BY 4.0 license Open Access Published by De Gruyter Open Access December 17, 2020

Streamlining possibility of transport-supply logistics when using chosen Operations Research techniques

Ondrej Stopka, Vladimír Ľupták, Mária Stopková, Martin Jurkovič and Karel Jeřábek
From the journal Open Engineering


The subject of this article is to model and streamline processes in the area of the transport-supply logistics in a specific enterprise. The topic of the manuscript was implemented in a particular enterprise with the residence in the city of České Budějovice (South Bohemia region). The aim of the article is to step by step analyze the current state of the supply logistics of the specific subject and propose appropriate measures contributing to optimize the entire process using selected techniques of the Operations Research. By applying the methods of multi-criteria decision analysis (such as Weighted Sum Approach and Technique for Order Preference by Similarity to Ideal Solution), the most attractive option is chosen; i.e. the optimal supplier for the implementation of the transport-supply process that will enhance the effectiveness of specific logistics activities in the operation being examined. The conclusion in detail discusses individual contributions in terms of the suggested ways of modeling and improving the current state with respect to supply processes in the selected enterprise.

1 Introduction

The sphere of logistics has recently seen an incremental influence. Although generally presumed so, the term itself denotes not only transporting goods from location A to B but also covers a large scale of business processes [1]. Rather than that, it refers to the whole value-creating chain composed not only of corporeal flows, but also energy, human resources and detailed and valuable information. Supplying and stock storage represent the most complex areas of logistics. These activities allow a wide range of possibilities and solutions to optimize and develop methods within the process [2].

Supplying is considered as one of the most important activities of the enterprise. Companies have to get necessary materials to a required amount, quality, within the deadline and for the optimal price [3]. Keeping an adequate stock which would ensure a smooth running of the enterprise currently presents the most important aspect for enterprises. It is at the same time necessary to maintain optimal stock levels since stocks are closely related to the capital [4].

The scientific purpose of this research study will be to compare opted Operations Research methods to identify appropriate wholesaler for providing the entire spectrum of transport-supply processes for the enterprise under investigation. Our scientific manuscript brings value-added to understand an efficient setting of supply chains in the Czech Republic and points to the inevitability of choosing the proper criteria (factors). Hence, it can be stated that no analogous publication has been published yet when applying identical Operations Research methods, same set of criteria, nor addressing an equal subject. And that is right where the novelty of our research lies.

2 Literature review

The issue of supply logistics has been discussed in various publications. For instance, the article [5] focuses on designing an innovative approach regarding the multi-criteria decision analysis which objective is to estimate an independent criteria set deemed to be an option to represent the original criteria decision matrix in terms of TOPSIS method. The authors of the literature [6] fully disclose sources relating to TOPSIS Technique. These authors provide two scenarios to address a specific type of multi-attribute decision-making issues, while they rank outcomes on the basis of several approaches to depict the usefulness of ≥ -approximation spaces. The modified TOP-SIS approach implemented in the decision-making problems is also discussed in the publication [7], where the authors enhance current knowledge in the subject being investigated by implementing a supply partner selection framework for continuous-aid procurement. Namely, suggested fuzzy AHP method is applied to quantify criterion weights, and fuzzy TOPSIS is applied to sort considered supply partner variants.

The article (Agarski et al. [8]) compares the performance and safety attributes by means of multi-criteria decision analyses. Specifically, the authors’ research involves examination of multi-criteria techniques to determine working devices in order to streamline performance and occupational safety when utilizing numerous criteria weight quantification methods. To this end, a set of economic, technical and safety criteria were stipulated, as well as a series of weight scenarios were compared. Group decision-making related to choosing suppliers is discussed in the article [9], in which the compilation of a progressive approach of decision-making sustainable supplier determination, when applying modified TOPSIS method under interval-valued Pythagorean fuzzy environment, is discussed.

