Multi-criteria Mathematical Model Research Articles

Multi-criteria model for selection of optical linear terminals based on FUZZY TOPSIS method

Optical networks are an integral part of modern telecommunication systems. Huge traffic and ever-increasing requirements for data transmission capacity and quality encourage the wider use of modern optical technologies in telecommunications. The rational choice of equipment for the design of optical networks is an urgent task at present. The subject of this study is the process of selecting optical line terminals, which is associated with the evaluation of possible options by a set of indicators. The OLT (optical line terminal) in PON technology implements the function of organizing subscriber lines and is also a node equipment - an L4 switch that combines the functions of routing (IP), traffic fragmentation (VLAN), switching (MAC), quality of service (QoS), and some necessary network service functions. The optimal structuring of PON access networks demands a judicious selection of software and hardware, guided by their tactical and technical characteristics, in view of the substantial information load they entail. One of the effective approaches to solving such problems is the use of MCDM (Multiple Criteria Decision Making) methods. Purpose: to construct a TOPSIS model of the optimal choice of optical linear terminals in the conditions of unclear information for different cases of aggregation of evaluations of decision makers. Task: to formalize the process of selecting optical linear terminals; develop a multi-criteria mathematical model for the effective selection of optical line terminals. Methods used in the study: The fuzzy TOPSIS method, four methods of aggregating the opinions of decision makers. The following results were obtained. Alternatives and criteria for their evaluation are defined. On the basis of interviews with decision makers, evaluations of the degree of importance of the criteria and alternatives to the criteria were determined. Linguistic changes were used to describe decision-makers’ evaluations, which were interpreted as triangular fuzzy numbers. During this study, four methods of aggregating the evaluations of decision makers were used. A fuzzy TOPSIS model for selecting an optical line terminal is constructed. The ranking of the selected optical line terminals is obtained and the best alternative is determined. The results of modeling with different methods of aggregating assessments of decision makers are compared. Conclusions. The use of the Fuzzy TOPSIS method for optimal selection of optical linear terminals is proposed. The influence of the methods of aggregation of evaluations of decision-makers is analyzed.

Correspondence distribution over a network in designing public urban passenger transportation tasks

Introduction. The process of planning public transport is divided into a few number of tasks in strategic, tactical and operational levels, which include the development route system, the establishment of traffic intensity along routes, the design of the structure of road transport vehicles, the distribution of the current road transport vehicles along the routes, determining the required amount of the subsidies, etc. Materials and methods. The article presents a multi-criteria mathematical model of transportation design, according to which the tasks have been solved by distributing (limited or unlimited) transport resources between the permissible routes of the transport network in accordance with a variety of efficiency criteria, which can be the subject to appropriate restrictions. The formation acceptable routes on the transport network can be carried out by means of the algorithms developed, for example, in the framework of solving TNDP and TNDFSP tasks. The routes can also be adjusted by experts. Transport demand is set by a matrix of passenger correspondence generated for the entire period of traffic on a weekday, to ensure that all passenger flows along the route network are taken into account, and not only the periods of the greatest traffic intensity. The calculation of the parameters of the transport offer in the process of solving the problems of transportation design is carried out based on the results of the passenger correspondence distribution on the route network (PAP), which is a complex problem unsolved today. The article describes the developed PAP methodology based on a flexible passenger strategy that takes into account the waiting time for transport, the proximity of the route through an empirical model of dividing demand by the length of trips, the preferences of transport modes, the possible redistribution of passenger flows between the stopping points of the network located within a walking distance. Results. The tasks of designing public transport transportation have been formulated, a multi-criteria mathematical model of their solution has been developed. The method of distribution of passenger flows on the route network based on a flexible passenger strategy has been described. The effectiveness of the developed PAP methodology is shown on test calculations, which were carried out using passenger correspondence, an average weekday in October 2019, obtained by processing validations of e-tickets of urban passenger transport in Krasnoyarsk. Discussion and conclusion. The practical implementation of the described methodology for the distribution of passenger flows on the route network using relational database management systems (DBMS) MS SQL Server has been carried out.

