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1

A new geometric approach to multiobjective linear programming problems

Kaci Mustapha, Radjef Sonia

Mathematica Applicanda

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2023

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Vol. 51, no. 1

3--12

EN

This paper is a follow-up to a previous work where we developed a new geometric approach to sensitivity analysis. In this paper, we present a simple method to determine whether a given multiobjective linear programming problem (MOLPP) has an ideal solution (i.e. all of the objective functions are optimized simultaneously) without having to calculate the optimal value of each objective function. First, we divide the space of linear forms into a finite number of sets based on a fixed convex polygonal subset of R2 using an equivalency relationship. All the elements from a given equivalency class have the same optimal solution. Next, we characterize the equivalence classes of the quotient set using a geometric approach to sensitivity analysis. Finally, a numerical example is given to illustrate the method.

PL

W tym artykule przedstawiamy nową metodę rozwiązywania problemów programowania liniowego z wieloma celami (MOLPP), która eliminuje potrzebę obliczania optymalnej wartości każdej funkcji celu. Metoda ta jest kontynuacją naszych wcześniejszych prac dotyczących analizy wrażliwości, gdzie opracowaliśmy nowe podejście geometryczne. Pierwszym krokiem naszego podejścia jest podział przestrzeni form liniowych na skończoną liczbę zbiorów opartych na stałym wypukłym podzbiorze wielokąta R2. Dokonujemy tego za pomocą relacji równoważności, która zapewnia, że wszystkie elementy z danej klasy równoważności mają takie same rozwiązanie optymalne. Następnie charakteryzujemy klasy równoważności zbioru ilorazowego za pomocą podejścia geometrycznego do analizy wrażliwości. Ten krok jest kluczowy w identyfikacji rozwiązania idealnego dla MOLPP. Korzystając z tego podejścia, możemy określić, czy dana MOLPP ma rozwiązanie idealne, bez konieczności obliczania optymalnej wartości każdej funkcji celu. Jest to znacząca poprawa w stosunku do istniejących metod, ponieważ znacznie zmniejsza złożoność obliczeniową i czas wymagany do rozwiązania MOLPP. Aby zilustrować naszą metodę, przedstawiamy numeryczny przykład, który dowodzi jej skuteczności. Nasza metoda jest prosta, ale potężna i może być łatwo zastosowana do szerokiego zakresu MOLPP. Niniejsza praca przyczynia się do dziedziny optymalizacji poprzez przedstawienie nowego podejścia do rozwiązywania MOLPP, które jest wydajne, skuteczne i łatwe do zaimplementowania.

2

The Method for Assessing the Impact of Variable Coal Demand on the Efficiency of Mine Operations

Fuksa Dariusz

Inżynieria Mineralna

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2023

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no. 1

267--273

EN

The method presented in the article is based on Monte Carlo simulation and involves studying the impact of random demand fluctuations on the efficiency of mines and mine groups (companies). For random demand fluctuations, a normal distribution is assumed, and the analysis variants present-ed include: • Adopting the mean and variance values based on retrospective data, • Considering the most probable forecast error resulting from predictive formulas, • Taking into account correlated changes in demand. The results obtained are presented in the form of histograms of the degree of operational lever-age. These histograms allow for predicting how the degree of operational leverage of mines will develop, as well as estimating the direction and probability of these changes. The developed and veri-fied sensitivity analysis using real examples constitutes a useful element in rationalizing decision-making processes.

PL

Zaprezentowana w artykule metoda oparta jest na symulacji Monte Carlo i obejmuje badanie wpływu wahań losowych zapotrzebowania na efektywność kopalń oraz ich grup (spółek). Dla losowych wahań zapotrzebowania przyjęto rozkład normalny, a przedstawione warianty analizy uwzględniają: • przyjęcie wartości oczekiwanej i dyspersji według danych retrospektywnych; • przyjęcie najbardziej prawdopodobnego błędu prognozy wynikającego z formuł predykcyjnych; • uwzględnienie skorelowanych zmian zapotrzebowania. Uzyskane wyniki przedstawiono w postaci histogramów stopnia dźwigni operacyjnej. Pozwalają one przewidywać, jak będzie kształtował się stopień dźwigni operacyjnej kopalń, jak również umożliwia oszacować, w którym kierunku zmiany te będą postępować i z jakim prawdopodobieństwem. Opracowana i zweryfikowana na realnych przykładach analiza wrażliwości stanowi przydatny element racjonalizacji procesów decyzyjnych.

