Linear Ordering Methods Research Articles

Comparison of Several Linear Ordering Methods for Selection of Locations in Order‑picking by Means of the Simulation Methods

When a company uses a shared storage system, selection of locations during the order‑picking process is not an obvious task. Every location where the picked product is placed, can be described by means of several variables, such as: storage time, distance from the I/O point, degree of demand satisfaction, or the number of other picked products in the order. Therefore, the “attractiveness” of each location from the point of view of a certain order can be described by means of synthetic variable, on the basis of which a ranking is created. For each product, the decision‑maker selects the highest‑ranking locations and designates a route for the picker. In the article, by means of the simulation methods, results obtained by several classification methods will be compared. These methods are: Taxonomic Measure of Location’s Attractiveness (based on the Hellwig’s Composite Measure of Development), the TOPSIS method with the Euclidean and GDM distances and the Gen­eralised Distance Measure used as the composite measure of development.

Efficient Nordsieck second derivative general linear methods: construction and implementation

In this paper, by considering the order conditions for second derivative general linear methods of order p and stage order $$q=p-1$$ , we investigate construction and implementation of these methods in the Nordsieck form with $$r=s+1=p$$ , where s and r are the number of internal and external stages of the method, respectively. Constructed methods are A- and L-stable which possess Runge–Kutta stability property. Some numerical experiments are provided in a variable stepsize environment to validate the efficiency of the constructed methods and reliability of the proposed error estimates.

O wyborze metody porządkowania liniowego do oceny gospodarki odpadami w Polsce w ujęciu przestrzennym

Celem artykułu jest przedstawienie techniki wyboru metody porządkowania liniowego obiektów ze względu na poziom zjawiska złożonego jakim jest stan gospodarki odpadami w województwach Polski. Do realizacji tego celu wyselekcjonowano cechy diagnostyczne opisujące badane zjawisko oraz wytypowano metody porządkowania liniowego. Następnie wykorzystując procedurę wyboru metody porządkowania dokonano wytypowania sposobu konstrukcji cechy syntetycznej, który pozwolił zbudować ranking województw ze względu na poziom analizowanego zjawiska. W dalszej kolejności dokonano podziału województw na cztery grupy: bardzo wysokiego, wysokiego, przeciętnego i niskiego poziomu rozwoju omawianego zjawiska. Badania pokazały, że wybór procedury konstrukcji cechy syntetycznej wpływa na ranking badanych obiektów. Otrzymany ranking pozwala sformułować wniosek, iż gospodarka odpadami w Polsce jest regionalnie zróżnicowana.

Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs

In this paper, we study the construction and implementation of special Nordsieck second derivative general linear methods of order p and stage order $$q=p$$ in which the number of input and output values is $$r=p$$ rather than $$r=p+1$$ . We will construct A- and L-stable methods of orders three and four in this form with Runge–Kutta stability properties. The efficiency of the constructed methods and reliability of the proposed error estimates are shown by implementing of the methods in a variable stepsize environment on some well-known stiff problems.

Ocena sytuacji towarowych gospodarstw rolnych państw UE z wykorzystaniem metod porządkowania liniowego

Celem badań przedstawionych w artykule była ocena sytuacji towarowych gospodarstw rolnych w krajach UE, którą określano poprzez potencjał, wykorzystanie ziemi oraz pracy. Cel zrealizowano wykorzystując metody porządkowania liniowego. Celem dodatkowym, o charakterze metodyczny, było porównanie różnych metod doboru wag w formule agregacyjnej. Okazało się, że najlepszy jest stan gospodarstw holenderskich oraz w wysoko rozwiniętych krajach Europy Zachodniej. Spośród krajów postkomunistycznych dobry jest stan gospodarstw w Czechach i na Słowacji. W sytuacji słabej znajdują się gospodarstwa towarowe z Europy Południowej i z pozostałych państw postkomunistycznych. Polska w sporządzonym rankingu znalazła się na dalekiej 23 pozycji.

Classification of gminas of Ostrołęka-Siedlce subregion in terms of their financial condition

The aim of the article is to classify gminas of Ostrołęka-Siedlce subregion in terms of their financial condition. The research was conducted on the basis of data from the Local Data Bank for the years 2013—2016 concerning the state of finances in 84 gminas of the analysed subregion. The method of linear ordering was used. On the basis of the constructed synthetic development measure, four typological classes were distinguished. The first group consisted of gminas achieving the best financial results, whereas the fourth one included gminas with the weakest financial situation. The research indicates that the most numerous group consists of units with lower than average financial condition (the third class) — 55% of all local governments.