Alike to the previous, even the study [10] written by Hruška et al. deals with a possible scenario in relation to desirable supplier selection, however, in that case, using the Analytic Hierarchy Process. In the publication [11], a specific model for solving problems with the routing of supplier shipments by utilizing one of the most used heuristic methods which address tasks of vehicle routing, namely Clarke-Wright algorithm, is rigorously applied. The European Journal of Social Sciences published the study [12] also focusing on TOPSIS and WSA method applications in terms of the multi-criteria decision analysis of economic activity for the EU states and candidate countries assessed by these two techniques. In this view, the system managed through decision-making is analyzed in the research work [13], where the authors introduce expert-opinion criteria to the methodology of managing system obsolescence applying multi-criteria decision-making, specifically the TOPSIS method and Monte Carlo simulations are suggested as a background for the article. The particular case study conducted in their research work was elaborated with a participation of military and civilian experts.

The article [14] refers to several methods of multi-criteria decision analysis in specific examples. Above all, an implementation of the approaches AHP, WSA and TOP-SIS into the localization and allocation tasks in practice is outlined. The supplier quality assessment and requirements for a transport system user are discussed in the manuscripts [15, 16], in which the definition of fundamental approaches and guidelines in association with supplier quality assessment is highlighted [15]. The aim of the designed model is to fortify the efficiency of the supply chain management to better respond to newly generated situations regarding the collaboration among logistics companies.

In line with this context, what also constitutes an integral part is an acceptable imposition of requirements of transport system users – these aspects are discussed in the article [16]. The authors emphasize the matter of elementary features affecting the choice of transport mode by a transport infrastructure user. To this end, they propose to use the Saaty pairwise comparison method to calculate weights of significance of individual factors being defined. As far as logistics chains in intermodal transport are concerned, the literature [17] is focused on the ascertainment, analysis as well as classification of restrictive criteria occurred in intermodal transport in order to compare criteria degrees in a variety of scenarios of the logistics chain implementation.

3 Data and methods

The manuscript deals with process streamlining in the area of supply logistics in the selected enterprise. The project consists in choosing the optimal logistics partner. Here, we look for the optimal supplier cargo delivery of the specific company using TOPSIS and WSA methods. Both approaches choose the ideal variant by classifying assessed alternatives according to the proximity to the ideal variant, i.e. depending on decreasing values of the examined indicator [18].

The implementation of the WSA method comprises steps as follows [14, 19]:

  1. A)

    The first step consists in defining the optimal and basal variant. Ideal alternative H represents the maximal value of the specific indicator, whereas basal variant D presents the lowest rate for the particular criterion.

  2. B)

    The next step comprises establishing normalized criteria matrix R by the formula 1:

(1) r i j = g i j d j h j d j

Where: rij – normalized values for i alternative and j criterion, gij – matrix elements situated in ith line in jth column, dj – the lowest value in jth matrix column (values of the basal alternative), hj – the highest value in jth matrix column (values of the ideal alternative). Basal alternative denotes theoretically the worse alternative (artificially indicated) that could exist, it has the worse values determined from each criterion. Ideal alternative entails the opposite, as it has the best values in each criterion. If the ideal alternative indeed exists, it will be the top alternative in the ranking. By this calculation, the comparability of the values is ensured. Values rij are assigned from the interval (0,1). The way of the normalization has one disadvantage – big difference between maximum and minimum value of one criterion can affect final outcomes.

  1. C)

    Third step encompasses calculating the utility function for individual variants (alternatives); “utility” means the total evaluation of the given alternative u according to all the criteria mentioned above. We obtain the utility if we sum up normalized values rij multiplied by weights of the criteria vj. The very calculation of the utility function for individual alternatives uses the following formula 2:

(2) u = j = 1 n v j r i j

Where: vj – level of importance, rij – normalized matrix elements situated in ith line and jth column.

  1. D)

    The last step comprises resulting variants classified in descending order according to calculated values. The variant with the highest utility value provides a solution to the problem.

The TOPSIS method application is made as follows [12, 17]:

  1. A)

    Each cj is assigned a quantitative value, gij, with respect to each Ci representing the performance of cj with respect to Cj. Compilation of the normalized matrix according to the relevant formula 3 is presented as follows:

(3) r i j = g i j i = 1 m g 2 i j

Where: gij – matrix elements situated in ith line in jth column, g i j 2 - all values of the respective column.