3

Choice of the p-norm for high level classification features pruning in modern convolutional neural networks with local sensitivity analysis

Jeczmionek Ernest, Kowalski Piotr A.

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 4

663--672

EN

Transfer learning has surfaced as a compelling technique in machine learning, enabling the transfer of knowledge across networks. This study evaluates the efficacy of ImageNet pretrained state-of-the-art networks, including DenseNet, ResNet, and VGG, in implementing transfer learning for prepruned models on compact datasets, such as FashionMNIST, CIFAR10, and CIFAR100. The primary objective is to reduce the number of neurons while preserving high-level features. To this end, local sensitivity analysis is employed alongside p-norms and various reduction levels. This investigation discovers that VGG16, a network rich in parameters, displays resilience to high-level feature pruning. Conversely, the ResNet architectures reveal an interesting pattern of increased volatility. These observations assist in identifying an optimal combination of the norm and the reduction level for each network architecture, thus offering valuable directions for model-specific optimization. This study marks a significant advance in understanding and implementing effective pruning strategies across diverse network architectures, paving the way for future research and applications.

4

Modeling of the influence of elevated temperature on oxygen distribution in soft tissue

Jasiński Marek, Zadoń Maria

Engineering Transactions

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2023

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Vol. 71, iss. 3

287--306

EN

The purpose of the study was to analyze the combined model of bioheat transfer and oxygen distribution in tissue during exposition to the external heat impulse. The effect of temperature and thermal damage to the tissue on the values of its thermophysical parameters was taken into account. The variable value of the perfusion coefficient affects the blood velocity in the capillary and thus the distribution of the partial oxygen pressure in the tissue. Various models of the oxygen dissociation curves were also considered and a sensitivity analysis was performed for the parameters of the oxygen distribution model. In the numerical realization stage, the finite difference method and the shooting method were used.

5

Maintenance policy of degradation components based on the two-phase Wiener process

Song Minqiao, Zhang Yingzhi, Yang Fang, Wang Xiaofeng, Guo Guiming

Eksploatacja i Niezawodność

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2023

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Vol. 25, no. 4

art. no. 172537

EN

This paper proposes a condition-based maintenance policy for the two-phase Wiener degradation process components. The main contribution of this article is to provide the time distribution of degradation failures for the two-phase Wiener process degradationcomponent, as well as the modeling and solving methods for two-phase maintenance. The two-phase maintenance policy includes two-phase inspection and preventive replacement maintenance operations. The established optimization maintenance policy model aims to minimize long-term operation costs. The specific cost calculation equation and the solution method of the maintenance model are given. The feasibility of the maintenance policy model is verified using the two-phase degradation data of the Liquid Coupling Devices. The Particle swarm optimization algorithm can stably solve the described problem, and the results show that the two-phase maintenance policy can be more economical and improve components availability. After that, we also analyzed the impact of the cost parameters on the maintenance policy through sensitivity analysis.

6

Sensitivity analysis of the dem model numerical parameters on the value of the angle of repose of lunar regolith analogs

Młynarczyk Przemysław, Kolusz Adam, Gallina Alberto

Artificial Satellites : Journal of Planetary Geodesy

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2023

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Vol. 58, Special Issue 1

188--202

EN

The discrete element method (DEM) is a numerical technique used in many areas of modern science to describe the behavior of bulk materials. Terramechanics of planetary soil analogs for in situ resource utilization activities is a research field where the use of DEM appears to be beneficial. Indeed, the close-to-physics modeling approach of DEM allows the researcher to gain much insight into the mechanical behavior of the regolith when it interacts with external devices in conditions that are hard to test experimentally. Nevertheless, DEM models are very difficult to calibrate due to their high complexity. In this paper, we study the influence of fundamental model parameters on specific simulation outcomes. We provide qualitative and quantitative assessments of the influence of DEM model parameters on the simulated repose angle and computational time. These results help to understand the behavior of the numerical model and are useful in the model calibration process.

7

Modeling and experimental investigation of a controllable rotary fluid damper

Cao X., Zhou J., Yu M., Wang Y.