MULTI-OBJECTIVE OPTIMIZATION MODEL FOR A MULTI-DEPOT MIXED FLEET ELECTRIC VEHICLE SCHEDULING PROBLEM WITH REAL-WORLD CONSTRAINTS

This paper presents the problem of public transport planning in terms of the optimal use of the available fleet of vehicles and reductions in operational costs and environmental impact. The research takes into account the large fleet of vehicles of various types that are typically found in large cities, including the increasingly widely used electric buses, many depots, and numerous limitations of urban public transport. The mathematical multi-criteria mathematical model formulated in this work considers many important criteria, including technical, economic, and environmental criteria. The preliminary results of the Mixed Integer Linear Programming solver for the proposed model on both theoretical data and real data from urban public transport show the possibility of the practical application of this solver to the transport problems of medium-sized cities with up to two depots, a heterogeneous fleet of vehicles, and up to about 1500 daily timetable trips. Further research directions have been formulated with regard to larger transport systems and new dedicated heuristic algorithms.

DIGITALIZATION MODEL DEVELOPMENT OF IT COMPANY'S HARDWARE PROCUREMENT PROCESS

The article sets the scientific task of creating a model of digitization of the business process of hardware procurement management for IT companies. The relevance and practical value of such a model is emphasized. Scientific studies on the optimization and digitization of the business process of procurement management in various industries have been reviewed and analyzed. The analysis of the following models and methods that can be used in the construction of an integral model was carried out: a multi-criteria mathematical model of supplier selection, an adaptive convolution method, a controlling method, an optimization model of cost determination, a threshold delivery point model. Based on the analysis, a model of digitalization of the business process of hardware procurement management for IT companies was developed. The following model structure is proposed: the company's internal database; software module for analyzing the current state of material resources (hardware); external sources of hardware; program-algorithm for finding offers of necessary hardware; configuration data to determine hardware compliance with IT company requirements; a module for processing existing proposals based on an artificial neural network; graphic interface of interaction with the system; integration layers. The product that implements the created model has been identified – it is a decision support system for IT company purchases based on an artificial neural network. A functional description of each of the modules of the future system has been made. Recommendations on the application of the analyzed models of algorithms and methods in the implementation of the software product have been developed. A conclusion was made regarding the proposed model, its integrity, flexibility, and scalability were emphasized. The direction of further research is formulated - the detailing of each layer of the digitalization model of the business process of hardware procurement for an IT company.

Teorijsko-metodološka analiza izazova, rizika i pretnji u savremenoj teoriji nacionalne bezbednosti

Basically, every type of government organization defines the defence system with functions that provide deterrence from threats, as well as countering various types and forms of threats to main social values. The subject of this paper is the national security strategy, i.e. security challenges, risks and threats that are essential for the fulfilment of the highest state security interests. The author has analysed the main categories of national security theory: "danger", "challenge", "risk" and "threat". On the basis of the definition and comparative analysis of these categories, presented in different sources, he reveals their content and essence and comes to the conclusion that, despite the semantic similarity of the categories "challenge", "risk and "threat", each of them defines a different degree of threat, that is, damage. Accordingly, it has been noticed that the National Security Strategy of the Republic of Serbia does not make a distinction between security challenges, risks and threats, but speaks of them as a single syntagm and category. Since this document is the basis for the integrated activities of the defence forces, in the function of protecting vital national interests, the considered issue indicates the importance of as precise definition of SCRT as possible because inaccurate definition could prevent an adequate response when some of security challenges, risks and threats manifest themselves on security object references. On the basis of the definition and comparative analysis of the definitions of these categories, mentioned in different sources, it can be concluded that, despite the semantic similarity of the categories "challenge", "risk and "threat", each of them defines a different degree of threat, that is, harmful consequences. The subject of this paper has been to make a distinction between SCRT in order to improve the methodology for identifying and assessing military and non-military challenges, risks and threats when developing the National Security Strategy and other strategic and doctrinal documents. Accordingly, in reality, dynamics from several security sectors (political, military, economic, social, ecological and informational) is intertwined in most security problems. The analytical framework of the sectoral approach of the Copenhagen School has been proposed for the analysis of manifest forms of threats to national security. The implementation of the analytical framework is possible within the multicriteria mathematical model. Since risk is a measurable value, the implementation of this concept increases the objectivity of the identification and assessment of SCRT for state security. This approach is important not only in terms of defining national security policy and defence policy, but also has the greatest impact on the development plans of the defence system as a whole, particularly the development of the capabilities of the Serbian Armed Forces.

