Choosing a transportation provider is one of the most important choices for a successful business. Forwarding companies rely on past relationships and managerial skills to choose a logistics service providers. There is a number of criteria that need to be taken into account when evaluating a transportation service provider, which are, i.e. one criterion should be as high as possible and the other as low as possible. Multi-criteria decision making methods are commonly used to solve this problem. This article uses VIKOR and TOPSIS multi-criteria decision making methods. 10 transport service providers are ranked, the results of the methods are compared and the expert opinion is compared with the criteria calculated from the actual data. The ranking results are similar for both methods, but difer the ranking of experts and criteria is based on actual data.
tant.
Diferent criteria for choosing a logistics provider In today’s business world, it is very dificult to de- are important for diferent loads and types of cargo. velop products without partners. The company should For companies that want to bring their food products, take care of the entire supply chain of the product, the most important thing is the delivery time, the qualfrom the selection of raw materials, production, pack- ity of the cargo storage or the undamaged cargo and aging, promotion, storage, and transportation to the price. And when it comes to transporting large quancustomer. It is dificult for a company to be compet- tities of non-food items, the key is low price, fleet caitive. As a result, companies buy services from other pabilities, and quality delivery. And in companies, the companies that specialize in a particular area. One of manager is still deciding which company to choose as the most common areas of cooperation is transporta- a logistics provider, considering all the criteria. It is tion because transporting their own products would a job that requires a lot of experience and skills, and require considerable costs and investment in vehicles many aspects need to be evaluated. A person with and human resources to manage them. Most compa- many years of experience still can make mistakes. Mathnies choose to cooperate with transportation service ematical estimation methods are used to eliminate huproviders. But there is another problem of choosing man errors and subjective judgment when choosing a the most suitable one from a large number of trans- transportation service provider. port service providers.
According to data provided by the Ministry of
Transport and Communications of the Republic of Lithua- 2. Literature review
nia, the transport sector continues to grow [
As it is mentioned above, there is a number of
ranking methods. In this paper, we experiment with
TOPSIS [10] and VIKOR [11] methods. These methods are
based on an aggregating function representing
“closeness to the ideal”, which originated in the compromise
programming method. In VIKOR linear normalization
and TOPSIS vector normalization is used to eliminate
the units of criterion functions [12]. We chose these
methods because they are quick and easy to use [
The elements of the normalized decision matrix are given by the following equation: = √ ∑ 2 =1 , = 1, 2, … , , = 1, 2, … , . 3. Calculate the weighted normalized decision matrix.
Calculate the weighted normalized matrix elements using the following expression: = ⋅ , = 1, 2, … , , = 1, 2, … , . 4. Determine the ideal and negative-ideal solution.
The ideal positive solution is the solution that maximizes the benefit criteria and minimizes the cost criteria whereas the negative ideal solution maximizes the cost criteria and minimizes the benefit criteria. [13].
Expression of a positive ideal solution +:
+ = { +} = {(max | ∈ ), (min | ∈ )}
Expression of a negative ideal solution −:
− = { −} = {(min | ∈ ), (max | ∈ )},
′
′
relates to the cost criterion [
where ′ relates to the benefit criterion and ′′ 5. Calculate the separation measures, using the ndimensional Euclidean distance.
The separation of each alternative from the ideal solution is given as: √ √ =1 6. Calculate the relative closeness to the ideal solution. the formula: The relative closeness of the i-th element to the positive ideal solution can be calculated using =
− − + +
where 0 ⩽ ⩽, = 1, 2, … , .
Items highest number indicates the best solution.
are ordered in descending order. The (1) (2) ′′ (3) ′′ (4) (5) (6) (7) 3.2. VIKOR The VIKOR [11] was introduced as one applicable technique to implement within MCDM. It focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria, and on proposing compromise solution (one or more) [14]. The compromise ranking algorithm VIKOR has the following steps [12,
function represents a benefit then: 1. Determine the best of all criterion functions, = 1, 2, … , . If the th ∗ and the worst − values ∗ = max , − = min .
the relations 2. Compute the values and , = 1, 2, … , , by = ∑ (
=1 = max[ ( ∗ − )/( ), ∗
− ∗
− )/( ∗ −)], where their relative importance.
are the weights of criteria, expressing lation where = ( − ∗)/( − − ∗) + (1 + )( − ∗)/( − − ∗) ∗ = min , − = max , ∗ = min , − = max , ranking lists. and is introduced as weight of the strategy of “the majority of criteria” (or “the maximum group utility”), here = 0.5. 4. Rank the alternatives, sorting by the values , and , in decreasing order. The results are three 5. Propose as a compromise solution the alternasatisfied: tive ( ′) which is ranked the best by the measure (minimum) if the following two conditions are C1. Acceptable advantage: ( ′′) − ( ′) ⩾ (14) where ′′ is the alternative with second position in the ranking list by ; 1); is the number of alternatives.