Archives of Mechanics

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2023

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Vol. 75, nr 4

493--516

EN

Controllable rotary fluid damper (CRFD) is an efficient and cheap energy dissipation device, which is used to reduce the impact of vibration in mechanical systems. In this paper, the CRFD controlled by a servo motor is developed to reduce the effects of vibrations in the helicopter flight control system. The dynamic mechanical characteristic of the CRFD is experimentally investigated by the MTS machine. Due to the complex factors such as high shear thinning rate and compressibility of the damping medium, inertia of moving parts and internal friction, the CRFD studied has highly nonlinear hysteresis characteristics. The accuracy of the damper modeling is of great significance for designing effective vibration reduction methods. Therefore, a new generalized viscous–nonlinear elastic model is proposed to track the mechanical characteristics of CRFD. On the basis of parameter sensitivity analysis, the proposed generalized viscous–nonlinear elastic model is modified. According to the identification results of the modified model, the main parameters are fitted as polynomial functions of motor rotation angle. Through error analysis between analytical torques and experimental torques, it is concluded that the modified generalized viscous–nonlinear elastic model has the smallest error compared with Kwok and Maxwell models, which indicates that the proposed modified model can accurately describe the mechanical characteristics of the CRFD under different working conditions.

8

Analysis of seismic damage features of HSR CRTS III SBT simply supported bridge system

Liu Lili, Jiang Lizhong, Zhou Wangbao, Liu Xiang, Feng Yulin

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 2

art. no. e76, 2023

EN

In order to investigate the seismic damage features of high-speed railway (HSR) China Railway Track Slab III (CRTSIII) slab ballastless track (SBT) simply supported bridge systems, a nonlinear finite element model of HSR CRTS III SBT simply supported bridge system was established. The damage mechanisms and peak and residual displacement distribution patterns of their critical components under seismic action were investigated. In addition, the sensitivity of rail irregularity to the seismic residual deformation in such critical components was analyzed. The results indicated that midspan piers and bearings are more susceptible to failure than side span piers and bearings, and fixed bearings are more prone to failure than sliding bearings. Fastener and isolation layer deformation increases sharply on both sides of the beam joint. Rail deformation exhibits a parabolic shape that is large in the middle and small at both ends. The critical components of even-span and odd-span systems have significantly different patterns of seismic deformation distribution. Rail irregularity is mainly attributable to bearing residual deformation, pier residual deformation, and fastener residual deformation successively, and the superposition of bearing residual deformation and pier residual deformation is approximately equivalent to rail deformation. Rail irregularity is most sensitive to pier deformation, followed successively by bearing and fastener deformation.

9

A comparative study of the sensitivity analysis for systems with viscoelastic elements

Łasecka-Plura Magdalena

Archive of Mechanical Engineering

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2023

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LXX, nr 1

5--25

EN

This paper discusses the different methods used for calculating first- and second-order sensitivity: the direct differentiation method, the adjoint variables method, and the hybrid method. The solutions obtained allow determining the sensitivity of dynamic characteristics such as eigenvalues and eigenvectors, natural frequencies, and nondimensional damping ratios. The methods were applied for analyzing systems with viscoelastic damping elements, whose behavior can be described by classical and fractional rheological models. However, the derived formulas are general and can also be applied to systems with damping elements described by other models. Their advantage is a compact and easy to code form. The paper also presents a comparison of the computational costs of the discussed methods. The correctness of all the proposed methods has been illustrated with numerical examples.

10

Application of goal programming in the textile apparel industry to resolve production planning problems : a meta-goal programming technique using weights

Malik Zahid Amin, Kumar Rakesh, Pathak Govind, Roy Haridas

Operations Research and Decisions

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2022

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Vol. 32, No. 2

74--88

EN

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.

11

Complex Fibonacci (c, p) : numbers

Prasad Bandhu

Mathematica Applicanda

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2022

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Vol. 50, no. 2

235-247

EN

In this paper a new complex Fibonacci Q_{p,c} matrix for complex Fibonacci (c,p)-numbers, where p is a positive integer and c is a non-zero complex number, is introduced. Thereby, we discuss various properties of Q_{p,c} matrix, coding and decoding method followed from the Q_{p,c} matrix.

PL

W artykule przedstawiono nową macierz zespoloną Fibonacciego oznaczaną Qp,c dla liczb zespolonych Fibonacciego (c, p), gdzie p jest liczbą całkowitą dodatnią, a c jest niezerową liczbą zespoloną. Omówiono różne własności macierzy Qp,c, oraz sposób kodowania i dekodowania wynikający z macierzy Qp,c.

12

A coding theoretical interpretation of Gaussian-Pell polynomials

Prasad Bandhu

Mathematica Applicanda

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2022

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Vol. 50, no. 1

129--138

EN

In this paper, we establish a new result followed from Gaussian Pell polynomials matrix, Qn(x)P(x) (cf. Serpil and Sinan (2018)) whose elements are Gaussian Pell polynomials and we develop new coding and decoding method follow from Gaussian Pell polynomials matrix, Qn(x)P(x). The correction ability of this method is 93:33%.

