**3. Results**

### **3.1. Technical and scale efficiency**

Technical and scale efficiency were determined individually for each forest office. Results obtained by the application of the output-oriented DEA are given in table 3.

The average CCR efficiency of the investigated forest offices is 0.829, which means that an average (assumed) forest office should only use 82.9% of the currently used quantity of inputs and produce the same quantity of the currently produced outputs, if it wishes to do business at the efficiency frontier. In other words, this average organisational unit, if it wishes to do

According to the BCC model, the average efficiency is 0.904. This means that an average forest office should only use 90.4% of the current input and produce the same quantity of output, if it wishes to be efficient. In other words, to be BCC efficient it should produce 10.6%4 more

In spite of a relatively high mean efficiency (83 or 90%) and regardless of the used model (CCR or BCC), the lowest level of relative efficiency ranges between 0.407 (CCR) and 0.524 (BCC). This implies firstly that individual units can reduce the level of used input up to 59.3% or 47.6%, without affecting the output level, and secondly that there are significant differences

According to the CCR model, 15 forest offices are relatively efficient (31%), while a total of 24 units (50%) are rated '1' according to the BCC model. Incompatibility between CCR and BCC efficiency is most conspicuous with forest offices with extremely low values of one or more input variables. According to the model with variable returns (BCC), the efficiency of such units is much higher than according to the model with constant returns (CCR). This may indicate the influence of size or volume of activities of the observed units on the level of their efficiency, but it can also mean that the BCC model with the selected input and output variables cannot make proper distinction between efficient and inefficient units. Such results may, however, also be useful if additional models of decision making are applied. The results of DEA analysis may then be used as the first filter of inefficient units. The survey of DEA results

Number of forest offices (DMU) 48 48 48 Relatively efficient DMUs 15 24 16 Relatively efficient DMUs (in %) 31 % 50 % 33 % Average relative efficiency, E 0.829 0.904 0.919 Maximum 1 1 1 Minimum 0.407 0.524 0.501 Standard deviation 1.170 0.129 0.138 DMUs with efficiency lower than E 23 18 12

in production and business activities between the analysed units.

more output with the same input level.

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**CCR model BCC model Scale eff. (SE)**

business efficiently, should produce 20.6%3

outputs with the same inputs.

is given in Table 4.

**Table 4.** Results obtained with the base case DEA models

3 It can be easily obtained that 20.6 % = (1 – 0.829)/0.829 4 It can be easily obtained that 10.6 % = (1 – 0.904)/0.904


**Table 3.** Relative efficiency of Forest offices

The average CCR efficiency of the investigated forest offices is 0.829, which means that an average (assumed) forest office should only use 82.9% of the currently used quantity of inputs and produce the same quantity of the currently produced outputs, if it wishes to do business at the efficiency frontier. In other words, this average organisational unit, if it wishes to do business efficiently, should produce 20.6%3 more output with the same input level.

According to the BCC model, the average efficiency is 0.904. This means that an average forest office should only use 90.4% of the current input and produce the same quantity of output, if it wishes to be efficient. In other words, to be BCC efficient it should produce 10.6%4 more outputs with the same inputs.

In spite of a relatively high mean efficiency (83 or 90%) and regardless of the used model (CCR or BCC), the lowest level of relative efficiency ranges between 0.407 (CCR) and 0.524 (BCC). This implies firstly that individual units can reduce the level of used input up to 59.3% or 47.6%, without affecting the output level, and secondly that there are significant differences in production and business activities between the analysed units.

According to the CCR model, 15 forest offices are relatively efficient (31%), while a total of 24 units (50%) are rated '1' according to the BCC model. Incompatibility between CCR and BCC efficiency is most conspicuous with forest offices with extremely low values of one or more input variables. According to the model with variable returns (BCC), the efficiency of such units is much higher than according to the model with constant returns (CCR). This may indicate the influence of size or volume of activities of the observed units on the level of their efficiency, but it can also mean that the BCC model with the selected input and output variables cannot make proper distinction between efficient and inefficient units. Such results may, however, also be useful if additional models of decision making are applied. The results of DEA analysis may then be used as the first filter of inefficient units. The survey of DEA results is given in Table 4.