A fuzzy synthetic evaluation of vulnerabilities affecting supply chain resilience of industrialized construction in Hong Kong

PurposeDemands for Industrialized Construction (IC) have intensified with growing construction industry imperatives to (A) boost performance; (B) reduce reliance on “in-situ and on-site” operations; and (C) strengthen supply chain resilience (SCR) not just for survival but also to fulfill obligations to clients in the coronavirus disease 2019–induced (COVID-19–induced) “new normal”. In addressing these imperatives, this paper targets more effective leveraging of latent efficiencies of off-site-manufacture, based on findings from a Hong Kong (HK)–based study on assessing and improving SCR in IC in a high-density city.Design/methodology/approachStarting with the identification of critical supply chain vulnerabilities (CSCVs), this study developed a multilevel–multicriteria mathematical model to evaluate the vulnerability levels of IC supply chains (SCs) in HK based on an in-depth questionnaire survey followed by experts' inputs and analyzing them using fuzzy synthetic evaluation (FSE).FindingsThe overall vulnerability index indicates that IC in HK is substantially vulnerable to disruptions, while production-based vulnerabilities have the highest impact. Top management attention is needed to address these CSCVs in IC in HK.Originality/valueTo the authors' knowledge, this is the first structured evaluation model that measures the vulnerability level of IC, providing useful insights to industry stakeholders for well-informed decision-making in achieving resilient, sustainable and performance-enhanced SCs.

Biomass Selection Method to Produce Biogas with a Multicriteria Approach

The first step in the biogas production process consists of analyzing how biomass alternatives are available in the locality and in the surroundings of the region where the biodigester is installed to make a selection that serves as an input for the system or food. Each biomass has different sources of nutrients, energy potential, chemical composition, processing, and ways of management that require decision making, which will be the option selected. This is often a problem for handlers, to safely decide which will be the best option for their reality. As a way to contribute to the solution of this problem, this study aimed to propose a mathematical method able to list the main criteria for selecting biomass, establishing a ranking ranging from the most preferable to the least preferable one. For the application of the multicriteria mathematical model (AHP–TOPSIS), the biomass of cattle (bovine), pigs (swine), sheep (ovine), chicken and horses (equine) were used as alternatives, taking into account the following criteria: (1) logistics cost, (2) potential for waste production from each herd, (3) the volume of biogas, and (4) energy capacity of each biomass. It was found a ranking for the alternatives and the consistency of the method was tested through sensitivity analysis.

An approach to the optimal timber transport scheduling

An approach to the optimal timber transport scheduling is described in the paper. A description of this problem is given, a multi-criteria mathematical model is created. It is noted that the problem belongs to the class of General vehicle routing problems (GVRP) associated with the job-shop scheduling. A hybrid algorithm for solving this problem based on the decomposition method using the simplex method and the genetic algorithm is developed. Testing of the proposed approach using real data from wood harvesting enterprises showed its effectiveness. The algorithm was implemented in “Opti-Wood” decision support system for wood harvesting planning and management, developed by Opti-Soft company (Russia).