PL

W artykule z wykorzystaniem macierzy wielomianów Gaussa Pella, Qn(x)P(x) (v. Serpil and Sinan (2018)), opracowano nową metodę kodowania. Ta metoda wynika z własności tej macierzy. Uzyskany kod daje możliwość korekcji na poziomie 93:33% .

13

Mathematical modeling and analysis of mycobacterium tuberculosis transmission in humans with hospitalization and reinfection

Mustapha Umar T., Idris Buhari, Musa Salihu S., Yusuf Abdullahi

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 1

55--66

EN

Tuberculosis (TB), a serious public health infection that mainly affects the lungs, is caused by bacteria (Mycobacterium tuberculosis, TB). This research is designed and analyzed using a compartmental modelling approach to study the transmission dynamics of TB with different stages of infection. Qualitative analysis of the proposed model reveals that the model exhibits two equilibrium points: the disease-free equilibrium point (DFE) and the endemic equilibrium (EE). The basic reproduction number (R0 ) is determined using the next generation matrix technique, and stability analysis is carried out to show whether the disease can persist or die out in population. Further analysis of the model shows that the EE is globally asymptotically stable (GAS) when R0 > 1. With the aid of the forward sensitivity index method, we determine the most sensitive parameters of the model to control the spread of TB infection effectively. Our analysis shows that treatment (medication) and campaign awareness coupled with other key control measures, could help maintain the spread of MTB infection in human geographical boundaries.

14

Using Bayesian methods in the task of modeling the patients' pharmacoresistance development

Voronenko Mariia A., Zhunissova Ulzhalgas M., Smailova Saule S., Lytvynenko Luidmila N., Savina Nataliia B., Mulesa Pavlo P., Lytvynenko Volodymyr

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2022

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T. 12, nr 2

77--82

EN

In this paper, we propose a methodology for using static Bayesian networks (BN) in modeling the development of pharmacoresistance in patients with a diagnosis of epilepsy. Methods for constructing the structure of a static BN, their parametric training, validation, sensitivity analysis and “What-if” scenario analysis are considered. The model was designed in collaboration with expert doctors, as well as expert pharmacologists in the selection and quantification of input and output variables.

PL

W niniejszej pracy zaproponowano metodologię wykorzystania statycznych sieci bayesowskich (BN) w modelowaniu rozwoju farmakooporności u pacjentów z rozpoznaniem padaczki. Rozważane są metody konstruowania struktury statycznej BN, jej parametrycznego treningu, walidacji, analizy wrażliwości i analizy scenariuszy "co-jeśli". Model został zaprojektowany we współpracy z ekspertami – lekarzami, a także ekspertami – farmakologami w zakresie doboru i kwantyfikacji zmiennych wejściowych i wyjściowych.

15

Sensitivity Analysis of the Nasgro Equation Based on the PZL-130 TC-II Orlik Trainer Aircraft Full Scale Fatigue Test

Reymer Piotr, Leski Andrzej, Kurdelski Marcin

Fatigue of Aircraft Structures

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2022

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Iss. 14

8--17

EN

The study investigates the sensitivity of numerical crack propagation estimations based on the Nasgro equation. The equation is widely used for crack propagation calculations since it considers the whole range of crack propagation speed from threshold to critical values of stress intensity factor range (∆K). The presented investigation is based on the actual results of the full scale fatigue test (FSFT) of the PZL-130 ‘Orlik’ TC-II aircraft. We provide a brief description of the test and the general approach followed in crack propagation estimations originally carried out after the test. The obtained results are verified in terms of variation of the input data. Overall results are compared and discussed.

16

Insight into Damping Sources in Turbines

Moneta Grzegorz

Fatigue of Aircraft Structures

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2022

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Iss. 14

69--82

EN

Blade vibrations in aircraft engines are a significant challenge that must be overcome during the design and development of modern turbine engines. Vibrations lead to cyclic displacements and result in alternating stress and strain in undesired environments (high temperatures, erosion, corrosion of the surface, etc.). Under resonance conditions, stress amplitudes can increase and exceed their safety limits, and in extreme cases, can lead to engine failure. One method to reduce resonance vibrations is to increase damping in the turbine assembly. This paper presents and describes vibration damping sources in the turbine, including aerodynamic, material, and friction damping. Additionally, typical damping values for each damping component are presented and compared.