  1. B)

    Calculating normalized weighted criteria matrix (see formula 4):

(4) w i j = r i j v j

Where: rij – normalized matrix elements situated in ith line in jth column, vj – level of importance.

  1. C)

    This step determines the optimal and basal variant with respect to matrix values W. The ideal variant is represented by letter H and the basal one by letter D. In other words, it specifies the ideal and negative-ideal solution. Let H = ( H 1 + , H 2 + , , H n + ) , where H i + denotes the optimal value of any αj with respect to Ci. Let D = ( D 1 , D 2 , , D n ) , where D i denotes the least optimal performance of any αj with respect to Ci . H+ is the positive-ideal solution, while D is the negative-ideal solution.

  2. D)

    Determining the distance from the basal variant (see formula 5):

(5) d i + = j = 1 r ( w i j H j ) 2

Where: d i + - distance from the ideal variant, wij – individual elements in i matrix line, Hj – the highest values in j matrix columns.

  1. E)

    Determining the distance from the basal variant (see formula 6):

(6) d i = j = 1 r ( w i j D j ) 2

Where: d i - distance from the basal variant, wij – individual elements in i matrix line, Dj – the lowest values in j matrix columns.

  1. F)

    This step determines the indicator of the relative distance from the basal variant Ci according to the following formula 7:

(7) c i = d i d i + + d i

Where: ci – indicator of the relative distance from the basal variant, d i - individual resulting distances from the basal variant, d i + - individual resulting distance from the ideal variant.

  1. G)

    The last step classifies the variants according to decreasing values.

First of all, it is necessary to determine a list of assessed options relating to suppliers [19]. This case involves following companies operating in the gastronomic industry in the territory of the enterprise being investigated:

  • Makro,

  • JIP,

  • Astur & Qanto,

  • Exver Food.

These are wholesalers offering a wide range of food and non-food products, but especially supply and wholesale activities in the field of complex gastronomy. These companies offer transport of goods directly to restaurants and other facilities. They have built their own network of retail discount stores throughout the Czech Republic, and have launched the concept (logistics technology) of Cash & Carry stores. Hence, it can be stated that they provide their customers high-quality logistics and additional services associated with the process of modern supply and sale.

Thereafter, the crucial aspect is to identify attributes according to which the variants will be assessed [20]. For this study, the following factors were defined (if applicable, separate units are included) [21]:

  • C1 – Carriage charges (€/1 carriage),

  • C2 – Goods quality (-),

  • C3 – Delivery times (-),

  • C4 – Communication (-).

Table 1 summarizes all the input data – individual variants with specific criteria/factors and their respective values for the follow-up calculation (provided with the factor nature and levels of importance quantified according to expert’s opinions from the particular field of research). Maximizing criteria are assessed by scale 1-5 where 1 represents the worst possible result, whereas 5 refers to the best possible assessment.

Table 1

Input data on the multi-criteria decision analysis

Variant Carriage charges

(€/1 import)
Goods quality

(scale 1-5)
Delivery times

(scale 1-5)

(scale 1-5)
Makro 150 4 5 5
JIP 250 2 3 4
Astur & Qanto 200 3 4 5
Exver Food 350 4 4 3
Levels of importance 0.11 0.54 0.28 0.07

  1. Source: authors

Description of regarded factors as follows:

C1 – the price for goods supply plays an important role, because the owner of the operation under investigation does not want to spend too much money on this cost unit.

C2 – it entails the quality of supplied goods, which is also a very important factor. All participants who evaluated individual criteria among each other agreed that the goods quality always comes first. Quality significantly affects the selection of the desired assortment.

C3 – this factor was chosen by restaurant owners mainly by the way in which the considered suppliers are able to respond quickly and promptly to changes in supply operations.

C4 – restaurant owners prefer a quick agreement in regard to ordering the goods, as well as the helpfulness of sales representatives of wholesale centers.

Levels of importance (i.e. vector of criteria weights) refer to criteria preference values and these were assigned to each factor by using the modified pairwise comparison method – Saaty method (see Table 3), which takes into account only 3 relevant values (1, 3 and 5).