**Table 4.** Results obtained with the base case DEA models

**3. Results**

**DMU**

**3.1. Technical and scale efficiency**

464 Computational and Numerical Simulations

**Table 3.** Relative efficiency of Forest offices

Technical and scale efficiency were determined individually for each forest office. Results

1. Gunja 1.000 1.000 1.000 25. Gerovo 0.814 0.836 0.974 2. Otok 1.000 1.000 1.000 26. Gomirje 0.721 0.726 0.993 3. Strizivojna 0.831 0.926 0.897 27. Klana 0.807 0.820 0.984 4. Strošinci 0.826 0.865 0.955 28. Mrkopalj 0.810 0.827 0.979 5. Vinkovci 1.000 1.000 1.000 29. Prezid 0.738 0.762 0.969 6. Županja 1.000 1.000 1.000 30. R. Gora 0.755 0.782 0.965 7. N. Gradiška 0.952 0.981 0.970 31. Brinje 0.866 0.883 0.981 8. N. Kapela 0.677 0.723 0.936 32. D. Lapac 0.990 1.000 0.990 9. Novska 0.924 0.929 0.995 33. Gospić 0.984 0.996 0.988 10. Okučani 1.000 1.000 1.000 34. Gračac 0.779 0.786 0.992 11. S. Brod 1.000 1.000 1.000 35. Korenica 1.000 1.000 1.000 12. Trnjani 0.561 0.590 0.951 36. Udbina 1.000 1.000 1.000 13. D. Stubica 1.000 1.000 1.000 37. Buje 0.745 1.000 0.745 14. Krapina 1.000 1.000 1.000 38. Buzet 0.501 1.000 0.501 15. Novoselec 1.000 1.000 1.000 39. C-Lošinj 0.695 1.000 0.695 16. Popovača 0.879 0.897 0.981 40. Opatija 0.500 0.593 0.844 17. Samobor 1.000 1.000 1.000 41. Poreč 0.568 1.000 0.568 18. Zagreb 0.756 0.769 0.984 42. Rovinj 0.595 1.000 0.595 19. Čakovec 1.000 1.000 1.000 43. Brač 0.538 1.000 0.538 20. Ivanec 1.000 1.000 1.000 44. Dubrovnik 0.813 1.000 0.813 21. Koprivnica 0.645 0.645 1.000 45. Makarska 0.956 1.000 0.956 22. Križevci 0.898 0.904 0.994 46. Sinj 1.000 1.000 1.000 23. Ludbreg 0.816 0.819 0.996 47. Šibenik 0.591 0.867 0.682 24. Varaždin 0.407 0.524 0.777 48. Zadar 0.843 0.924 0.913

**DMU**

**CCR BCC SE CCR BCC SE**

**Efficiency**

obtained by the application of the output-oriented DEA are given in table 3.

**Efficiency**

<sup>3</sup> It can be easily obtained that 20.6 % = (1 – 0.829)/0.829

<sup>4</sup> It can be easily obtained that 10.6 % = (1 – 0.904)/0.904

The interpretation of scale efficiency scores allows for some interesting remarks. Scale efficiency shows how close or far the size of the observed unit is from its optimal size. The efficiency of 100% indicates that the size and volume of activities are well balanced. The values lower than 100% mean that the level of technical efficiency is at least partly under influence of size or volume of activities of the observed unit.

In the period concerned the observed units should have produced on average 25.64% more than the produced quantity of output O1, 168.04% more than the produced quantity of the second output O2, 119.45% more than output O3 and 67.61% more than the produced quantity of output O4. Similarly, they should have used 85.48% of the used quantity of the first input I1, 93.47% of the quantity of output I2, 96.60% of the third input I3 and 96.94% of the used

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For achieving BCC efficiency, it was necessary to produce on average 18.68% more than the produced quantity of the first output I1, 58.94% more than the second output O2, 107.23% more than output O3 and 56.03% more than output O4. With such an average increase of output,

It should be noted that the projected values are achievable because some forest offices involved

Forest offices differ among themselves in a series of structural characteristics and hence professional and technical operations are carried out in different conditions with respect to the surface area, number of employees, means of work, growing stock, etc. Differences between the basic structural characteristics of the analysed forest offices are shown in Table 1 and 2. Based on the efficiency results of forest offices grouped according to the values of their basic structural characteristics – surface area, growing stock and number of employees, it has been determined to what extent the given environment affects the efficiency of specific units.