Multi-criteria mathematical model of the pilot training process

In most NATO countries, helicopter pilots are prepared in accordance with a modern system of threestage training: selection, basic and advanced. The training in the air is performed according to the parallelism of the training. The scheduling of pilot training process based on parallel model, which includes the technological relationships between the individual exercises, whereby for each air exercise, the exercises are specified, which must be done beforehand. The purpose of this contribution is to propose a multi-criteria mathematical model which would enable the selection of exercises for each pilot, the appropriate selection of the aircraft and the moment of beginning of each exercise, so that all required exercises will be carried out in the shortest possible time and the number of trained, in a state of readiness pilots, should be as high as possible. Additionally, in this paper the sketch of a multi-criteria solution is presented. A crucial feature of this work is the model application to optimize pilot training.

Proposition of a methodological framework for measuring innovation capacity of Tunisian companies

This paper proposes and experiments a framework for the evaluation of innovation capacity, in the context of Tunisian companies. A literature review of methodological frameworks for measuring innovation at the company level was carried out. Seven dimensions of innovation were identified, and additional three dimensions, considered potentially important in the context of Tunisian companies have been introduced (information and communication technologies (ICT), access to incentives and eco-innovation). A methodological innovation framework composed of 10 dimensions based on activities and leveraging best practices of innovation was proposed. Then, multi-criteria mathematical model was proposed in order in determine a composite index of innovation. Finally, a field study was carried out on Tunisian companies in order to experiment this model. Data were gathered from experts and companies thanks to interviews and online questionnaires. One key learning from this experiment is that the proposed method is useful for Tunisian companies and governmental stakeholders as a tool for strategic orientation and positioning regarding to the National Innovation System (NIS).

Combinatorial optimization in foundry practice

The multicriteria mathematical model of foundry production capacity planning is suggested in the paper. The model is produced in terms of pseudo-Boolean optimization theory. Different search optimization methods were used to solve the obtained problem.

Joint venture formation and partner selection in upstream crude oil section: goal programming application

In the past three decades, the magnitude of business dynamics has increased rapidly due to increased complexity, uncertainty and risk of international projects. This fact made it increasingly tough to ‘go alone’ into the international projects. As a consequence, companies with diverse strengths and weaknesses cooperatively bid for joint ventures (JV) formation. Joint venture is also a well-established aspect of the crude oil industry, specifically in the upstream segment. Making decision on the optimal form of JVs is still a challenging problem. In addition, the success of a JV is intertwined with the accuracy of the partner selection phase. Therefore, this paper formulates a multi-criteria mathematical model to select the best partners and form an optimal JV for undertaking oilfield projects. The lexicographic goal programming technique is employed to minimise undesirable deviations from diverse goals such as resources needs (technological and expertise), budgetary requirements, time, etc. The model is validated with a real-life-based example and provides insightful views on alternative formats of cooperation.

Logistics Process Improvement Using Simulation and Stochastic Multiple Criteria Decision Aiding

The paper is concentrated on improvement of a delivery process of parts and components for a vehicle production company based on just-in-time system. The authors have proposed a four-stage solution procedure. In the first stage the logistics process has been analysed and modelled using EPC notation in ARIS Business Architect. The major activities in the process, cause and effect relationships, key resources (personal and technical) and their assignment to the activities have been identified. In the second stage, multicriteria mathematical model has been constructed to evaluate the process performance. In the third stage, the simulation model has been built with an application of simulation tool ARIS Business Simulator, and the computational experiments have been carried out. Next, in the fourth stage the set of variants representing changes in the current logistics process have been created, equivalent changes have been introduced to the simulation model and computational experiments have been carried out. Based on the nondeterministic simulation results, in the next stage the variants have been ranked with an application of stochastic decision aiding method – stochastic ELECTRE III. Finally, the compromise variant of the logistics process improvement has been recommended.