Table 2

A list of experts cooperating within a process of determining the weights of criteria

Name of the expert Expertise Date of evaluation
PhD. Marin Marinov Simulation modeling; transport and logistics; rail freight; freight logistics; urban freight November 14, 2019
PhD. Petr Nachtigall Road transport and forwarding; combined transport and logistics; integrated transport systems November 25, 2019
Prof. Larisa M. Kapustina Supply chain management; Operations Research in logistics; road and urban transport November 27, 2019
Assoc. Prof. Stefano Ricci Transport engineering; urban transport planning; supply logistics; transport management and scheduling December 3, 2019
Assoc. Prof. Milos Hitka Personal management in transport and logistics January 12, 2020
Prof. Pawel Droździel Automotive engineering; Operations Research in transport; public passenger transport January 12, 2020
Assoc. Prof. Ádám Török Sustainable transport development; urban planning; automotive engineering February 1, 2020
Prof. Borna Abramović Supply chain management; transport planning and management; transport engineering and logistics February 9, 2020
prof. Gabriel Fedorko Industrial logistics; structural analysis and dynamics; computational mechanics; simulation modeling February 11, 2020
Prof. Jozef Gašparík Rail transportation planning and modeling; traffic engineering; supply logistics; accident analysis February 26, 2020

  1. Source: authors

Table 3

Calculation of the vector of criteria weights by the modified Saaty method

Criterion C1 C2 C3 C4 Geometric mean Vector of criteria weights
C1 1 1/5 1/5 3 0.59 0.11
C2 5 1 3 5 2.94 0.54
C3 5 1/3 1 3 1.49 0.28
C4 1/3 1/5 1/3 1 0.38 0.07
Sum - - - - 5.4 1

  1. Source: authors

In our case, quantifying the weights of criteria was conducted by the following procedure [14, 16]:

  1. First, a relation between each criterion pair being assessed needs to be specified, in which a degree of importance is calculated within a point scope of 1–5. All input values in terms of criteria weights can be obtained by executing a survey; i.e. experts’ opinion examination in our case. Undoubtedly, specification of an adequate set of decision-making factors in relation to supply logistics is regarded highly delicate process, wherein a wide array of experts focused on particular topics of logistics are demanded to assign individual evaluation values. In order to secure as high objectivity as possible, ten experts dealing with topics encompassing supply chain management were demanded to assign importance values among each pair of factors. The following Table 2 describes the expert representatives who participated in a research of defining a set of factors as well as evaluating their weights.

  2. As for the Saaty matrix, scoring of factors being evaluated by the experts were performed, and thereafter, arithmetic means out of all the partial matrix values were counted.

  3. Consequently, individual values of the Saaty matrix were implemented in a sequential quantification process; i.e. geometric mean determination, calculation of the final vector of criteria weights; see Table 3.

The whole quantification process along with all the necessary formulas related to the Saaty method are summarizes, for example, in the literature [16].

Scoring of factors being evaluated by the experts was performed as follows:

1 – given factors are equally important,

3 – the first factor is slightly more important than the second one,

5 – the first factor is flagrantly more important than the second one.

4 Choosing the ideal variant of a supplier by the TOPSIS method

TOPSIS method minimizes distances from the ideal variant while maximizing spans from the basal alternative. The multi-criteria analysis allows the examined enterprise to pick the optimal variant from the suggested suppliers [22].

Table 4 demonstrates three maximizing and one minimizing criterion. The minimizing model, particularly carriage charges, must be converted to a maximizing principle by subtracting all column values from the largest number in the respective line. The following Table 4 shows the conversion of minimizing criteria to maximizing ones [23, 24].

Table 4

Conversion of minimizing criteria to maximizing ones

Variant Carriage charges

(€/1 import)
Goods quality

(scale 1-5)
Delivery times

(scale 1-5)

(scale 1-5)
Makro 200 4 5 5
JIP 100 2 3 4
Astur & Qanto 150 3 4 5
Exver Food 0 4 4 3
Levels of importance 0.11 0.54 0.28 0.07

  1. Source: authors

The next step comprises creating a normalized criteria matrix using formula 3 (see Table 5).