The average efficiency with respect to surface area was determined as the arithmetic mean of the efficiency of forest offices that belong to a certain surface area class (Figure 4). The highest levels of efficiency according to all three models were recorded for forest offices that manage a surface area ranging between 10 and 15,000 hectares (the average efficiency is 0.969 according to the CCR model, 0.977 according to the BCC model and 0.991 according to the SE model). The lowest levels of efficiency were determined for the group of forest offices with a surface

The volume of the managed growing stock was taken as the second criteria for grouping the analysed units. Forest offices are divided into classes with respect to the growing stock

the lowest average relative efficiency, according to the CCR and SE model (0.676 and 0.689, respectively). According to these models the highest level of efficiency is recorded for forest

/ha and it was not separated in a special class but was included in the group IV.

Forest offices that manage the lowest growing stock volume (less than 100 m3

offices with growing stock ranging between 200 and 300 m3

and 0.984 (SE) for the group III (200-300 m3

per hectare, and the average efficiency of individual classes is presented in

/ha i.e. over 300 m3

/ha). Only one forest office manages the growing stock exceeding

/ha) and 0.824 (CCR) and 0.980 (SE) for the group

/ha) also have

/ha – 0.890 (CCR)

the observed forest offices would do business efficiently according to the BCC model.

quantity of input I4. Then they would be CCR-efficient.

**3.3. Structural characteristics and efficiency of forest offices**

in the analysis achieved them successfully.

area from 5 to 10,000 hectares.

IV of forest offices (> 300 m3

expressed in m3

Figure 5.

400 m3

The scale efficiency of 0.919 means that the analysed forest offices would increase their relative efficiency on average by 8% if they adapted their size or volume of activities to the optimal value. Relatively efficient are 16 (33%) units. Almost all of them (15) are also efficient according to the CCR model (Table 3). Forest offices that are efficient only according to the BCC model (Table 3) do not show the same efficiency level in case of determination of scale efficiency. This indicates their inadequate size or inadequate volume of activities expressed by the main parameters of their production and business performance. These are mostly the units with low values of one or more input and output variables – Karst/Mediterranean forest offices with low growing stock, number of employees, annual cut, etc.

### **3.2. Sources and values of inefficiency**

By selecting output-oriented models projection course of inefficient units against the efficiency frontier was determined. By comparing empirical and projected data, it is possible to identify the sources of inefficiency as well as their value. The lower the percentage of projected input values in empirical input values, the higher is on average the source of inefficiency caused by this input. The higher the percentage of projected output values in empirical output values, the higher is the source of inefficiency caused by this output. Table 5 shows percentage shares of average projected values in total empirical input and output values of CCR and BCC model.


**Table 5.** Sources and average amounts of inefficiency, CCR and BCC model

It can be concluded from the above Table that the second and third output – annual cut and investments - affect the inefficiency of forest offices most seriously. Then follow the activities of forest regeneration and achieved income with a somewhat lower impact on inefficiency of forest offices.

In the period concerned the observed units should have produced on average 25.64% more than the produced quantity of output O1, 168.04% more than the produced quantity of the second output O2, 119.45% more than output O3 and 67.61% more than the produced quantity of output O4. Similarly, they should have used 85.48% of the used quantity of the first input I1, 93.47% of the quantity of output I2, 96.60% of the third input I3 and 96.94% of the used quantity of input I4. Then they would be CCR-efficient.

For achieving BCC efficiency, it was necessary to produce on average 18.68% more than the produced quantity of the first output I1, 58.94% more than the second output O2, 107.23% more than output O3 and 56.03% more than output O4. With such an average increase of output, the observed forest offices would do business efficiently according to the BCC model.

It should be noted that the projected values are achievable because some forest offices involved in the analysis achieved them successfully.

### **3.3. Structural characteristics and efficiency of forest offices**

The interpretation of scale efficiency scores allows for some interesting remarks. Scale efficiency shows how close or far the size of the observed unit is from its optimal size. The efficiency of 100% indicates that the size and volume of activities are well balanced. The values lower than 100% mean that the level of technical efficiency is at least partly under influence of

The scale efficiency of 0.919 means that the analysed forest offices would increase their relative efficiency on average by 8% if they adapted their size or volume of activities to the optimal value. Relatively efficient are 16 (33%) units. Almost all of them (15) are also efficient according to the CCR model (Table 3). Forest offices that are efficient only according to the BCC model (Table 3) do not show the same efficiency level in case of determination of scale efficiency. This indicates their inadequate size or inadequate volume of activities expressed by the main parameters of their production and business performance. These are mostly the units with low values of one or more input and output variables – Karst/Mediterranean forest offices with

By selecting output-oriented models projection course of inefficient units against the efficiency frontier was determined. By comparing empirical and projected data, it is possible to identify the sources of inefficiency as well as their value. The lower the percentage of projected input values in empirical input values, the higher is on average the source of inefficiency caused by this input. The higher the percentage of projected output values in empirical output values, the higher is the source of inefficiency caused by this output. Table 5 shows percentage shares of average projected values in total empirical input and output values of CCR and BCC model.

