Application of the DEA Model in Tourism SMEs: An Empirical Study from Slovakia in the Context of Business Sustainability
Abstract
:1. Introduction
2. Literature Review
2.1. Corporate Efficiency–Theory Background
2.2. Approaches to Measuring Business Efficiency
- The ratios—by [44], the ratios are the most common method of efficiency evaluation, as their relatively simple quantification is based on the current financial statements. Their biggest drawback is that they focus only on a limited number of factors that do not have a sufficient impact on the overall efficiency of the production unit. However, they are useful for the basic orientation of the operation of the monitored unit. For a more detailed analysis of efficiency, it is then necessary to use more complex tools of economic analysis based on mathematical modelling.
- Parametric methods—a group of parametric methods is stochastic in nature, i.e., they contain at least one random component. The aim of the methods is to distinguish inefficiency from the effects of random errors, related to a higher reliability of the final results. Their disadvantage is that the given methods define a specific functional dependence, which determines the shape and course of the efficiency limit. If these assumptions do not correspond to reality and the functional dependence is not defined correctly, the final results may be damaged by specific errors and the final results are distorted. The methods quantify economic efficiency, such as stochastic frontier approach, distribution free approach, thick frontier analysis, corrected ordinary least squares.
- Nonparametric methods—a group of nonparametric methods is of a deterministic nature, i.e., they do not contain any random component. Therefore, it is not possible to effectively eliminate the negative consequences of accidental errors, measurement errors or incomplete data in the quantification of efficiency. With these methods, the assumptions for production technology are not as strict as with parametric methods, therefore a higher degree of freedom is permissible for the examined units. Compared to parametric methods, this group quantifies not economic but technical efficiency. The group includes methods such as DEA, free disposal hull, stochastic data envelopment analysis [45].
2.3. Data Envelopment Analysis and Its Use
3. Materials and Methods
3.1. Description of the Research Sample
3.2. Data and Methods
3.3. Construction of the DEA Model and the Input/Output Variables
3.4. Selection of Input and Output Variables
- (a)
- Total number of beds (Input_01)—bed stock of spa facilities, including year-round and seasonal beds, properly equipped with linen and other accessories and complying with medical requirements and regulations.
- (b)
- Total number of employees (Input_02)—total recalculated number of employees working in a spa care facility, regardless their job and classification.
- (c)
- Number of medical staff (Input_03)—the total recalculated number of employees working in a spa care as doctors, nurses, physiotherapists, nurse assistants and nutritionists.
- (d)
- Use of bed capacity (Output_01)—is given by the ratio of the number of treatment days and the actual bed capacity in the number of treatment days, expressed in%.
- (e)
- Number of treated clients (Output_02)—the total number of treated clients (in a calendar year), provided with comprehensive health care in a given spa facility, regardless of the method of payment and the country of origin.
4. Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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DEA Model | Mathematical Formulation | ||
---|---|---|---|
CCR-I input-oriented model | Maximize | , | |
Subject to | ui ≥ ε, vj ≥ ε, | k = 1, 2, …, n, i = 1, 2, …, r, j = 1, 2, …, m. | |
CCR-O output-oriented model | Minimize | , | |