Table 5

Normalized criteria matrix by the TOPSIS method

Variant Carriage charges Goods quality Delivery times Communication
Makro 0.743 0.596 0.615 0.577
JIP 0.371 0.298 0.369 0.462
Astur & Qanto 0.557 0.447 0.492 0.577
Exver Food 0 0.596 0.492 0.346
Levels of importance 0.11 0.54 0.28 0.07

  1. Source: authors

The table suggested above depicts the resulting normalized criteria matrix. The next step encompasses structuring a weighted normalized criteria matrix [25]. The weighted normalized criteria matrix entails the normalized matrix multiplied by individual criteria using formula 4 (see Table 6 below) [26].

Table 6

Weighted normalized criteria matrix

Variant Carriage charges Goods quality Delivery times Communication
Makro 0.082 0.322 0.172 0.040
JIP 0.041 0.161 0.103 0.032
Astur & Qanto 0.061 0.241 0.138 0.040
Exver Food 0 0.322 0.138 0.024
Levels of importance 0.11 0.54 0.28 0.07

  1. Source: authors

Next, we determine ideal H (the variant highest values according to specific criteria) and basal D alternatives (the variant lowest values according to specific criteria):

H = { 0.082 ; 0.322 ; 0.172 ; 0.040 } D = { 0 ; 0.161 ; 0.103 ; 0.024 }

The next step involves determining the distance from the ideal variant through formula 5.

d 1 + = A = 0


A = ( 0.082 0.082 ) 2 + ( 0.322 0.322 ) 2 + ( 0.172 0.172 ) 2 + ( 0.040 0.040 ) 2 d 2 + = B = 0.180


B = ( 0.041 0.082 ) 2 + ( 0.161 0.322 ) 2 + ( 0.103 0.172 ) 2 + ( 0.032 0.040 ) 2 d 3 + = C = 0.090


C = ( 0.061 0.082 ) 2 + ( 0.241 0.322 ) 2 + ( 0.138 0.172 ) 2 + ( 0.040 0.040 ) 2 d 4 + = D = 0.090


D = ( 0 0.082 ) 2 + ( 0 , 322 0.322 ) 2 + ( 0.138 0.172 ) 2 + ( 0.024 0.040 ) 2

Subsequently, formula 6 determines the distance from the basal variant.

d 1 = A = 0.194


A = ( 0.082 0 ) 2 + ( 0.322 0.161 ) 2 + ( 0.172 0.103 ) 2 + ( 0.040 0.024 ) 2 d 2 = B = 0.042


B = ( 0.041 0 ) 2 + ( 0 , 161 0.161 ) 2 + ( 0.103 0.0103 ) 2 + ( 0.032 0.024 ) 2 d 3 = C = 0.108


C = ( 0.061 0 ) 2 + ( 0.241 0.161 ) 2 + ( 0.138 0.103 ) 2 + ( 0 , 040 0.024 ) 2 d 4 = D = 0.165


D = ( 0 0 ) 2 + ( 0.322 0.161 ) 2 + ( 0.138 0.103 ) 2 + ( 0.024 0.024 ) 2

The next step resolves indicators of relative distance from the basal variant according to formula 7.

c 1 = 0.194 0 + 0.194 = 1
c 2 = 0.042 0.180 + 0.042 = 0.189
c 3 = 0.108 0.090 + 0.108 = 0.546
c 4 = 0.165 0.090 + 0.165 = 0.647

The following Table 7 summarizes the findings in relation to the final variant order specification [27]. The first place is held by Makro Cash & Carry wholesale store.

Table 7

The resulting variant order

Makro 1 1.
Exver Food 0.647 2.
Astur & Qanto 0.546 3.
JIP 0.189 4.

  1. Source: authors

The above-mentioned table shows that according to the resulting values, the first place is occupied by Makro Cash & Carry wholesale store. The next places (2nd – 4th), in descending order, are held by suppliers as follows: Exver Food, Astur & Qanto and JIP.

5 Choosing the ideal variant of a supplier by the WSA method

The multi-criteria analysis provides for the enterprise being examined the optimal variant from the suggested suppliers. Firstly, a maximizing matrix must be determined (see Table 4). The next step embraces setting values of ideal (H) and basal (D) variant, which must be considered in the following step [28].