**Inputs/Outputs CCR BCC**

Area. I1 85.48 93.85 G. stock. I2 93.47 98.06 Costs. I3 96.60 96.64 Employees. I4 96.94 97.37

Income. O1 125.64 118.68 Harvest. O2 268.04 158.94 Investments. O3 219.45 207.23 B. renewal. O4 167.61 156.03

It can be concluded from the above Table that the second and third output – annual cut and investments - affect the inefficiency of forest offices most seriously. Then follow the activities of forest regeneration and achieved income with a somewhat lower impact on inefficiency of

size or volume of activities of the observed unit.

466 Computational and Numerical Simulations

low growing stock, number of employees, annual cut, etc.

**Table 5.** Sources and average amounts of inefficiency, CCR and BCC model

**3.2. Sources and values of inefficiency**

*Inputs*

*Outputs*

forest offices.

Forest offices differ among themselves in a series of structural characteristics and hence professional and technical operations are carried out in different conditions with respect to the surface area, number of employees, means of work, growing stock, etc. Differences between the basic structural characteristics of the analysed forest offices are shown in Table 1 and 2. Based on the efficiency results of forest offices grouped according to the values of their basic structural characteristics – surface area, growing stock and number of employees, it has been determined to what extent the given environment affects the efficiency of specific units.

The average efficiency with respect to surface area was determined as the arithmetic mean of the efficiency of forest offices that belong to a certain surface area class (Figure 4). The highest levels of efficiency according to all three models were recorded for forest offices that manage a surface area ranging between 10 and 15,000 hectares (the average efficiency is 0.969 according to the CCR model, 0.977 according to the BCC model and 0.991 according to the SE model). The lowest levels of efficiency were determined for the group of forest offices with a surface area from 5 to 10,000 hectares.

The volume of the managed growing stock was taken as the second criteria for grouping the analysed units. Forest offices are divided into classes with respect to the growing stock expressed in m3 per hectare, and the average efficiency of individual classes is presented in Figure 5.

Forest offices that manage the lowest growing stock volume (less than 100 m3 /ha) also have the lowest average relative efficiency, according to the CCR and SE model (0.676 and 0.689, respectively). According to these models the highest level of efficiency is recorded for forest offices with growing stock ranging between 200 and 300 m3 /ha i.e. over 300 m3 /ha – 0.890 (CCR) and 0.984 (SE) for the group III (200-300 m3 /ha) and 0.824 (CCR) and 0.980 (SE) for the group IV of forest offices (> 300 m3 /ha). Only one forest office manages the growing stock exceeding 400 m3 /ha and it was not separated in a special class but was included in the group IV.

hectares.

hectares.

m3

m3

Relative efficiency

The average efficiency with respect to surface area was determined as the arithmetic mean of the efficiency of forest offices that belong to a certain surface area class (Figure 4). The highest levels of efficiency according to all three models were recorded for forest offices that manage a surface area

The average efficiency with respect to surface area was determined as the arithmetic mean of the efficiency of forest offices that belong to a certain surface area class (Figure 4). The highest levels of efficiency according to all three models were recorded for forest offices that manage a surface area ranging between 10 and 15,000 hectares (the average efficiency is 0.969 according to the CCR model,

efficiency were determined for the group of forest offices with a surface area from 5 to 10,000

Figure 4. Average relative efficiency of forest offices grouped with respect to surface area **Figure 4.** Average relative efficiency of forest offices grouped with respect to surface area The volume of the managed growing stock was taken as the second criteria for grouping the analysed units. Forest offices are divided into classes with respect to the growing stock expressed in

The volume of the managed growing stock was taken as the second criteria for grouping the analysed units. Forest offices are divided into classes with respect to the growing stock expressed in

per hectare, and the average efficiency of individual classes is presented in Figure 5.

Growing stock, m<sup>3</sup> /ha Figure 5. Average relative efficiency of forest offices grouped with respect to growing stock **Figure 5.** Average relative efficiency of forest offices grouped with respect to growing stock

< 100 100-200 200-300 > 300

13 Figure 5. Average relative efficiency of forest offices grouped with respect to growing stock 13 According to the BCC model, the average efficiency of all groups is assessed as relatively high. The highest average efficiency of forest offices with low growing stocks in the Karst and Mediterranean areas is the effect of increasing returns to scale, where it is considered that little increase of input (growing stock, etc.) would result in more than proportional increase of output (income, allowable cut, etc.). This assumption may be considered wrong for the said forest offices, if bad structure and poor quality of growing stock in the Karst and Mediterranean area are taken into account.