Subject to | ui ≥ ε, vj ≥ ε, | k = 1, 2, …, n, i = 1, 2, …, r, j = 1, 2, …, m. | |
BCC-I input-oriented model | Maximize | , | |
Subject to | ui ≥ ε, vj ≥ ε, μ-random | k = 1, 2, …, n, i = 1, 2, …, r, j = 1, 2, …, m, | |
BCC-O output-oriented model | Minimize | , | |
Subject to | ui ≥ ε, vj ≥ ε, μ-random | k = 1, 2, …, n, i = 1, 2, …, r, j = 1, 2, …, m, |
Input_1 | Input_2 | Input_3 | Output_1 | Output_2 | |
---|---|---|---|---|---|
Input_1 | 1.0000 | ||||
Input_2 | 0.6137 | 1.0000 | |||
Input_3 | 0.4412 | 0.5723 | 1.0000 | ||
Output_1 | 0.4740 | 0.5768 | 0.4266 | 1.0000 | |
Output_2 | 0.5778 | 0.6265 | 0.4858 | 0.3145 | 1.0000 |
Spa Enterprise | Efficiency Scores | Average Ranking | ||||||
---|---|---|---|---|---|---|---|---|
CCR-I | CCR-O | BCC-I | BCC-O | CCR-I | CCR-O | BCC-I | BCC-O | |
SE01 | 0.6556 | 0.6556 | 0.7030 | 0.8771 | 12. | 12. | 14. | 13. |
SE02 | 0.5630 | 0.5630 | 0.5984 | 0.7164 | 13. | 13. | 15. | 18. |
SE03 | 0.7573 | 0.7573 | 0.8617 | 0.9569 | 6. | 6. | 8. | 8. |
SE04 | 0.4075 | 0.4075 | 0.5328 | 0.8641 | 19. | 19. | 17. | 14. |
SE05 | 0.7238 | 0.7238 | 0.7757 | 0.9172 | 9. | 9. | 10. | 9. |
SE06 | 0.4979 | 0.4979 | 0.8779 | 0.9712 | 15. | 15. | 7. | 7. |
SE07 | 0.7460 | 0.7460 | 0.7674 | 0.8839 | 7. | 7. | 11. | 12. |
SE08 | 0.7106 | 0.7106 | 0.7631 | 0.8991 | 10. | 10. | 12. | 10. |
SE09 | 0.4498 | 0.4498 | 0.4582 | 0.7716 | 17. | 17. | 20. | 17. |
SE10 | 0.4344 | 0.4344 | 0.5005 | 0.6197 | 18. | 18. | 18. | 21. |
SE11 | 0.4068 | 0.4068 | 0.4126 | 0.7127 | 20. | 20. | 21. | 19. |
SE12 | 0.4836 | 0.4836 | 0.4999 | 0.8207 | 16. | 16. | 19. | 15. |
SE13 | 0.6774 | 0.6774 | 0.7166 | 0.8191 | 11. | 11. | 13. | 16. |
SE14 | 0.5322 | 0.5322 | 0.5536 | 0.7047 | 14. | 14. | 16. | 20. |
SE15 | 0.3924 | 0.3924 | 1.0000 | 1.0000 | 21. | 21. | 1. | 1. |
SE16 | 1,.0000 | 1.0000 | 1.0000 | 1.0000 | 1. | 1. | 1. | 1. |
SE17 | 0.7704 | 0.7704 | 1.0000 | 1.0000 | 5. | 5. | 1. | 1. |
SE18 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1. | 1. | 1. | 1. |
SE19 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1. | 1. | 1. | 1. |
SE20 | 0.7418 | 0.7418 | 0.7845 | 0.8927 | 8. | 8. | 9. | 11. |
SE21 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1. | 1. | 1. | 1. |
Efficiency Scores (BCC-I DEA Model) | ||||||
---|---|---|---|---|---|---|
2013 | 2014 | 2015 | 2016 | 2017 | 2018 | |
Min | 0.4483 | 0.4368 | 0.3724 | 0.4120 | 0.4053 | 0.3744 |
Median | 0.7215 | 0.7293 | 0.7269 | 0.7561 | 0.7195 | 0.6983 |
Mean | 0.7550 | 0.7573 | 0.7687 | 0.7577 | 0.7503 | 0.7269 |
Max | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
Standard deviation | 0.2248 | 0.2078 | 0.2132 | 0.2089 | 0.2312 | 0.2189 |
Year | Input_01 | Input_02 | Input_03 | ||||||
---|---|---|---|---|---|---|---|---|---|
Actual Value | Optimum Value | % Change | Actual Value | Optimum Value | % Change | Actual Value | Optimum Value | % Change | |
2013 | 541.05 | 417.01 | −24.71 | 188.03 | 143.54 | −27.06 | 55.34 | 40.20 | −32.11 |
2014 | 544.14 | 387.62 | −29.58 | 186.97 | 143.82 | −27.32 | 54.03 | 37.69 | −34.32 |
2015 | 543.14 | 397.76 | −27.01 | 186.63 | 146.24 | −25.26 | 53.22 | 37.09 | −34.07 |
2016 | 539.71 | 356.76 | −32.07 | 187.20 | 145.41 | −26.57 | 52.34 | 35.81 | −34.88 |
2017 | 551.48 | 359.18 | −32.33 | 191.48 | 146.90 | −26.95 | 53.25 | 36.15 | −34.42 |
2018 | 550.33 | 351.97 | −34.36 | 193.70 | 144.10 | −30.10 | 48.88 | 33.36 | −34.33 |
Spa Enterprise | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | Average Ranking (2013–2018) | Change (2013–2018) |
---|---|---|---|---|---|---|---|---|
SE01 | 13. | 12. | 14. | 12. | 11. | 11. | 13. | ↑ 2 |
SE02 | 14. | 15. | 16. | 17. | 16. | 16. | 15. | ↓ 2 |
SE03 | 1. | 7 | 8. | 9. | 10. | 13. | 8. | ↓ 12 |
SE04 | 21. | 19. | 15. | 14. | 19. | 17. | 17. | ↑ 4 |
SE05 | 9. | 11. | 10. | 10. | 12. | 10. | 11. | ↓ 1 |
SE06 | 15. | 14. | 1. | 1. | 1. | 7. | 7. | ↑ 8 |