H = { 200 ; 4 ; 5 ; 5 } D = { 0 ; 2 ; 3 ; 3 }

Separate steps are calculated through the normalized matrix and provided by the formula 1 [29]. Table 8 suggests results of the normalized criteria matrix.

Table 8

Normalized criteria matrix by the WSA method

Variant Carriage charges Goods quality Delivery times Communication
Makro 1 1 1 1
JIP 0.5 0 0 0.5
Astur & Qanto 0.75 0.5 0.5 1
Exver Food 0 1 0.5 0
Levels of importance 0.11 0.54 0.28 0.07

  1. Source: authors

The subsequent step involves quantifying the utility function for individual variants according to formula 2.

u 1 = 0.11 1 + 0.54 1 + 0.28 1 + 0.07 1 = 1
u 2 = 0.11 0.5 + 0.54 0 + 0.28 0 + 0.07 0.5 = 0.09
u 3 = 0.11 0.75 + 0.54 0.5 + 0.28 0.5 + 0.07 1 = 0.56
u 4 = 0.11 0 + 0.54 1 + 0.28 0.5 + 0.07 0 = 0.68

The last step encompasses the classification of resulting variants in descending order according to the very quantification (see Table 9).

Table 9

Resulting variant order

Makro 1 1.
Exver Food 0.68 2.
Astur & Qanto 0.56 3.
JIP 0.09 4.

  1. Source: authors

Table 9 illustrates the findings containing individual utility function values sorted in the descending order [30]. Analogously to the TOPSIS method, the highest value is allocated to Makro Cash & Carry even according to the WSA method.

6 Evaluation of findings

The application of the Operations Research methods allowed adopting effective measures contributing to effectively model the transport-supply process of the enterprise being investigated. In particular, four scenarios to efficiently supply the enterprise were designed. The variants were represented by suppliers who may positively influence the whole enterprise transport-supply system. To choose the ideal scenario, fresh approaches of the Operations Research (TOPSIS and WSA) were adopted, showing that Makro Cash & Carry Company appears to be the ideal option for the enterprise supplier, followed by the wholesalers Exver Food and Astur & Qanto, and the worst result was assigned to JIP.

The owner of the examined company has had long experience of buying goods in the above-mentioned wholesale store. This way of transport-supply process appears to be the optimal approach with respect to the quality, price and transport costs. The new way of transport-supply operation ensures goods delivery in the prescribed amount, for the required price and just-in-time. The designated wholesale store keeps customers satisfied, having favorable feedback from its subscribers.

The enterprise is currently supplied in-house each separate weekday; i.e. a new supplier would sufficiently supply the goods twice a week.

7 Conclusion

On the basis of the elaborated literature review, executed calculations, obtaining the final results, and following the evaluation of individual scenarios by using the specific Operations Research techniques, wholesaler 1 (i.e. Makro Cash & Carry Company) is recommended to be the optimal supplier for the implementation of the transport-supply process that will enhance the effectiveness of specific logistics activities in the operation being examined.

Based on the existing criteria set, variant 1 achieved the best possible results by both methods, especially due to the fact that it demonstrated a strong relationship with high-weight-value factor C2 (goods quality) as well as C3 (delivery times). Of course, the recommended wholesaler can differ depending on the kind and range of defined factors, as well as the Operations Research technique implemented in each step of the process of multi-criteria evaluation. The research findings entail valuable data for optimizing specific activities of suppliers, not only those who were compared in this particular study, but such outcomes may even represent the very principle for ranking suppliers’ priorities in order to provide optimal conditions and quality of supply logistics.

The crucial objective of this research study was to compare two Operations Research techniques in order to select the optimal wholesaler to ensure the complex transport-supply process. For this purpose, four enterprises providing their customers high-quality logistics and additional supply services were taken into consideration, while individual preference weight values of four defined criteria were counted by using the Saaty method.

