Choosing the Suitable Method for Multimodal Logistics Object Location in the Slovak Republic and Setting up the Criteria Matrix

This paper deals with the choosing of a suitable method for multimodal logistics object location in the Slovak Republic. The paper also describes several methods concerning the multimodal logistics object location in particular area, determines the crucial method related to this issue and presents setting up the criteria matrix for the needs of this object location in the Slovak Republic.


Introduction
Choosing the appropriate area for multimodal logistics object location can be considered a decision problem.
The decision means in a given situation choosing one option from a list of potentially viable variants against a large number of criteria.
Next to the list of criteria indirectly forming the objective of the decision analysis it is necessary to have a list of variants from which to choose. Cases where a clearly defined list of potential variants is available are more the exception than the rule. This list can be explicitly specified as the sum of a finite number of options, or specify the conditions that are considered acceptable and with which the decision options must comply.
If there is a list of criteria and a list of decision variants, it is necessary to consider in detail what form the final decision should take. If we insist that it is really necessary to choose only one optimal variant, we need to accept that in typical cases we want to get something out of unreliable and insufficient information that is almost certainly not included. For a task formulated in this way there is a requirement to create the order of variants.

Overview of Several Methods for Multimodal Logistics Object Location in Particular Area
Methods for the selection of a variant (variant for multimodal logistics object location) are divided depending on what information about the preference among the criteria is required [1-3]: 1. Methods not requiring information about criteria preference.
Methods that do not require information about the preference between criteria are very simple and in their plain form are rarely used.

Methods requiring aspiration level of criteria.
For methods that are based on work with aspiration information on preferences between criteria, it is characteristic that they do not try to transform the information of a user into a weight vector. Information about the importance of the criteria is expressed as the aspiration level of the criteria. These methods are useful in cases where aspiration values of criteria are known and cardinal evaluation of the variants according to individual criteria can be used.
3. Methods using ordinal information about the criteria. Methods working with ordinal information about the criteria or variants require a specification of the order of criteria importance and the order of variants according to indi- There are several methods that require cardinal information about the criteria in terms of weights and about the variants in the form of a criteria matrix with cardinal values. In this area there are three basic approaches to the evaluation of variants, according to:  Maximizing the benefits,  Minimizing the distance from the ideal variant,  Preferential relationship.

Simple Method of Scoring
This method can be used if the model is specified using only the preference of variants according to individual criteria and criteria preferences are not known [1][2][3].
Appropriateness of method -Using the method in this paper is inappropriate.

Simple Method of Ranking
The method can also be used if the model is specified using only the preference of variants according to individual criteria and criteria preferences are not known [1][2][3].
Appropriateness of method -Using the method in this paper is inappropriate.

Lexicographical Method
The lexicographical method is based on the principle that the most important criterion has the greatest influence on the choice of an multimodal logistics object location variant. Only in cases where several variants are rated the same is the next most important criterion taken into account.
If an alternative variant is not selected on the basis of this second criterion, the third most important variant is taken into account, and so on. The algorithm stops at the moment when only one variant is selected or when all criteria taken into account have been considered. The alternative variants are then all those that remained equally evaluated after the last criterion [1][2][3].
Appropriateness of method -Using this method in this paper is inappropriate because it does not take into account values obtained by other criteria.

Permutation Method
With this method it is important to know the order of importance of individual criteria. Further, it is important to realize that the number of variant permutations m is m!, which is a major drawback of this method. For this method it is necessary to know either the weights of individual criterion or at least the order of their importance [1][2][3].
Appropriateness of method -Using this method in this paper is inappropriate.

Oreste Method
The method requires as input only ordinal information on criteria and variants. The investigator is required to complete quasi-ordering of criteria and to complete quasi-ordering of variants according to individual criteria, i.e. indifference of criteria and variants is permitted [1][2][3].
First, the distance of each variant according to each criterion from the fictional start is determined (order numbers of the fictional variant and fictional criterion are 0). On the basis of this calculated distance, the variants are arranged according to certain rules.
Appropriateness of method -Using the method in this paper is inappropriate.

Topsis Method
The TOPSIS method is one of the methods where the evaluation of options is performed by comparison with ideal variants. To express the distance between variants, different units are used. The TOPSIS method is based on the classical Euclidean metric space [1][2][3].
Appropriateness of method -Using this method in this paper is less suitable.

Weighted Sum Analysis -WSA
The weighted sum method requires cardinal information, criteria matrix Y and a vector of criteria weightings v. It constructs the overall rating for each variant and so it can be used for finding one of the most appropriate variants as well as for arranging variants on a scale from the best to the worst [1][2][3].
With this method we work with the weights of individual criterion which are either entered or estimated appropriately (see previous scoring method for determining criteria weightings). Thus we get the weightings v=(v 1 ,v 2 ,...,v k ) for k of maximization criteria [1][2][3].
The method of weighted sum then maximizes the weighted sum, i.e.: Hence, we calculate the value of the weighted sum for each variant and, as a compromise variant, select the one with the highest weighted sum.
Appropriateness of method -Using the method in this paper is appropriate because it constructs the overall rating for each variant.