14

/ha) also have

/ha and it

469

/ha – 0.890 (CCR) and 0.984

CCR BCC SE

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Forest offices that manage the lowest growing stock volume (less than 100 m<sup>3</sup>

with growing stock ranging between 200 and 300 m<sup>3</sup>

was not separated in a special class but was included in the group IV.

of forest offices with respect to the number of employees is presented in Figure 6.

Figure 6. Average relative efficiency of forest offices according to the number of employees

**Figure 6.** Average relative efficiency of forest offices according to the number of employees

It can be seen that the highest level of CCR and SE efficiency is achieved by Forest offices with the highest number of employees (group IV and V). For forest offices with 61 to 80 employees, the determined BCC, CCR and scale efficiency is 0.914, 0.920 and 0.992, respectively. In the group with more than 80 employees there are only two forest offices and their efficiency is approximately

It can be seen that the highest level of CCR and SE efficiency is achieved by Forest offices with the highest number of employees (group IV and V). For forest offices with 61 to 80 employees, the determined BCC, CCR and scale efficiency is 0.914, 0.920 and 0.992, respectively. In the group with more than 80 employees there are only two forest offices and their efficiency is

0-20 21-40 41-60 61-80 81-100 Number of employees, N

The sample of forest offices included in the analysis comes from eight Forest administrations. Six Forest offices from each selected Forest administration account for 35% (FA Split) to 67% (FA Nova Gradiška and Buzet) of the total number of offices that make individual Forest administrations. The efficiency level of individual Forest administrations is calculated as the weighted arithmetic mean of the pertaining Forest offices' relative efficiency (Figure 7). Surface areas of Forest offices are

The sample of forest offices included in the analysis comes from eight Forest administrations. Six Forest offices from each selected Forest administration account for 35% (FA Split) to 67% (FA Nova Gradiška and Buzet) of the total number of offices that make individual Forest administrations. The efficiency level of individual Forest administrations is calculated as the weighted arithmetic mean of the pertaining Forest offices' relative efficiency (Figure 7). Surface

On average Forest administrations A (0.959), C (0.934) and F (0.916) have the highest relative efficiency according to the CCR model. FA G has the lowest average efficiency (0.613), while the Forest Administrations D, E and H are assessed better with average values between 0.778,

According to the scale efficiency, the Forest administrations A, B, C, D, E and F are assessed similarly, and the level of their average efficiency ranges between 0.963 and 0.993. Like in CCR model, FA G and FA H represent the 'worst' units with average scale efficiency 0.687 and 0.855,

The average efficiency of the most successful forest administration according to the BCC model is 0.974 (A). Then follow Forest administrations H (0.957), C (0.939), F (0.924) and G (0.913).

For success assessment of Forest administrations, besides their average efficiency, it is also important to take into account the number of Forest offices that define the efficiency frontier.

(SE) for the group III (200-300 m<sup>3</sup>

0.985 regardless of the applied model.

areas of Forest offices are taken as weights.

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Relative efficiency

taken as weights.

respectively.

3.4 Relative efficiency of forest administrations and regions

**3.4. Relative efficiency of forest administrations and regions**

and 0.822. FA B (0.868) gets closer to the average efficiency of 90%.

Forest administrations B, D and E have the lowest BCC efficiency.

approximately 0.985 regardless of the applied model.

offices (> 300 m<sup>3</sup>

account.

the lowest average relative efficiency, according to the CCR and SE model (0.676 and 0.689, respectively). According to these models the highest level of efficiency is recorded for forest offices

/ha). Only one forest office manages the growing stock exceeding 400 m<sup>3</sup>

According to the BCC model, the average efficiency of all groups is assessed as relatively high. The highest average efficiency of forest offices with low growing stocks in the Karst and Mediterranean areas is the effect of increasing returns to scale, where it is considered that little increase of input (growing stock, etc.) would result in more than proportional increase of output (income, allowable cut, etc.). This assumption may be considered wrong for the said forest offices, if bad structure and poor quality of growing stock in the Karst and Mediterranean area are taken into

The observed forest offices employ 2,007 workers. Their number ranges from a minimum of 8 workers to a maximum of 100 workers per forest office. The number of workers in individual forest offices is mainly connected with the quantity and volume of production tasks. The average efficiency

/ha i.e. over 300 m<sup>3</sup>

/ha) and 0.824 (CCR) and 0.980 (SE) for the group IV of forest

Nonparametric Model for Business Performance Evaluation in Forestry

The observed forest offices employ 2,007 workers. Their number ranges from a minimum of 8 workers to a maximum of 100 workers per forest office. The number of workers in individual forest offices is mainly connected with the quantity and volume of production tasks. The average efficiency of forest offices with respect to the number of employees is presented in Figure 6.