= 1/( − (8) (9) (10) (11) (12) (13) 3. Compute the values , = 1, 2, … , , by the re
is the weight of the decision making strategy “the majority of criteria” (or “the maximum group utility”) [12].
We use real data collected by the logistic company, which includes companies, trucks, trailers, cargo orders, trip data. Data were collected from January 2, 2015, to May 10, 2019. Companies that provide transportation services were selected from this data. We estimated from data: 1. number of company trucks,
ument, 5. average daily payment period for purchase doc6. average loading time for purchase documents.
We also have an expert evaluation of logistic providers. The expert rated the logistic provider on a ten-point scale where 1 is very bad and 10 is very good. The expert evaluated according to 4 criteria: 1. speed of sending documents of the company,
the analysis, we will compare expert judgment with factual evaluation. For this purpose, we randomly selected 10 transport service providers for which we have an expert judgment (see table 1) and actual data (see table 2).
TOPSIS expert
TOPSIS data
Both of these methods used the same criteria weights to compare the results of the methods. In the TOPSIS method higher score means higher rank. The reverse is true for the VIKOR method. In VIKOR method smaller coeficient means higher rank. Table 3 shows the results of the TOPSIS model and table 4 shows the results of the VIKOR model.
First of all, we calculated the correlation matrix (see tabel 5) to compare the obtained methods. Correlation matrix values closeness to these values indicate relationships between rankings: 1. 1 if the agreement between the two rankings is perfect; the two rankings are the same, 2. 0 if the rankings are completely independent, 3. -1 if the disagreement between the two rankings is perfect; one ranking is the reverse of the other. As can be seen from the correlation matrix, the experts evaluated TOPSIS ranking is completely identical with VIKOR expert assessment. This correlation equal to 1. Other correlation values are greater than 0, that means rankings are slightly similar.
The two methods of expert assessments ofered by the best P3 and P6 logistics providers. When evaluating 3PL suppliers based on actual data, both methods gave P1 provider as the best alternative.
Comparing the results of each method on its own, it can be seen that expert judgment in the vast majority of places does not coincide with evaluations of criteria calculated from actual data. This is because diferent criteria have been chosen for the evaluation. The experts evaluated the sending of the documents, we evaluated the speed of the loading of the documents according to the data. But it is dificult to evaluate communication, quality of service and price from the data e.g. as the price depends on the number of kilometers and type of cargo.
The results calculated by the VIKOR method coincide with estimates made by experts and factual data. Supplier P7 took 3rd place. But looking at other suppliers, the P3 and P6 are ranked high by experts: 2 and 1 respectively. And according to the actual data low: 10 and 9 places. The analysis should combine expert judgment with criteria calculated from actual data, thus better describing the logistics providers.
According to VIKOR and TOPSIS models and actual data, P1 is the best choice and P3 the worst from this ten providers. If we included other logistics service providers in the ranking, the results would change.
The choice of a transport service provider is one of the most important cooperation (outsourcing) solutions to increase the competitiveness of the company. With a large supply of logistics providers, it is dificult to choose the best partner. The goal of this research is application and comparison of TOPSIS and VIKOR multicriteria decision making methods, to determine which transportation supplier is the best. These logistics service provider were analyzed for the period from 2nd January 2015 to 10th May 2019.
The main results of this article: 1. Overview of transportation service providers issues. 2. Comparison of the TOPSIS and VIKOR methods. 3. Evaluation of both methods.
Conclusions: 1. Expert judgment and evaluation of data-based criteria are more correlated in the VIKOR method than in the TOPSIS. 2. According to expert assessments, both methods ofered the same ranking of logistics services providers. 3. Approach of The VIKOR method better reflected expert judgment in the evaluation of actual data.
In future, we plan to perform sensitivity analysis of criteria weights obtained by the VIKOR method, as well as adapting other logistics provider choices MCDM techniques, statistical approaches, artificial intelligence.
We thank Egidijus Grigas and UAB Terra IT1 for cooperation and useful insights. Research was partially funded by Lithuanian Business Support Agency (J05LVPA-K-04-0079).
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