oraz raportów wyników, wrażliwości i granic. Na tak przygotowanej podbudowie teoretycznej w dalszej części rozdziału zaprezentowano praktyczne rozwiązanie krok po kroku prostego zadania decyzyjnego. Takie podejście przygotowuje Czytelnika do treści zawartych w rozdziale trzecim. Przedstawiono tutaj różnorodne i znacznie bardziej złożone problemy decyzyjne. Dobór przykładów ma na celu pokazanie potencjału Solvera.

Celem niniejszego opracowania jest zaprezentowanie sposobu szybkiego rozwiązywania logistycznych problemów optymalizacyjnych przez zastosowanie łatwo dostępnego i taniego narzędzia, jakim jest Solver wchodzący w skład pakietu MS Office (dodatek arkusza kalkulacyjnego Excel). Zadanie to wykonano na przykładzie małej firmy kurierskiej, która prowadzi swoją działalność bez żadnego wsparcia informatycznego. W pracy przedstawiono charakterystykę tej firmy i specyfikę realizowanych procesów transportowych, a następnie z wykorzystaniem Solvera opracowano rozwiązanie problemu wytyczenia szlaku przejazdu kuriera w taki sposób, aby osiągnąć jak najkrótszą całkowitą długość trasy, a tym samym zminimalizować koszty transportu.

Em vários domínios do conhecimento científico são usados modelos matemáticos para descrever um conjunto de dados empíricos. Se no caso dos modelos lineares, a análise de regressão para obter os parâmetros dos modelos é “simples” e vulgarizada, é mais difícil ajustar aos dados funções (matematicamente) mais “complicadas”, p.ex. modelos não-lineares. Neste artigo, pretende-se 1) apresentar os conceitos fundamentais da análise de regressão não-linear, 2) descrever, usando um exemplo, a utilização da ferramenta Solver® do Microsoft Excel® para analisar problemas cujo objectivo é “descrever” relações estatísticas (não-lineares) entre variáveis, e 3) compilar os “problemas” identificados com a utilização do Excel® (incluindo o Solver®) como ferramenta de análise estatística.

This book shows how Microsoft Excel can be used as an effective educational platform for thermofluid analyses. Excel provides a rich library of built-in functions and powerful tools for data visualisation and analysis. The Solver add-in that comes with it enables the students to perform multi-variable optimisation analyses of thermofluid systems. Building on these capabilities, the Excel-based platform for thermofluid analyses presented in this book also utilises the Visual Basic for Applications (VBA) programming language that comes with Microsoft Office. The book shows how VBA can be used for developing additional user-defined functions (UDFs) for supplementing Excel’s built-in functions and introduces an Excel add-in, called Thermax, that provides UDFs for determining the thermodynamic fluid properties. The fluids covered by Thermax include twelve ideal gases, saturated water and superheated steam mixtures, six refrigerants, humid air for psychrometric analyses, and air at standard atmospheric pressure. Property add-ins developed by other academic and research institutions or individuals can be used to extend the range of thermofluid analyses that can be performed with the Excel-based platform.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Computer-Aided Thermofluid Analyses using Excel Mohamed Musadag El-Awad

Heat exchanger is mainly associated with transfer heat from one fluid to another fluid either in direct contact with each other or separated by wall. The heat exchangers characteristics are concerned with the rate of heat transfer between the fluids with assuming the flow to be uniform throughout the core of the exchanger. But in actual practice it is usually the flow Non-uniformity that occurs and adversely affects the Heat Transfer rate and heat exchange properties of the heat exchanger. The major non-uniform flow is caused due to poor header design or restrictions in flow at microscopic level as a result of manufacturing operations on the surface. The CFD analysis of Heat exchanger is achieved considering the concept of Viscosity induced flow Non-Uniformity through the exchanger tubes. With the application of Computational Fluid Dynamics package FLUENT relative analysis pertaining to Non-uniform flow is carried out. The matter of interest of this paper is to analyze the heat transfer related to two mean temperatures namely cross-sectional and adiabatic mean temperature.