Following the outcomes achieved, it can be stated that by applying the techniques such as Saaty method,WSA as well as TOPSIS, the wholesaler 1 is regarded the most appropriate variant based on the specified set of factors. It also can be concluded that no similar publication has been published yet by implementing analogous Operations Research techniques, same set of factors, nor dealing with the similar topic when determining identical publication objective. Our scientific work adds value to knowledge of the proper functioning of supply chains in the Czech Republic and points out the importance to define corresponding criteria. And just this fact represents an aspect in which the novelty and innovative solution of this work lies.

The subject of further research may consist in an extension of the criteria set being compared or an extension of individual criteria by sub-criteria.


This manuscript was supported within solving the research project entitled “Autonomous mobility in the context of regional development LTC19009” of the INTER-EXCELLENCE program, the VES 19 INTER-COST subprogram.

Manuscript is also the result of the project VEGA No. 1/0128/20: Research on the Economic Efficiency of Variant Transport Modes in the Car Transport in the Slovak Republic with Emphasis on Sustainability and Environmental Impact, Faculty of Operation and Economics of Transport and Communications: University of Zilina, 2020-2022.


[1] Szumska E, Pawełczyk M, Pistek V. Evaluation of the Life Cycle Costs for urban buses equipped with conventional and hybrid drive trains. The Archiv. of Autom. Eng. – Archiw. Motor. 2019;83(1):73-86. Search in Google Scholar

[2] Török Á, Fedorko G, Molnar V, Husaková N, Csiszár C. How to choose and when to start best ITS projects that enhance logistic performance? Period. Polyt. Transp. Eng. 2017;45(1):8-11. Search in Google Scholar

[3] Poliakova B, Stoklosa J. The impact of proposed prices on the public transport providers and passengers for integrated transport system in Kosice region. Communic. – Scient. Lett. of the Univer. of Zilina 2016;18(2):133-138. Search in Google Scholar

[4] Vojtek M, Kendra M., Široký J., Magdechová K., Šipuš D. Supply Chain Simulation in Educational Process. LOGI – Scient. Jour. on Transp. and Logist. 2019;10(1):72-78. Search in Google Scholar

[5] Pelegrina GD, Duarte LT, Romano JMT. Application of independent component analysis and TOPSIS to deal with dependent criteria in multicriteria decision problems. Exp. Syst. with Applicat. 2019;122:262-280. Search in Google Scholar

[6] Yu B, Cai M, Li Q. A λ-rough set model and its applications with TOPSIS method to decision making. Knowledge-Based Syst. 2019;165:420-431. Search in Google Scholar

[7] Venkatesh VG, Zhang A, Deakins E, Luthra S, Mangla S. A fuzzy AHP-TOPSIS approach to supply partner selection in continuous aid humanitarian supply chains. Ann. of Operat. Res. 2019;283:1517–1550. Search in Google Scholar

[8] Agarski B, Hadzistevic M, Budak I, Moraca S, Vukelic D. Comparison of approaches to weighting of multiple criteria for selecting equipment to optimize performance and safety. Intern. Jour. of Occupat. Saf. and Ergon. 2019;25(2):228-240. Search in Google Scholar

[9] Yu C, Shao Y, Wang K, Zhang L. A group decision making sustainable supplier selection approach using extended TOPSIS under interval-valued Pythagorean fuzzy environment. Exp. Syst. with Applicat. 2019;121:1-17. Search in Google Scholar

[10] Kauf S, Tłuczak A. Allocation of logistic risk-investment in public-private-partnership - Use of fuzzy TOPSIS method. MATEC Web of Conf. 2018;184:Art. No. 04025. Search in Google Scholar

[11] Hlatká M, Bartuška L, Ližbetin, J. Application of the Vogel Approximation method to reduce transport-logistics processes. MATEC Web of Conf. 2017;134:Art. No. 00019. Search in Google Scholar

[12] Dinçer SE. Multi-criteria analysis of economic activity for European Union member states and candidate countries: TOPSIS and WSA applications. Europ. Jour. of Soc. Scien. 2011;21(4):563-572. Search in Google Scholar

[13] Adetunji O, Bischoff J, Willy CJ. Managing system obsolescence via multicriteria decision making. Syst. Engin. 2018;21(4):307-321. Search in Google Scholar