Effect of adopted diagnostic variable weighing system on the results of investigation of socioeconomic development of voivodships in Poland

The regional development is certain, complex and multidimensional statistics, ambiguously defined, and although it is frequently used, both in theory and practice, its measurement method remains inconclusive. The proper assessment of the region development level is mostly performed by the methods of linear ordering, whose basic tool is a synthetic measure, being a function aggregating partial information, contained in individual attributes (measures). The results of the research are determined at the same time not only the final list of diagnostic variables, but also the choice of the distance measure and aggregation formulas. As there are many formulas for variable standardisation, methods for weight determination, methods for averaging of standardised values, methods for establishment of reference object coordinates and formulas for distance calculation, lots of different aggregate measures. However, the literature frequently encourages to, in the absence of unambiguous indications for varied meaning and role of individual features, tacitly assume that all diagnostic variables are of the same weight, in general, there are two methods of obtaining weights for individual diagnostic variables: the weights are established by the experts’ method (a priori method) or with the use of the computation algorithms based on information included in the primary (raw) data (a posteriori method). This study will be conducted on the basis of statistical methods for obtaining weights for individual diagnostic variables (a posteriori weights).

Application methods of multidimensional comparative analysis to the assessment of environmental state in Dolnośląskie voivodship

The aim of this article is to present the results of multidimensional comparative analysis methods used to assess the state of the environment in Dolnośląskie voivodship in the cross-section of powiats. The research was conducted on the basis of data from the CSO of Poland for 2015 concerning the state and environmental protection in 30 powiats of Dolnośląskie voivodship. The method of linear ordering of objects based on a pattern object (or an anti- -pattern object) was used in the research. Many of them described in the subject literature usually lead to differing results (rankings of objects are not the same). It results from i.a. the adopted methods of normalization and weighing of variables and aggregations (creation of synthetic variables). The article is an attempt to compare the results of linear ordering of powiats due the environmental state with the use of method based on a pattern object (or an anti-pattern object). In the rankings correctness analysis, quality indicators were used to evaluate the quality of linear ordering methods.

ORGANIC FARMING IN POLAND IN THE LIGHT OF MULTIVARIATE COMPARATIVE ANALYSIS

Organic farming is an environmentally-friendly production system, which has been dynamically developing since 2004. The study attempts to conduct a spatial assessment of the development of this management method. The analysis covered data at the level of voivodships, originating from GIJHARS1 and from the Central Statistical Office (GUS) from 2014, concerning producers respecting the production in the environmentally-friendly system. They include characteristics such as: average surface area, proportion of the area of arable lands, number of processing plants, production volume of: milk, cereals, vegetables, and fruit. The analysis uses the method of linear ordering of a set of objects, based on the created synthetic variable. The results of the study suggest that Polish voivodships are generally characterised by an average or low level of development of organic farming. A positive phenomenon is observed in the fact that organic farming develops in voivodships with a more fragmented agrarian structure.

A Summary Assessment of Innovativeness of The New Member States of The European Union

This paper attempts to assess the level of innovativeness of the economies of the ‘new’ EU member states1 in the years 2008–2015, with particular attention paid to the position of the Polish economy. This assessment was carried out on the basis of a summary index constructed with the use of statistical methods of linear ordering. The paper also presents conclusions from the analysis of the evolution of selected factors characterizing the innovativeness of the new EU member states. In the conducted analysis, statistical data from Eurostat were used to de­scribe the innovativeness of economies with respect to two areas: (a) science and technology; and (b) education and training. The developed ranking of innovativeness of the new EU Member States, built on the basis of a summary index, makes it possible to state that the countries with the highest level of innovativeness among 13 analyzed countries were Slovenia, the Czech Republic and Malta. Poland’s above‑average value of the summary index for these countries occupied sixth position in the ranking, which indicates a relatively low level of innovativeness of the Polish economy.

Starting procedures for general linear methods

We present a systematic approach to the construction of starting procedures for general linear methods (GLMs) of order p and stage order q=p. Order conditions for starting procedures based on the generalized Runge–Kutta (RK) are derived using the theory of rooted trees, elementary differentials, and elementary weights, and examples of generalized RK formulas are given up to the order p=4.

Once More about the Selection Procedure for the Linear Ordering Method

In this paper once again the issue of selecting the method of linear ordering was analyzed as a response to proposed procedure presented in Kisielińska’s paper (2016). It was shown in two examples that the ranking depends on the method used, and the differences are significant. Underlined the need to apply several methods before the construction of the final ranking and eliminating the “outliers” rankings. The article proposes a procedure for their elimination. It is based on the arithmetic mean and deviation of average measures of rankings’ similarity obtained with the use of several linear ordering methods. The research shows that when choosing a linear ordering methods calculations should be carried out using several procedures and make a selection using the already existing solutions in the literature or verify with the experts of analyzed subject.