The need to solve large sparse linear systems of equations efficiently lies at the heart of many applications in computational science and engineering. For very large systems when using direct factorization methods of solution, it can be beneficial and sometimes necessary to use multiple processors, because of increased memory availability as well as reduced factorization time. We report on the development of a new parallel code that is designed to solve linear systems with a highly unsymmetric sparsity structure using a modest number of processors (typically up to about 16). The problem is first subdivided into a number of loosely connected subproblems and a variant of sparse Gaussian elimination is then applied to each of the subproblems in parallel. An interface problem in the variables on the boundaries of the subproblems must also be factorized. We discuss how our software is designed to achieve the goals of portability, ease of use, efficiency, and flexibility, and illustrate ...

Abstrak Persoalan transportasi yang tidak dikelola dengan baik dapat mempengaruhi harga jual barang yang diakibatkan tingginya biaya pengangkutan untuk mendistribusikan barang tersebut. Para ahli telah menciptakan metode optimisasi yang dapat digunakan untuk mengetahui cara pengalokasian yang terbaik (optimal). Namun metode ini tidak mudah digunakan apabila dilakukan secara manual apalagi bagi orang yang tidak memiliki latar belakang pendidikan yang sesuai. Dalam kasus seperti ini sangat dibutuhkan penggunaan komputer. Salah satu aplikasi yang dapat digunakan dan mudah didapat adalah solver add-ins yang terdapat pada microsoft excel. Solver ini sudah diuji keakuratannya dan dapat digunakan dalam menganalisis kemungkinan perubahan keputusan akibat perubahan-perubahan pada data biaya maupun data kuantitas distribusi. Kata Kunci : Model transportasi, Solver add-ins, distribusi, optimal 1. Pendahuluan Perusahaan yang bergerak di bidang perdagangan barang maupun perusahaan manufaktur tidak terlepas dari aktivitas distribusi. Bagi perusahaan yang memiliki saluran distribusi yang luas serta memiliki tempat penyimpanan (gudang) barang lebih dari 1 (satu) akan terdapat beberapa alternatif cara pengalokasian barang. Pemilihan cara pengalokasian barang untuk didistribusikan bertujuan untuk meminimumkan total ongkos distribusi, namun seluruh saluran distribusi atau pelanggan dapat dipenuhi permintaannya (demand). Saluran distribusi merupakan suatu jalur yang dilalui oleh arus barang-barang dari produsen ke perantara dan akhirnya sampai pada pemakai [1]. Dalam penyampaian barang tersebut sudah barang tentu dilakukan melalui transportasi, baik melalui darat, udara maupun laut. Transportasi merupakan suatu metode yang digunakan untuk mengatur distribusi dari sumber-sumber (gudang) yang menyediakan produk yang sama atau sejenis ke tempat tujuan secara optimal. Kasus seperti ini dapat dimodelkan dengan model transportasi serta dapat diselesaikan dengan teknik peneyelesaian persoalan transportasi. Salah satu model dalam model optimisasi adalah model transportasi. Model transportasi merupakan model matematika dan merupakan tipe khusus dalam model programa linier (linear programming). Selain model transportasi, juga termasuk dalam tipe khusus model transportasi adalah model transshipment dan model assignment (penugasan) dapat digunakan dalam mendukung pengambilan keputusan dengan hasil optimum, sehingga dalam pemodelan dan analisis pada decision support system, model linear programming sangat luas digunakan [2]. Pemodelan matematika serta penggunaan teknik matematika membutuhkan keahlian sehingga tidak semua orang dapat menggunakannya. Bagi orang yang memiliki keahlian dalam bidang tersebut juga masih memiliki kendala yakni membutuhkan waktu lama dan