[14] Dockalikova I, Klozikova J. MCDM Methods in Practice: Localization Suitable Places for Company by the Utilization of AHP and WSA, TOPSIS Method. In Conf. on Europ. Manag. Leadersh. and Govern., Military Academy, Lisbon, Portugal 2015, 543-552. Search in Google Scholar

[15] Ližbetin J, Černá L, Ľoch M. Model evaluation of suppliers in terms of real company for selected criteria. Nase More 2015;62:147-152. Search in Google Scholar

[16] Kampf R, Lizbetin J, Lizbetinová L. Requirements of a transport system user. Communic. – Scient. Lett. of the Univer. of Zilina 2012;14(4):106-108. Search in Google Scholar

[17] Kudlac S, Gasparik J, Dedik M, Kurenkov PV. Identification of Restricting Criteria for Comprehensive Assessment of Logistics Chains in Intermodal Transport. LOGI – Scient. Jour. on Transp. and Logist. 2018;9(2):18-27. Search in Google Scholar

[18] Korecki Z, Adámková B. Multi-criteria evaluation of critical infrastructure resilience and economic impacts in selected airports in the Czech Republic. Scient. Jour. of Siles. Univ. of Techn. Series Transp. 2020;108:95-106. Search in Google Scholar

[19] Droździel P, Rybicka I, Brumercikova E, Bukova B. The application of the progressive decision-making methods in the electronic payment system in public transport. Transp. Probl. 2019;14(3):135-144. Search in Google Scholar

[20] Jaskiewicz M, Koralewski G, Stoklosa J. Adaptation of city buses to the needs of airport terminal passenger transport. In 11th Intern. Scien. and Techn. Conf. Autom. Saf. 2018;Code 13699:1-7, Casta, Papiernicka, Slovakia, 18-20 April 2018. Search in Google Scholar

[21] Meszaros F, Markovits-Somogyi R, Bokor Z. Modelling and multi-criteria optimization of road traffic flows considering social and economic aspects. LOGI – Scient. Jour. on Transp. and Logist. 2012;3(1):70-82. ISSN 1804-3216. Search in Google Scholar

[22] Slávik R, Gnap J. Selected problems of night - Time distribution of goods within city logistics. Transp. Resea. Proc. 2019;40:497-504. Search in Google Scholar

[23] Jurkovic M, Kalina T, Kadnar R, Illes L. Black Sea - Caspian Sea scenario of LNG transport. In Trans. Means 2019: proceed. of the 23rd intern. scien. conf. 2019;1229-1233, October 2019, Kaunas, Lithuania. Search in Google Scholar

[24] Alkhayyal BA, Gupta SM. A linear physical programming approach for evaluating collection centers for end-of-life products. Applic. of Manag. Scien. 2018;19:65-79. Search in Google Scholar

[25] Duleba S, Moslem S. Examining Pareto optimality in analytic hierarchy process on real Data: An application in public transport service development. Exp. Syst. with Applicat. 2019;116:21-30. Search in Google Scholar

[26] Droździel P, Wińska M, Madleňák R, Szumski P. Optimization of the position of the local distribution centre of the regional post logistics network. Transp. Probl. 2017;12:43-50. Search in Google Scholar

[27] Fedorko G, Molnár V, Dovica M, Tóth T. Conveyor belt quality assessment for in-house logistics. Qual. – Acc. to Succ. 2018;19:3538. Search in Google Scholar

[28] Houska M, Domeova L, Berankova M. The conversion of cost and beneft criteria in the TOPSIS method. Intern. Jour. of Appl. Decis. Scien. 2012;5:329-341. Search in Google Scholar

[29] Houska M. Reply to the paper ’Multi-criteria analysis of economic activity for European union member states and candidate countries: TOPSIS and WSA applications’ by S. E. Dincer. Europ. Jour. of Soci. Scien. 2012;30:290-295. Search in Google Scholar

[30] Varmus M, Kubina M, Koman G. Ensuring the long-term sustainability cooperation with stakeholders of sports organizations in Slovakia. Sustain. 2018;10(6):1-19. Search in Google Scholar

Received: 2020-09-17
Accepted: 2020-11-08
Published Online: 2020-12-17

© 2021 O. Stopka et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.