Procesy koncentracji działalności przemysłowej w strefie podmiejskiej na przykładzie Dolnego Śląska

W dobie postindustrialnej narastające koszty funkcjonowania miast, postęp naukowo-techniczny, wzrost poziomu wykształcenia ludności i liczne bariery ekologiczne przyczyniają się do decentralizacji działalności gospodarczej. Jedną z konsekwencji tego zjawiska jest zwiększenie atrakcyjności lokalizacyjnej strefy podmiejskiej. Celem opracowania jest ukazanie zróżnicowania przestrzennego oraz dokonanie oceny stopnia rozwoju współczesnych procesów koncentracji działalności przemysłowej w strefach podmiejskich największych miast Dolnego Śląska. Zakres zagadnień przyjętych do analiz uzależniony był dostępnością danych, zwłaszcza na poziomie lokalnym. W artykule zaprezentowano analizy dotyczące: podmiotów w przemyśle, obszarów przemysłowych, pracujących i produkcji sprzedanej przemysłu. Zagadnienie suburbanizacji analizowano na podstawie salda migracji wewnętrznych, natężenia oddanych mieszkań czy skali zameldowania w obszarze strefy podmiejskiej badanych miast. Do diagnozy stopnia rozwoju i poziomu zróżnicowania przestrzennego procesu koncentracji działalności przemysłowej wykorzystano wskaźnik lokalizacji LQ (location quotient) oraz taksonomiczną metodę porządkowania liniowego odległości od tzw. wzorca rozwoju. Przyjęte do badania parametry zaprezentowano w układach lokalnych (gmin i powiatów) województwa dolnośląskiego, z określeniem ich przestrzennego zróżnicowania i natężenia.

Diversity in the socio-economic development of voivodships in terms of implementing cohesion policy goals

The article aims to evaluate the degree of diversification of socio-economic development of voivodships in 2005 and 2015 in the context of cohesion policy. This policy focuses on reducing the distance between some European Union countries and the most developed EU members, as well as on decreasing national disparities in development. The analysis was conducted on the basis of the CSO data, using the Hellwig’s method of linear ordering. The selected diagnostic variables relate to three dimensions of cohesion policy: economic, social and territorial. The applied method enabled to assess social and economic situation in Poland, indicating voivodships with high development potential and also those facing difficulties. The research confirmed persistent differences in the development level between the examined territorial units

DISPARITIES OF HIGH-TECH INDUSTRIES IN THE EUROPEAN UNION COUNTRIES

The main objective of this study is to identify disparities in the development of high-tech industries between twenty eight European Union countries in 2013, by building a selected synthetic measure and prioritize them according to the estimated values of these measures. Operationalization of the research takes into account a number of diagnostic variables describing the high-tech sector in the EU member states, along with the attempt to explain the determinants of their position in the created ranking. The study used a Hellwig’s synthetic measure of development, which is one of the reference methods of linear ordering.

Zróżnicowanie rozwoju handlu wewnętrznego w Polsce według województw w latach 2005–2014

The article presents the changes observed in the internal trade in Poland in 2004–2015. The aim of the study is to determine the degree of development of internal trade in individual regions in Poland. The second aim is to create ranking for Polish regions for 2014 using four methods of linear ordering. These methods are as follows: standardization, zero unitarization, Z. Hellwig and TOPSIS. In accordance with the selection supporting procedure the ranking best-reflecting real trade development was chosen. The significant role of trade sector in the economy and labour market was emphasized.

Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size

Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.

Zastosowanie rozmytych metod porządkowania liniowego w ustalaniu hierarchii ważności cech usługi związanych z jakością

The principal aim of the article is to characterise and assess the application possibilities for selected fuzzy linear ordering methods in determining the hierarchy of the importance of service quality characteristics. The report presents the results of a study whose aim was to assess the quality of Poland's Central Statistical Office's website. A tool known as WebQual was used, after modification by the author for two areas: quality of listed service characteristics and how respondent opinions were measured. The survey questionnaire enables the transformation of the measurement results from linguistic values to numerical ones using fuzzy sets. The primary data prepared this way formed the basis for the application of fuzzy linear ordering methods.

On variable step Hermite–Birkhoff solvers combining multistep and 4-stage DIRK methods for stiff ODEs

Variable-step (VS) 4-stage k-step Hermite---Birkhoff (HB) methods of order p = (k + 2), p = 9, 10, denoted by HB (p), are constructed as a combination of linear k-step methods of order (p ? 2) and a diagonally implicit one-step 4-stage Runge---Kutta method of order 3 (DIRK3) for solving stiff ordinary differential equations. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep and Runge---Kutta type order conditions which are reorganized into linear confluent Vandermonde-type systems. This approach allows us to develop L(a)-stable methods of order up to 11 with a > 63°. Fast algorithms are developed for solving these systems in O (p2) operations to obtain HB interpolation polynomials in terms of generalized Lagrange basis functions. The stepsizes of these methods are controlled by a local error estimator. HB(p) of order p = 9 and 10 compare favorably with existing Cash modified extended backward differentiation formulae of order 7 and 8, MEBDF(7-8) and Ebadi et al. hybrid backward differentiation formulae of order 10 and 12, HBDF(10-12) in solving problems often used to test higher order stiff ODE solvers on the basis of CPU time and error at the endpoint of the integration interval.

Construction of efficient general linear methods for stiff Volterra integral equations

General linear methods in the Nordsieck form have been introduced for the numerical solution of Volterra integral equations. In this paper, we introduce general linear methods of order p and stage order q=p for the numerical solution of Volterra integral equations in general form, rather than Nordsieck form. A- and V0(α)-stable methods are constructed and applied on stiff problems to show their efficiency.