# Development of a Model for Evaluating the Efficiency of Transport Companies: PCA–DEA–MCDM Model

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Review of Applying the DEA Method for Evaluating the Efficiency in the Field of Transport

#### 2.2. Review of Applying the PCA–DEA Model for Evaluating the Efficiency in the Field of Transport and the Supply

#### 2.3. Review of Applying Integrated Models in the Field of Transport

#### 2.4. A Review of Studies of Pandemic Impact on Transport and the Supply Chain

## 3. Methodology

#### 3.1. DEA Model

_{ij}, while s represents the output parameters for each alternative y

_{ij}, taking into account weights of the parameters denoted by w

_{i}, and n represents the total number of DMUs. The DEA CCR output-oriented model (max) is as follows:

#### 3.2. PCA Model

- Standardization of variables;
- Computation of the matrix of correlations between all initial standardized variables;
- Finding the eigenvalues of the principal components;
- Rejection of the components that are carriers of a proportionally small share of variance (usually the first several components carry 80–90% of the total variance).

#### 3.3. CRITIC Method

_{ij}

_{.}

#### 3.4. Entropy Method

#### 3.5. MARCOS Method

_{ij}]

_{mxn}are obtained by applying Equations (14) and (15):

_{ij}and x

_{ai}represent the elements of matrix X.

_{ij}]

_{mxn}, Equation (16).

_{i}applying Equations (17) and (18).

_{i}(i = 1,2, …, m) represents the sum of the elements of the weighted matrix V, Equation (19).

_{i}) defined by Equation (20).

## 4. Integrated Model for Determining the Efficiency of Transport Companies

#### 4.1. Analysis of Representative Transport Companies

#### 4.2. Data Collections for Inputs and Outputs

#### 4.3. Determining Efficiency Using an Integrated PCA–DEA Model

#### 4.4. Determining the Weight Values of Parameters Applying the CRITIC Method

_{j}is obtained by multiplying the value of standard deviation by the previously obtained individual value of the sum per column. The values obtained in this way, as well as the final values of the weights of the criteria, are given in Table 4. The final values of the weight coefficients are obtained when the individual value of C

_{j}is divided by the previously calculated sum of C

_{j}, i.e., by applying Equation (7). The sum of C

_{j}, in this case, is 25.834.

_{1}= 0.071; w

_{2}= 0.071; w

_{3}= 0.071; w

_{4}= 0.206; w

_{5}= 0.091

_{6}= 0.196; w

_{7}= 0.069; w

_{8}= 0.069; w

_{9}= 0.074; w

_{10}= 0.082

#### 4.5. Determining the Weight Values of Parameters Applying the Entropy Method

_{1}= 0.986; e

_{2}= 0.986; e

_{3}= 0.987; e

_{4}= 0.985; e

_{5}= 0.994;

_{6}= 0.981; e

_{7}= 0.993; e

_{8}= 0.993; e

_{9}= 0.988; e

_{10}= 0.926

_{j}are obtained by applying Equation (10). An example of the calculation is as follows:

_{1}= 0.079; w

_{2}= 0.076; w

_{3}= 0.073; w

_{4}= 0.082; w

_{5}= 0.033;

_{6}= 0.103; w

_{7}= 0.0409; w

_{8}= 0.0410; w

_{9}= 0.066; w

_{10}= 0.408

_{1}= 0.052; w

_{2}= 0.051; w

_{3}= 0.046; w

_{4}= 0.101; w

_{5}= 0.020;

_{6}= 0.049; w

_{7}= 0.041; w

_{8}= 0.037; w

_{9}= 0.042; w

_{10}= 0.561

_{1}= 0.075; w

_{2}= 0.073; w

_{3}= 0.072; w

_{4}= 0.249; w

_{5}= 0.008;

_{6}= 0.231; w

_{7}= 0.0200; w

_{8}= 0.0201; w

_{9}= 0.080; w

_{10}= 0.172

#### 4.6. Ranking the Alternatives Applying the MARCOS Method

## 5. Sensitivity Analysis and Comparative Analysis

#### 5.1. Comparative Analysis with Other MCDM Methods

#### 5.2. Changes in Parameter Significance

## 6. Discussion

#### 6.1. Discussion of Obtained Results

#### 6.2. Discussion Related to Other Studies

#### 6.3. Managerial Implications

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Graphical representation of a comparative analysis of the number of vehicles, drivers, operating hours, vehicle maintenance costs, fuel costs, and transport staff costs.