/ha) also have

/ha and it

/ha – 0.890 (CCR) and 0.984

offices is mainly connected with the quantity and volume of production tasks. The average efficiency

Forest offices that manage the lowest growing stock volume (less than 100 m<sup>3</sup>

with growing stock ranging between 200 and 300 m<sup>3</sup>

was not separated in a special class but was included in the group IV.

(SE) for the group III (200-300 m<sup>3</sup>

offices (> 300 m<sup>3</sup>

account.

the lowest average relative efficiency, according to the CCR and SE model (0.676 and 0.689, respectively). According to these models the highest level of efficiency is recorded for forest offices

/ha). Only one forest office manages the growing stock exceeding 400 m<sup>3</sup>

According to the BCC model, the average efficiency of all groups is assessed as relatively high. The highest average efficiency of forest offices with low growing stocks in the Karst and Mediterranean areas is the effect of increasing returns to scale, where it is considered that little increase of input (growing stock, etc.) would result in more than proportional increase of output (income, allowable cut, etc.). This assumption may be considered wrong for the said forest offices, if bad structure and poor quality of growing stock in the Karst and Mediterranean area are taken into

/ha i.e. over 300 m<sup>3</sup>

/ha) and 0.824 (CCR) and 0.980 (SE) for the group IV of forest

Figure 6. Average relative efficiency of forest offices according to the number of employees **Figure 6.** Average relative efficiency of forest offices according to the number of employees

of forest offices with respect to the number of employees is presented in Figure 6.

It can be seen that the highest level of CCR and SE efficiency is achieved by Forest offices with the highest number of employees (group IV and V). For forest offices with 61 to 80 employees, the determined BCC, CCR and scale efficiency is 0.914, 0.920 and 0.992, respectively. In the group with more than 80 employees there are only two forest offices and their efficiency is approximately 0.985 regardless of the applied model. 3.4 Relative efficiency of forest administrations and regions It can be seen that the highest level of CCR and SE efficiency is achieved by Forest offices with the highest number of employees (group IV and V). For forest offices with 61 to 80 employees, the determined BCC, CCR and scale efficiency is 0.914, 0.920 and 0.992, respectively. In the group with more than 80 employees there are only two forest offices and their efficiency is approximately 0.985 regardless of the applied model.

#### The sample of forest offices included in the analysis comes from eight Forest administrations. Six Forest offices from each selected Forest administration account for 35% (FA Split) to 67% (FA **3.4. Relative efficiency of forest administrations and regions**

13

13

CCR BCC SE

CCR BCC SE

CCR BCC SE

CCR BCC SE

The average efficiency with respect to surface area was determined as the arithmetic mean of the efficiency of forest offices that belong to a certain surface area class (Figure 4). The highest levels of efficiency according to all three models were recorded for forest offices that manage a surface area ranging between 10 and 15,000 hectares (the average efficiency is 0.969 according to the CCR model, 0.977 according to the BCC model and 0.991 according to the SE model). The lowest levels of efficiency were determined for the group of forest offices with a surface area from 5 to 10,000

The average efficiency with respect to surface area was determined as the arithmetic mean of the efficiency of forest offices that belong to a certain surface area class (Figure 4). The highest levels of efficiency according to all three models were recorded for forest offices that manage a surface area ranging between 10 and 15,000 hectares (the average efficiency is 0.969 according to the CCR model, 0.977 according to the BCC model and 0.991 according to the SE model). The lowest levels of efficiency were determined for the group of forest offices with a surface area from 5 to 10,000

Figure 4. Average relative efficiency of forest offices grouped with respect to surface area

Figure 4. Average relative efficiency of forest offices grouped with respect to surface area

per hectare, and the average efficiency of individual classes is presented in Figure 5.

**Figure 4.** Average relative efficiency of forest offices grouped with respect to surface area

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

area are taken into account.