17

Sensitivity analysis for a hybrid off-grid PV/DG/BATT system for the electrification of rural communities

Pedro Pazmiño-Zapatier, Juan Lata-García

Diagnostyka

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2022

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Vol. 23, No. 1

art. no. 2022103

EN

One of the pillars for the development of isolated communities is electricity, however the implementation of conventional networks is limited as a result of the difficulties of the terrain. This paper aims to analyze the technical-economic feasibility of implementing a hybrid off-grid solar photovoltaics (PV)/diesel generator (DG)/battery (BATT) based power system for the electrification of rural communities, using a case study in Bameno, Ecuador. The simulation and optimization of the system is done using Hybrid Optimization of Multiple Energy Resources (HOMER) software. As a result, the optimal sizing is composed of 23 kW PV modules, a DG 27 kW, 88.4 kWh storage batteries and 9.4 kW converter system, obtaining a levelized cost of energy (LCOE) of 0.359 $/kWh. After the optimization is executed, a sensitivity analysis is performed to establish the effects of the variations of solar radiation, demand, fuel, and component costs on the system. The PV/DG/BATT system is considered the best choice for fuel prices up to $0.83 per liter. For higher values the optimal system is the PV/BATT. It is also established that the LCOE is mostly affected by the cost of technological components, followed by variations in solar radiation and demand.

18

GIS as a Support Tool for Sensitivity and Decision-Making Analysis for Transport Infrastructure Development

Păunescu Cosmin, Dobre Robert, Comănescu Laura, Drăghici Traian, Nedelea Alexandru

Rocznik Ochrona Środowiska

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2021

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Tom 23

23--41

EN

The sustainable implementation of highway projects requires a sensitivity analysis of the terrain and all of its components that have a direct influence on road design, construction and operation. The result of this inquiry involving GIS techniques and methods regarding environmental and economic factors helps in choosing the optimal road route, in order to meet the real-world connectivity requirements. The sensitivity analysis can be applied to road and rail infrastructure projects, aiming to develop a decision-making tool that can be employed by their potential beneficiaries, according to their purposes and interests. This paper aims to create an objective decision-making tool for transport infrastructure development in correlation with the current needs of society regarding the development of transport infrastructure in an economic sustainable manner with low environmental impact. Furthermore, the study tries to identify the best highway corridor in an area with environmental constraints (especially geomorphological), that is in balance with both environment and financial resources.

19

Feasibility Analysis Regarding the Manner of Development of the Former Edmund Szyc Stadium Area in Poznań

Walczak Zbigniew, Topolińska Magdalena, Walczak Natalia, Laks Ireneusz, Szymczak-Graczyk Anna

Rocznik Ochrona Środowiska

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2021

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Tom 23

11--22

EN

The paper presents a feasibility analysis of changes in the manner of development a former sports facility, Edmund Szyc Stadium in Poznań. The terrain and adjacent areas were inventoried, including the assessment of inter-area relationships. Based on the inventory and authors' surveys, three developmental variants were selected for further analysis. Particular attention was paid to the purpose of the area in the local zoning plan (local spatial development plan) and the preferences of its local community. A multi-criteria analysis carried out with three different methods – AHP, MAUT and PROMETHEE II indicated the second variant as optimal. Additionally, the authors performed a sensitivity analysis of the AHP method to determine the weight of adopted criteria. This allowed for observing what impact these changes had on the final result. The sensitivity analysis was performed only for 3 main groups of criteria. The implementation of activities planned in the concept will allow for optimal land development, improvement in functionality as well as improvement in visual and landscape characteristics of the city.

20

Sensitivity analysis of grey linear programming for optimization problems

Darvishi Davood, Pourofoghi Farid, Forrest Jeffrey Yi-Lin

Operations Research and Decisions

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2021

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Vol. 31, No. 4

35--52

EN

Sensitivity analysis of parameters is usually more important than the optimal solution when it comes to linear programming. Nevertheless, in the analysis of traditional sensitivities for a coefficient, a range of changes is found to maintain the optimal solution. These changes can be functional constraints in the coefficients, such as good values or technical coefficients, of the objective function. When real-world problems are highly inaccurate due to limited data and limited information, the method of grey systems is used to perform the needed optimisation. Several algorithms for solving grey linear programming have been developed to entertain involved inaccuracies in the model parameters; these methods are complex and require much computational time. In this paper, the sensitivity of a series of grey linear programming problems is analysed by using the definitions and operators of grey numbers. Also, uncertainties in parameters are preserved in the solutions obtained from the sensitivity analysis. To evaluate the efficiency and importance of the developed method, an applied numerical example is solved.