SE07 | 12. | 8. | 9. | 13. | 13. | 9. | 10. | ↑ 3 |
SE08 | 10. | 13. | 13. | 8. | 9. | 12. | 12. | ↓ 2 |
SE09 | 19. | 18. | 20. | 19. | 20. | 21. | 20. | ↓ 2 |
SE10 | 16. | 17. | 17. | 18. | 17. | 19. | 19. | ↓ 3 |
SE11 | 20. | 21. | 21. | 21. | 21. | 20. | 21. | ↓↑ 0 |
SE12 | 17. | 16. | 19. | 20. | 18. | 18. | 18. | ↓ 1 |
SE13 | 1. | 9. | 11. | 16. | 15. | 15. | 14. | ↓ 14 |
SE14 | 18. | 20. | 18. | 15. | 14. | 14. | 16. | ↑ 4 |
SE15 | 1. | 1. | 1. | 1. | 1. | 1. | 1. | ↓↑ 0 |
SE16 | 1. | 1. | 1. | 1. | 1. | 1. | 1. | ↓↑ 0 |
SE17 | 1. | 1. | 1. | 1. | 1. | 1. | 1. | ↓↑ 0 |
SE18 | 1. | 1. | 1. | 1. | 1. | 1. | 1. | ↓↑ 0 |
SE19 | 1. | 1. | 1. | 1. | 1. | 1. | 1. | ↓↑ 0 |
SE20 | 11. | 10. | 12. | 11. | 1. | 8. | 9. | ↑ 3 |
SE21 | 1. | 1. | 1. | 1. | 1. | 1. | 1. | ↓↑ 0 |
Authors | Country | Inputs | Outputs |
---|---|---|---|
[81] | Greece | Number of doctors and nurses in the hospital | Number of medical examinations, laboratory tests and transfers from medical centers to hospitals |
[70] | Czech Republic | Amount of operating costs | Number of beds, number of hospitalized patients, use of bed (in days) |
[49] | Hungary | Number of beds, doctors, nurses and other professional staff | Number of days spent by patients on the ward, number of discharged patients |
[82] | Poland | Average length of hospital stay (in days), average cost of daily hospital care | Average number of patients per bed, share of accredited hospitals in total, net annual income of the doctor |
[83] | Iran | Number of doctors, number of nurses, number of active beds and facilities | Bed occupancy rate, number of patients discharged, price per bed, doctors’ fees |
[56] | Italy | Number of beds, number of employees, number of doctors, nurses and other medical staff, operating costs | Number of hospital days, number of outpatient visits |
[84] | China | Number of beds, number of medical technicians | Sales, number of discharged patients, number of outpatient visits |
Authors | Country | Inputs | Outputs |
---|---|---|---|
[86] | Spain | Assets, material costs, labor costs | EBIT |
[57] | Croatia | Energy costs, costs per room, food and beverage costs, costs associated with other services, labor costs | Sales, occupancy rate |
[65] | Spain | Number of employees, labor costs, number of rooms | Sales, amount of sales per room, market share |
[50] | Greece | Number of local units, number of employees, investments | Sales |
[87] | Italy | Tangible assets, intangible assets, labor costs | Sales |
[88] | Spain | labor costs, depreciation, operating costs | Sales |
[63] | Ecuador | Number of employees, fixed assets, consumption costs | Sales |
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Dobrovič, J.; Čabinová, V.; Gallo, P.; Partlová, P.; Váchal, J.; Balogová, B.; Orgonáš, J. Application of the DEA Model in Tourism SMEs: An Empirical Study from Slovakia in the Context of Business Sustainability. Sustainability 2021, 13, 7422. https://doi.org/10.3390/su13137422
Dobrovič J, Čabinová V, Gallo P, Partlová P, Váchal J, Balogová B, Orgonáš J. Application of the DEA Model in Tourism SMEs: An Empirical Study from Slovakia in the Context of Business Sustainability. Sustainability. 2021; 13(13):7422. https://doi.org/10.3390/su13137422
Chicago/Turabian StyleDobrovič, Ján, Veronika Čabinová, Peter Gallo, Petra Partlová, Jan Váchal, Beáta Balogová, and Jozef Orgonáš. 2021. "Application of the DEA Model in Tourism SMEs: An Empirical Study from Slovakia in the Context of Business Sustainability" Sustainability 13, no. 13: 7422. https://doi.org/10.3390/su13137422
APA StyleDobrovič, J., Čabinová, V., Gallo, P., Partlová, P., Váchal, J., Balogová, B., & Orgonáš, J. (2021). Application of the DEA Model in Tourism SMEs: An Empirical Study from Slovakia in the Context of Business Sustainability. Sustainability, 13(13), 7422. https://doi.org/10.3390/su13137422