Figure 6.

Relative efficiency

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Relative efficiency

Relative efficiency

468 Computational and Numerical Simulations

Relative efficiency

per hectare, and the average efficiency of individual classes is presented in Figure 5.

Figure 5. Average relative efficiency of forest offices grouped with respect to growing stock

Growing stock, m<sup>3</sup>

**Figure 5.** Average relative efficiency of forest offices grouped with respect to growing stock

< 100 100-200 200-300 > 300

Figure 5. Average relative efficiency of forest offices grouped with respect to growing stock

/ha

According to the BCC model, the average efficiency of all groups is assessed as relatively high. The highest average efficiency of forest offices with low growing stocks in the Karst and Mediterranean areas is the effect of increasing returns to scale, where it is considered that little increase of input (growing stock, etc.) would result in more than proportional increase of output (income, allowable cut, etc.). This assumption may be considered wrong for the said forest offices, if bad structure and poor quality of growing stock in the Karst and Mediterranean

The observed forest offices employ 2,007 workers. Their number ranges from a minimum of 8 workers to a maximum of 100 workers per forest office. The number of workers in individual forest offices is mainly connected with the quantity and volume of production tasks. The average efficiency of forest offices with respect to the number of employees is presented in

/ha

< 100 100-200 200-300 > 300 Growing stock, m<sup>3</sup>

The volume of the managed growing stock was taken as the second criteria for grouping the analysed units. Forest offices are divided into classes with respect to the growing stock expressed in

The volume of the managed growing stock was taken as the second criteria for grouping the analysed units. Forest offices are divided into classes with respect to the growing stock expressed in

< 5 5-10 10-15 > 15 Surface area, 1000 ha

< 5 5-10 10-15 > 15 Surface area, 1000 ha

hectares.

hectares.

m3

m3

Nova Gradiška and Buzet) of the total number of offices that make individual Forest administrations. The efficiency level of individual Forest administrations is calculated as the weighted arithmetic mean of the pertaining Forest offices' relative efficiency (Figure 7). Surface areas of Forest offices are taken as weights. The sample of forest offices included in the analysis comes from eight Forest administrations. Six Forest offices from each selected Forest administration account for 35% (FA Split) to 67% (FA Nova Gradiška and Buzet) of the total number of offices that make individual Forest administrations. The efficiency level of individual Forest administrations is calculated as the weighted arithmetic mean of the pertaining Forest offices' relative efficiency (Figure 7). Surface areas of Forest offices are taken as weights.

14 On average Forest administrations A (0.959), C (0.934) and F (0.916) have the highest relative efficiency according to the CCR model. FA G has the lowest average efficiency (0.613), while the Forest Administrations D, E and H are assessed better with average values between 0.778, and 0.822. FA B (0.868) gets closer to the average efficiency of 90%.

According to the scale efficiency, the Forest administrations A, B, C, D, E and F are assessed similarly, and the level of their average efficiency ranges between 0.963 and 0.993. Like in CCR model, FA G and FA H represent the 'worst' units with average scale efficiency 0.687 and 0.855, respectively.

The average efficiency of the most successful forest administration according to the BCC model is 0.974 (A). Then follow Forest administrations H (0.957), C (0.939), F (0.924) and G (0.913). Forest administrations B, D and E have the lowest BCC efficiency.

For success assessment of Forest administrations, besides their average efficiency, it is also important to take into account the number of Forest offices that define the efficiency frontier. 20 Computational and Numerical Simulations

average efficiency of Karst/Mediterranean forest offices is somewhat higher and namely 0.946. The average scale efficiency of continental regions is relatively uniform and it ranges around 0.980, while in the Karst/Mediterranean area it is much lower and namely 0.816. The average

Nonparametric Model for Business Performance Evaluation in Forestry

http://dx.doi.org/10.5772/57042

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In this very dynamic period of management of natural resources, when forest experts face the challenges of professional and responsible management of forests and forest land, having to observe at the same time the protection requirements of their ecological, social and economic functions, as well as challenges of profitable management of forestry companies, managers need different models for converting the accounting and financial data into useful information. In this paper the models of Data Envelopment Analysis were applied for the assessment and comparison of organisational units in croatian forestry. In applying these models, a number of variables can be taken into consideration, so as to obtain a more comprehensive indicator