Propositional satisfiability (SAT) is an NP-complete problem, holding a central place in computer science and engineering. SAT has numerous applications in formal verification, artificial intelligence and other areas. Modern SAT solvers, using an enhanced version of the backtrack search DavisLogemann-Loveland (DLL) algorithm, are able to successfully cope with instances comprising millions of variables. This work is an attempt to shed new light on the functionality of a modern SAT solver. We also propose a number of enhancements that are empirically useful, especially in the formal verification domain. We propose a framework for presenting and analyzing a modern DLLbased SAT solver. We provide a basic backtracking algorithm that explicitly shows the process of resolution refutation construction. Our approach is based on the notion of a parent resolution derivation – a resolution proof for validness of a flip operation. We show how to derive the algorithm of a modern SAT solver from basic backtracking step-by-step. This resolution-based approach allows us to define new criteria for measuring the practical impact of different schemes for conflict-driven learning by making the notion of search pruning more formal. We show that the 1UIP scheme, enhanced by conflict clause minimization, is better than other known schemes in terms of pruning. This explains its empirical advantage over other schemes. We propose an enhancement to the minimized 1UIP scheme, called local conflict clause recording. This technique improves the performance of a modern SAT solver by recording additional conflict clauses. Local conflict clause recording makes the learning less dependent on the variable polarity selection heuristic. Assignment stack shrinking is a technique whose goal is to shrink the size of the assignment stack and conflict clauses. We demonstrate the empirical usefulness of assignment stack shrinking and analyze its impact on the performance of a modern SAT solver, comparing it to the impact of conflict clause minimization and rapid restarts. Furthermore, a new decision heuristic for SAT, called the clause-based heuristic, is introduced. This heuristic is designed to increase the likelihood that interrelated variables will be chosen in proximity. It maintains a clause list containing both the initial and conflict clauses. The next decision literal is picked from the first unsatisfied clause. We propose various methods for initially organizing the clause list and for moving clauses within it. Our approach results in a significant performance boost over existing heuristics tested on hard real-world industrial benchmarks. Finally, we present an algorithm for minimal unsatisfiable core extraction that is able to find a minimal unsatisfiable core for large real-world formulas. Benchmark families, arising in formal verification of hardware, are of particular interest to us. Modern SAT solvers are able to produce a resolution refutation of a given unsatisfiable formula, whose sources are the input clauses and whose sink is the empty clause. Our method’s basic version removes the input clauses connected to the empty clause one by one from the resolution refutation, preserving the validity of the refutation by adding other clauses and resolution relations until no more input clauses can be removed. In the end, all the input clauses, connected to the empty clause, comprise the minimal unsatisfiable core.

Accurately predicting the onset of flutter is an important consideration when designing and certifying aircraft for an intended flight envelope. In addition to the typical aeroelastic motions considered in flutter analysis, recent computational studies [1, 2] have shown that the dynamic effects of fuel sloshing can further impact on the computed flutter profile. In this paper we aim to outline the development of a strongly coupled, partitioned fluid-structure interactions (FSI) solver, which includes the dynamic effects of fuel sloshing. The solver is implemented in OpenFOAM, and is based on an iterative coupling of an incompressible flow solver, a volume of fluid (VOF) based free surface flow solver and a reduced order model (ROM) for the structural domain. The structural ROM is based on a modal analysis approach which incorporates quadratic mode shape components. Linear modal analysis has been shown to provide an efficient approximation for aeroelastic applications, but is limited...

ABSTRACT For many years, there has been a strong intra Ghent University collaboration between the IBiTech-bioMMeda research group, focusing on the application of fluid and structural mechanics for biomedical problems, and the department of Flow, Heat and Combustion Mechanics with a strong background in developing algorithms for numerical fluid mechanics and fluid-structure interaction (FSI) problems. This collaboration joins the strengths of both groups, with ongoing applications in FSI simulations of heart valves, aortic coarctation, aortic aneurysms etc., thereby integrating in vivo (human and (small) animal) hydraulic bench and numerical research.

Standard technique for the prediction of dynamic derivatives is the use of wind tunnel simulations with expensive technical equipment and complex data processing. Numerical flow computations, on the other hand, can simulate arbitrary model motion and hence, all desired derivatives are directly accessible. The prediction of dynamic derivatives with the help of an efficient Navier-Stokes solver is investigated in the present work. The assessment is performed for a lifting body that represents the X-24A experimental vehicle. Comparisons with wind tunnel and flight test data indicate good agreement. We can also demonstrate that the numerical approach requires reasonably low computation resources.

This paper presents an alternative to the location of distribution centres considering a multi-objective model minimising insecurity cost and road access for a case study in the City of Barranquilla (Colombia). For the solution of the model, 15 different scenarios of variation of the importance of the proposed objectives are considered. As a basis for the design of the modelling, the characterisation and classification of the variables with the highest incidence in the location of distribution centres or warehouses are posed. It is possible to demonstrate the impact of the evaluation and analysis of the mathematical model for the location of this type of facility.