**Figure 7.**Graphical representation of a comparative analysis of the number of deliveries, quantity transported, kilometers traveled, and profit.

**Table 1.**The overview of a method for evaluating the efficiency in the field of transport and supply chain.

Method | Findings | Observed Inputs and Outputs | Authors |
---|---|---|---|

DEA | Analysis of the efficiency of the bus subsystem of public passenger transport | Realized kilometers, realized places/kilometers and number of operationally ready vehicles | Despić et al. [8] |

AHP and DEA | The analysis of the efficiency of airlines in the European Union | Operational costs, number of employees and offered capacity and realized passenger kilometers | Dožić and Babić [9] |

DEA | Efficiency analysis of the European inland trimodal terminals | Terminal area, total track length, total operational shore length, maximum draft depth, storage capacity and annual terminal capacity | Krstić et al. [10] |

DEA | An assessment of intermodal container transportation | The sum of transportation costs, time travel utilization, transportation work and strategy resistance factor | Radonjić et al. [11] |

DEA, PCA and VIKOR | Supplier selection and evaluation in the garment supply chain | Quality, price, location, lead-time, monetary position (variability), financial position, on-time delivery, ability to produce, support and service and technical capacity | Karami et al. [12] |

PCA and DEA | Developing A strategy-based framework for supplier selection | Delivery time, service relation combination, cost and organizational management | Hatami-Marbini et al. [13] |

PCA, DEA and MLR | An assessment of the Eco-Efficiency of Transport-Related Particulate Matter Pollution | Fuel consumption, the number of employees, trips per day, pollution and emissions of various harmful gases | Muge [14] |

DEA | Research in the new framework for logistics performance index | Freight price, logistic loss, fuel consumption, on-farm storage capacity, emissions (Eq. CO2/transported t), length of the route, production, corridor exports and inverted emission | Melo [15] |

ANP and DEA | Measuring the efficiency of transport infrastructure projects | 15 inputs/outputs related to energy, quality, operational indicators, utilization and resource indicators | Ivanović et al. [16] |

DEA, CRITIC and MARCOS | An assessment of Traffic Safety in South Africa | The average number of accidents (per km), the number of access (per km), road width, the number of lanes | Stević et al. [17] |

Year-DMU | Input Parameters | Output Parameters | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Number of Vehicles | Number of Drivers | Number of Operating Hours | Vehicle Maintenance Costs | Fuel costs Per Kilometers Traveled | Transport Staff Costs | Total Number of Deliveries | Quantity Transported | Kilometers Traveled | Profit | |

2013 | 30 | 30 | 74,000 | 248,505 | 0.67 | 1,463,427 | 2931 | 58,620 | 3,000,000 | 328,675 |

2014 | 32 | 34 | 81,000 | 344,852 | 0.60 | 1,769,294 | 2917 | 58,340 | 3,700,000 | 217,144 |

2015 | 44 | 44 | 107,000 | 419,855 | 0.51 | 1,904,486 | 3611 | 72,220 | 4,224,000 | 302,445 |

2016 | 48 | 49 | 119,600 | 503,687 | 0.44 | 2,190,264 | 3672 | 73,440 | 4,704,000 | 309,331 |

2017 | 47 | 49 | 117,600 | 505,906 | 0.53 | 2,016,107 | 3930 | 78,600 | 4,900,000 | 313,002 |

2018 | 58 | 61 | 146,000 | 427,432 | 0.46 | 1,785,322 | 3849 | 76,980 | 5,856,000 | 148,554 |

2019 | 45 | 48 | 115,000 | 390,278 | 0.42 | 981,066 | 3126 | 62,250 | 4,608,000 | 86,743 |