Organizational units in forestry, besides final 'products' (volume of the harvested wood, length of the constructed forest roads, renewed forest areas etc.), provide through forest management a range of services and beneficial functions that forests offer to users. Because of that the efficiency of forestry units is more difficult to assess than the efficiency of the ordinary production units which are dealing with simple commodity production. Specifically, it is difficult to quantify the amount of resources (inputs) that are needed to 'produce' a certain amount of such services and the general goods. It is also difficult to quantify the amount of these outputs. Thus, a common feature of the organizational units in forestry is that a part of their output consists of services and general benefits, most of which are difficult to express materially. The business analysis in forestry requires that such 'intangible' outputs are in the best way possible replaced by other more easily accessible and measurable substitute variables. Comprehensive business analysis also imposes the need to use multiple methodologies and models which together can give more integral description of production and business results

In this paper, Data envelopment analysis is presented and used for the evaluation and comparison of forestry organizational units' performance i.e. efficiency of Forest offices. DEA represents methodology which at the same time considers multiple variables, so that it can provide a more comprehensive measure of business conduct in forestry. As a technique for measuring productivity and efficiency DEA experienced wide usage in many areas. However, in the field of natural resource management it is still not represented enough. In the forestry literature there is only a limited number of papers based on the determination of the efficiency by nonparametric techniques such as DEA. This as well as other non-traditional methods should yet to be introduced and accepted in forestry as a management tool on both strategic

relative efficiency of organisational units grouped by regions is shown in Figure 8.

for evaluating business activities of organisational units in forestry.

**4. Discussion and conclusions**

and provide better performance indicators.

and operational level of planning and decision-making.

32 **Figure 7.** Average relative efficiency of Forest administrations **Figure 7.** Average relative efficiency of Forest administrations

32 **Figure 7.** Average relative efficiency of Forest administrations

3 administrations G and H according to the BCC model (table 3).

In this way it was determined that the efficiency frontier was on average most frequently determined by Forest offices of Forest administrations A and C (CCR and SE model) i.e. Forest administrations G and H according to the BCC model (table 3). In this way it was determined that the efficiency frontier was on average most frequently determined by Forest offices of Forest administrations A and C (CCR and SE model) i.e. Forest administrations G and H according to the BCC model (table 3). In this way it was determined that the efficiency frontier was on average most frequently determined by Forest offices of Forest administrations A and C (CCR and SE model) i.e. Forest

**Figure 8.** Average relative efficiency by geographic regions Geografic region

4

4

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31

 **Figure 8.** Average relative efficiency by geographic regions The average relative efficiency of forest management in different geographical regions is also calculated as the weighted (by areas) mean efficiency of Forest offices situated in individual regions. The highest average efficiency was achieved in the area (I) lowland flood-prone forests – 0.907, somewhat lower in the area (II) hilly forests of the central part and area (III) moun‐ tainous forest – 0.862 and 0.890, and the lowest in the area (IV) Karst/Mediterranean area – 0.773, according to the CCR model. According to the BCC model, the average efficiency of lowland, hilly and mountainous forest offices is 0.924, 0.874 and 0.899, respectively, while the The average relative efficiency of forest management in different geographical regions is also calculated as the weighted (by areas) mean efficiency of Forest offices situated in individual regions. The highest average efficiency was achieved in the area (I) lowland flood-prone forests – 0.907, somewhat lower in the area (II) hilly forests of the central part and area (III) moun‐ tainous forest – 0.862 and 0.890, and the lowest in the area (IV) Karst/Mediterranean area – 0.773, according to the CCR model. According to the BCC model, the average efficiency of lowland, hilly and mountainous forest offices is 0.924, 0.874 and 0.899, respectively, while the **Figure 8.** Average relative efficiency by geographic regions The average relative efficiency of forest management in different geographical regions is also calculated as the weighted (by areas) mean efficiency of Forest offices situated in individual regions. The highest average efficiency was achieved in the area (I) lowland flood-prone forests – 0.907, somewhat lower in the area (II) hilly forests of the central part and area (III) moun‐ tainous forest – 0.862 and 0.890, and the lowest in the area (IV) Karst/Mediterranean area –

11 0.773, according to the CCR model. According to the BCC model, the average efficiency of 12 lowland, hilly and mountainous forest offices is 0.924, 0.874 and 0.899, respectively, while the average efficiency of Karst/Mediterranean forest offices is somewhat higher and namely 0.946. The average scale efficiency of continental regions is relatively uniform and it ranges around 0.980, while in the Karst/Mediterranean area it is much lower and namely 0.816. The average relative efficiency of organisational units grouped by regions is shown in Figure 8.