AHP Method
This method provides a framework for making effective decisions in complex decision-making situations, helping to simplify and accelerate the natural process of decision making. AHP is a method of decomposition of a complex unstructured situation into simpler components, thereby creating a hierarchical system for a problem [1][2][3].
At each level of the hierarchical structure the Saaty method of quantitative pairwise comparison is used. Using subjective ratings of pairwise comparison, this method then assigns quantitative characteristics to each component indicating their importance. Synthesis of these evaluations then determines the component with the highest priority which the investigator focuses on in order to obtain a solution to the decision problem [1][2][3].
The arrangement of the individual levels of hierarchical structure corresponds with the arrangement from general to specific. The more general the elements in relation to the given decision problem are, the higher they are in the hierarchy associated with the problem and vice versa [1][2][3].
Appropriateness of method -Using the method in this paper is less suitable.

Ardolana Method
The Ardolana method is one of the heuristic methods which is used to find the optimal placement for the deployment of objects in an area according to certain criteria. Calculations for the optimal allocation of objects are carried out by analyzing all the criteria that are to some extent able to influence the choice of allocation [1][2][3].
Appropriateness of method -Using the method in this paper is less suitable.

Choosing the Crucial Method
The selection of the appropriate method depends on the point of view of the investigator interested in the subject. Operational analysis methods from the field of graph theory deal with classical solutions for the allocation tasks. Most of the tasks from a real environment are too complex in terms of calculations for the application of these methods. Finding solutions for these tasks cannot be done without the use of a computer or even specialized software. [1].
There are many different methods which can help in the multimodal logistics object location issue (for example, methods of multi-criteria analysis). In practice, however, many methods cannot be used because they do not allow for the processing of all the intricacies intended in this article.
Many methods cannot be applied to the multi-criteria function in our case. Another significant problem area for the application of certain methods is that we do not know the details of the customers and users of multimodal logistics object, which we could have analyzed [1][2][3].
On this basis it was decided to use the weighted sum method -WSA, which appears to be relatively easy to handle and easy to apply to the complex and difficult task of multimodal logistics object location.

Setting up the Criteria Matrix for the Needs of Multimodal Logistics Object Location in the Slovak Republic
In the theory of Multiple Criteria Decision Making we work with a general number of criteria k and with a general number of p. The value achieved by variant i or j-th criterion is labelled as y ij and is called the criterion value. The next step is to arrange these values into a matrix which we call the criteria matrix. The rows of the criteria matrix are formed by the individual variants. The columns of the criteria matrix correspond with the individual criteria [1].
The criteria matrix, therefore, has the following form ( Figure 1):

Identification of variants
In stage one it is necessary to identify a set of variants from which the final solution will be chosen. The regions of Slovakia where the multimodal logistics object should potentially be placed were identified as those of: Bratislava, Trnava, Trencin, Nitra, Zilina, Banska Bystrica, Presov and Kosice.
For a more accurate result it would be more appropriate to look at district level, but at this level it would be very difficult to obtain data to fulfil the criteria matrix (an essential part of multi-criteria analysis) because most of the data required is not available at district level.

Establishment of a set of criteria
Stage two of the process of multi-criteria analysis involves establishing a set of criteria which influence the process of decision making in the selection of variants. [4].
From the point of view of formality it is necessary to differentiate the criteria according to the type of preference and the way (form) of expressing and measuring the results of evaluations based on such criteria. Criteria according to their type preference can be placed in order of [5][6]:  Increasing preference (maximization, profit) -in which higher values are preferred over lower ones,  Decreasing preference (minimization, loss) -which are the opposite of the above,  Alternating preference -preference changes when a certain value is achieved. Criteria by way of expression and measurement of evaluations of results [5][6]:  Quantitatively, the values of which can be expressed numerically by the number of units of measure,  Qualitatively, which can only be expressed verbally, i.e. degrees of quality and a description of their intensity. After determining the objectives of the analysis of available knowledge, relevant to this article, 6 criteria from socio-economic and transport areas were defined. For these criteria critical data were obtained based on the study of the functions and perspectives that are related to the activities carried out in an multimodal logistics object. Due to the prerequisite that all the data (associated with different factors) should be related to the same time period, only data collected for 2010 appears in this article.
For clarity, the criteria (factors) are summarized in the following vak Republic) and it is also the criteria matrix for the purpose of this article. For the purposes of tasks related to the criteria matrix it is appropriate that all the criteria are of the same type (minimization or maximization). Transfer of the criteria to the same type is not difficult because each minimization criterion can be easily converted to maximization criterion [1,2].
1. The scale is given by the nature of the issue. In this case we take the maximum value that can be achieved, and subtract from it the value of the criterion.
2. The scale is not given. In this case, we find the variant with the highest (worst) value and subtract from it the value of the criterion. This step can be presented as protection against the worst variant.
In our case it is not necessary to perform a modification at any criterion, because all the criteria are of the same type (maximization).

Ideal and basal variant
Ideal variant is the best option which can be theoretically or practically achieved.
1. Relative (highest in criteria matrix for a given criterion), 2. Absolute (highest theoretically possible value). In our case ( Table 3): According to the above formulae we set up the required matrix ( Table 6):

Conclusion
In order to accomplish all steps of the multi-criteria evaluation of variants the above mentioned procedures should be followed by the determination of criteria weightings.
This step can be made using the Saaty pairwise comparison method. This method is able to determine final values of the vector of weights of individual criterion.
Subsequently, the most appropriate variant for the multimodal logistics object location in the Slovak Republic can be determined. One possible approach is to multiply the normalized matrix by the vector of weights indicated by Saaty method. But this article does not deal with this part of the multi-criteria evaluation of variants issue.