THE MODEL OF EVALUATING THE CRITERIA, DESCRIBING THE QUALITY OF ORGANIZATION AND TECHNOLOGY OF TRAVEL BY INTERNATIONAL TRAIN

The significance of the criteria describing various aspects of travel by train, e.g. passenger transportation comfort, safety, travel time, price of a journey, etc., differs considerably. The quality of particular trains, track sections and staff performance can be successfully evaluated by a single number, using the comprehensive quality index (CQI). The paper offers an additive model to calculate the normalized weight coefficients of particular criteria for CQI calculation. A multi-criteria mathematical model, which may be used for evaluating the significance of the criteria describing organization and technology of travel by train for determining its quality, is also presented. Based on the nineteen adopted criteria (the criteria of group B), reflecting the organization and technology of travel by train, the quantitative estimate KB is obtained. Case studies of calculating the comprehensive quality index KB , describing the organization and technology of travel by the train ‘Vilnius–Moscow’, which show the real quality of these processes, are presented. Finally, the conclusions based on the research results are provided.

Designing New Electoral Districts for the City of Edmonton

Every few years, the city of Edmonton, Canada must review and evaluate changes to its electoral district boundaries. The review process that was completed in 2009 resulted in modifying the district plan from a six-ward system with two council members in each to a single-member 12-ward system. The authors of this paper designed the redistricting plan. This paper describes the algorithm we applied to solve the problem and the decision support system we used. The algorithm is based on a multicriteria mathematical model, which is solved by a tabu search heuristic embedded within a geographic information system (GIS)-based decision support system. The resulting district plan meets districting criteria, including population balance, contiguity, compactness, respect for natural boundaries, growth areas, and integrity of communities of interest. This plan was formally approved as a city bylaw and used in the municipal elections in 2010.

Multi-criteria mathematical model for designing the distribution network of a consumer goods company

This paper describes a multiple criteria mixed-integer linear program used for designing the best possible supply chain distribution network for a consumer goods company. The model determines the optimal configuration of the manufacturing plants, distributors and customers in the distribution network. The model is intended for making tactical decisions for designing distribution networks, or more specifically, for designing the flow of products from the manufacturing plants to the customers. The customers have four options for receiving products in this model. Products can be supplied from (1) the regional distribution center (DC), (2) the manufacturing plant, (3) an independent distributor who is supplied from the regional DC, or (4) an independent distributor who is supplied directly from a manufacturing plant. The model selects the best option for each customer/distributor based on several criteria: profit, lead time, power, credit performance, and distributors’ reputation. The model is validated with real data from a consumer goods company to show its functionality. To account for variability in demand, the model is run under multiple scenarios and the results are analyzed to obtain the best solution. The company uses two DC’s located in the same region, but the model assumes only one regional DC with infinite capacity. With the proposed network, we show that one of the regional DC’s could be eliminated and distribution costs would be reduced from 12% to 3% of the Net Sales (approximately a monthly reduction of $574,000 in distribution expenses).

The mechanism and technology parameters optimization of alkali‐H2O2 one‐bath cooking and bleaching of hemp

AbstractHemp is cooked and bleached in alkali‐H2O2 one‐bath. The analysis of physical and chemical properties related to acid, alkali, and hydrogen peroxide about various types of components in hemp such as hemicelluloses and pectin, and lignin components makes it ascertained. In this one‐bath process, alkali and H2O2 have cooperative effects to remove most proportions of the noncellulosic components efficiently. The additive MgSO4 and a stabilizer of H2O2 as auxiliary agents are introduced to protect cellulose from degradation and, meanwhile, they improve the efficiency of H2O2. The universal rotatable composite experiment design is employed to get the highly precise equation, in which the variables of NaOH and H2O2 concentrations, and the processing time are considered to be the main technological parameters of this alkali‐H2O2 one‐bath process. The residual gum content and residual lignin content of hemp fiber are the evaluation indexes. Based on regression equations, the figures are plotted to analyze the influences of parameters on the evaluation indexes; the optimization multicriteria mathematical model is simultaneously established to obtain the optimum parameters. Finally, an experiment is carried out to further test the acceptance of the calculated optimum values. It is shown that, for the hemp taken from Anhui Province of China, this alkali‐H2O2 one‐bath process can substantially remove gum and lignin from raw hemp. NaOH 10.5 g/L, H2O2 9.8 g/L, and the processing time of 127 min with 0.1% MgSO4 + 2.7 g/L stabilizer of H2O2 at 100°C are recommended to be the optimum parameters; then, a compromise is achieved among the lowest lignin content, the residual gum content, and the best strength and whiteness of hemp fiber. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 2279–2285, 2005