2020 | 27 | 30 | 73,000 | 248,505 | 0.45 | 925,000 | 2168 | 43,360 | 2,880,000 | −205,389 |

Year-DMU | Input Parameters | Output Parameters | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Number of Vehicles | Number of Drivers | Number of Operating Hours | Vehicle Maintenance Costs | Fuel Costs Per kilometers Traveled | Transport Staff Costs | Total Number of Deliveries | Quantity TRANSPORTED | Kilometers Traveled | Profit | |

2013 | 12 | 13 | 31,000 | 25,000 | 0.54 | 200,000 | 1741 | 34,800 | 1,150,000 | 97,000 |

2014 | 14 | 14 | 36,000 | 27,000 | 0.52 | 240,000 | 2007 | 40,100 | 1,344,000 | 170,000 |

2015 | 16 | 16 | 41,500 | 32,000 | 0.47 | 260,000 | 2230 | 44,500 | 1,530,000 | 301,000 |

2016 | 20 | 22 | 51,800 | 54,000 | 0.37 | 220,000 | 2744 | 54,000 | 1,920,000 | 319,000 |

2017 | 23 | 23 | 55,000 | 61,000 | 0.37 | 245,000 | 2995 | 58,000 | 2,100,000 | 196,000 |

2018 | 19 | 21 | 50,400 | 53,000 | 0.48 | 180,000 | 2662 | 53,200 | 1,820,000 | 110,000 |

2019 | 16 | 17 | 41,000 | 40,000 | 0.5 | 130,000 | 2214 | 44,000 | 1,500,000 | 12,000 |

2020 | 12 | 13 | 31,000 | 35,000 | 0.4 | 155,000 | 1675 | 33,500 | 1,250,000 | 33,000 |

DEA | PCA–DEA | ||||
---|---|---|---|---|---|

6-4 | 3-3 | 3-2 | 2-2 | 1-1 | |

DMU_{1} | 0.966 | 0.942 | 0.756 | 0.609 | 0.593 |

DMU_{2} | 1.000 | 1.000 | 0.722 | 0.616 | 0.524 |

DMU_{3} | 0.969 | 0.954 | 0.900 | 0.842 | 0.532 |

DMU_{4} | 1.000 | 1.000 | 1.000 | 0.953 | 0.496 |

DMU_{5} | 1.000 | 1.000 | 0.941 | 0.881 | 0.530 |

DMU_{6} | 1.000 | 1.000 | 1.000 | 1.000 | 0.475 |

DMU_{7} | 1.000 | 1.000 | 0.936 | 0.935 | 0.485 |

DMU_{8} | 0.987 | 0.939 | 0.682 | 0.633 | 0.416 |

DMU_{9} | 1.000 | 0.989 | 0.987 | 0.985 | 0.807 |

DMU_{10} | 1.000 | 1.000 | 1.000 | 1.000 | 0.888 |

DMU_{11} | 1.000 | 1.000 | 1.000 | 1.000 | 0.970 |

DMU_{12} | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

DMU_{13} | 1.000 | 1.000 | 1.000 | 1.000 | 0.950 |

DMU_{14} | 1.000 | 1.000 | 1.000 | 0.999 | 0.888 |

DMU_{15} | 1.000 | 1.000 | 1.000 | 0.997 | 0.821 |

DMU_{16} | 1.000 | 1.000 | 0.980 | 0.980 | 0.817 |

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | |
---|---|---|---|---|---|---|---|---|---|---|

C_{j} | 1.636 | 1.692 | 1.697 | 5.549 | 2.561 | 4.555 | 1.848 | 1.854 | 1.644 | 2.797 |

w_{j} | 0.063 | 0.065 | 0.066 | 0.215 | 0.099 | 0.176 | 0.072 | 0.072 | 0.064 | 0.108 |

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | |
---|---|---|---|---|---|---|---|---|---|---|

C_{j} | 1.511 | 1.726 | 1.637 | 5.833 | 2.374 | 4.165 | 1.537 | 1.575 | 1.482 | 2.530 |

w_{j} | 0.062 | 0.071 | 0.067 | 0.239 | 0.097 | 0.171 | 0.063 | 0.065 | 0.061 | 0.104 |

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | |
---|---|---|---|---|---|---|---|---|---|---|

TC1 | 0.071 | 0.071 | 0.069 | 0.148 | 0.066 | 0.139 | 0.056 | 0.056 | 0.065 | 0.258 |

TC2 | 0.057 | 0.061 | 0.056 | 0.170 | 0.059 | 0.110 | 0.052 | 0.051 | 0.052 | 0.332 |

Both companies | 0.073 | 0.072 | 0.071 | 0.227 | 0.049 | 0.214 | 0.044 | 0.044 | 0.077 | 0.127 |

S_{i} | K_{i}^{−} | K_{i}^{+} | fK^{−} | fK^{+} | fKi^{+} | Rank | |
---|---|---|---|---|---|---|---|

AAI | 0.253 | 1.000 | |||||

DMU6 | 0.590 | 2.336 | 0.590 | 0.202 | 0.798 | 0.5615 | 5 |

DMU10 | 0.635 | 2.513 | 0.635 | 0.202 | 0.798 | 0.6042 | 3 |

DMU11 | 0.650 | 2.574 | 0.650 | 0.202 | 0.798 | 0.6187 | 2 |

DMU12 | 0.656 | 2.595 | 0.656 | 0.202 | 0.798 | 0.6239 | 1 |

DMU13 | 0.591 | 2.339 | 0.591 | 0.202 | 0.798 | 0.5623 | 4 |

AI | 1.000 | 1.000 |

MARCOS | WASPAS | ARAS | EDAS | |||||
---|---|---|---|---|---|---|---|---|

fK_{i} | Rank | A | Rank | K_{i} | Rank | AS_{i} | Rank | |

DMU6 | 0.562 | 5 | 0.464 | 5 | 0.615 | 1 | 0.500 | 5 |

DMU10 | 0.604 | 3 | 0.589 | 3 | 0.604 | 4 | 0.734 | 4 |

DMU11 | 0.619 | 2 | 0.617 | 2 | 0.613 | 2 | 0.770 | 2 |

DMU12 | 0.624 | 1 | 0.627 | 1 | 0.611 | 3 | 0.792 | 1 |

DMU13 | 0.562 | 4 | 0.572 | 4 | 0.558 | 5 | 0.740 | 3 |

Both Companies | |||
---|---|---|---|

DMU_{1} | 0.609 | DMU_{9} | 0.985 |

DMU_{2} | 0.616 | DMU_{10} | 1.000 |

DMU_{3} | 0.842 | DMU_{11} | 1.000 |

DMU_{4} | 0.953 | DMU_{12} | 1.000 |

DMU_{5} | 0.881 | DMU_{13} | 1.000 |

DMU_{6} | 1.000 | DMU_{14} | 0.999 |

DMU_{7} | 0.935 | DMU_{15} | 0.997 |

DMU_{8} | 0.633 | DMU_{16} | 0.980 |

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**MDPI and ACS Style**

Stević, Ž.; Miškić, S.; Vojinović, D.; Huskanović, E.; Stanković, M.; Pamučar, D.
Development of a Model for Evaluating the Efficiency of Transport Companies: PCA–DEA–MCDM Model. *Axioms* **2022**, *11*, 140.
https://doi.org/10.3390/axioms11030140

**AMA Style**

Stević Ž, Miškić S, Vojinović D, Huskanović E, Stanković M, Pamučar D.
Development of a Model for Evaluating the Efficiency of Transport Companies: PCA–DEA–MCDM Model. *Axioms*. 2022; 11(3):140.
https://doi.org/10.3390/axioms11030140

**Chicago/Turabian Style**

Stević, Željko, Smiljka Miškić, Dragan Vojinović, Eldina Huskanović, Miomir Stanković, and Dragan Pamučar.
2022. "Development of a Model for Evaluating the Efficiency of Transport Companies: PCA–DEA–MCDM Model" *Axioms* 11, no. 3: 140.
https://doi.org/10.3390/axioms11030140