Fuzzy multi-criteria approach to ordering policy ranking in a supply chain

In this paper, a new fuzzy multi-criteria mathematical model for the selection of the best among a finite number of ordering policy of raw material in a supply chain is developed. The problem treated is a part of the purchasing plan of a company in an uncertain environment and it is very common in business practice. Optimization criteria selected describe the performance measures of ordering policies and generally their relative importance is different. It is assumed that the values of the optimization criteria are vague and imprecise. They are described by discrete fuzzy numbers and by linguistic expressions. The linguistic expressions are modeled by discrete fuzzy sets. The measures of belief that one ordering policy is better than another are defined by comparing fuzzy numbers. An illustrative example is given.

CRITERIA AND METHODOLOGY OF COMPLEX EVALUATION OF BITUMINOUS CONCRETE MIXER QUALITY/ASFALTBETONIO MAIŠYTUVO KOKYBĖS KOMPLEKSINIO VERTINIMO KRITERIJAI IR METODIKA

The structure and sequence of technological operations of mixers for bituminous concrete mixtures, functioning in Lithuanian bituminous concrete mixing plants have been analyzed. The problems, which are subject to interest by the owners of bituminous concrete mixers, have been systematized. The necessity and objectives of quality evaluation of the functioning bituminous concrete mixers have been proved. A new multi-criteria mathematical model for determining quality of bituminous concrete—consisting of the sum of 4 group indicators, which evaluate quality of bituminous concrete mixture production in the mixer, environmental care, economy and technological universality—has been provided. The following 9 criteria make up the mathematical model, which can be used for calculation of quality indicator K of the working bituminous concrete mixer: accuracy of the bituminous concrete mixture content, produced in the mixer, ie the conformity of its component quantity with the project requirements (s); its temperature conformity with the temperature determined (t); its homogeneity in the batch, described by the mixing quality of batched components (h); environmental care, when the air is polluted by pollutants, thrown out from bituminous concrete (aa); bituminous concrete mixture production expenses as for one ton of (gi); level of physical and moral wear of the mixer (nl); expenses, needed for its maintenance and reconstruction (rr); use of its capacity when producing bituminous concrete mixture (pn); as well as technological universality of bituminous concrete mixer, ie ability to produce mixtures of different types and marks (tu). Coefficients of significance (importance) of all criteria are determined, using expert research methods. For this purpose a questionnaire for respondents (experts) has been prepared, which was filled by 43 scientists and production specialists, who have good knowledge of technology of bituminous concrete mixture production. The high value of concordation coefficient (W = 0,719) has shown good coordination of expert opinions, because X 2 = 247,5 is much higher than critical X 2 kr value with ε = 8 freedom level and 1% of accepted significance level, which makes up only 20,09. The experts believe that the most important criteria, reflecting the quality of bituminous concrete mixture are S([Xbar] j = 8,60), H([Xbar] j = 7,58), t(Xj = 7,3o), following in the range is the criterion AA (Xmac;j = 4,95), TU([Xbar]j = 4,56), GI([Xbar]j= 3,91), NL([Xbar]j = 3,47), and at the end least important RR([Xbar]j = 2,44) and PN([Xbar]j = 2,19). total sum of criteria is 45. The bituminous concrete mixer quality change when using it has been provided. The relation of its quality coefficient K reduction rhythm and level of conformity with the requirements imposed and constantly getting stricter has been analyzed.

A Multicriteria Problem of Distribution of System Blood Flow among Organs and Tissues and an Algorithm for its Solution

A multicriteria mathematical model is proposed for finding the volumetric rate of blood flow in human tissues with a known volumetric system circulation rate. An algorithm is developed for decision-making as to distribution of the system blood flow among different tissues with regard for data on the oxygen consumption and carbon dioxide discharge in different tissues.