**1. Introduction**

[10] Serizawa, M., Uda, T., Miyahara, S. (2013). Effects of anthropogenic factors on devel‐ opment of sand spits and cuspate forelands with rhythmic shapes, Asian and Pacific

[11] Ozasa, H., Brampton, A. H. (1980). Model for predicting the shoreline evolution of

[12] Serizawa, M., Uda, T., San-nami, T., Furuike, K. (2006). Three-dimensional model for predicting beach changes based on Bagnold's concept, Proc. 30th ICCE, pp.

[13] Mase, H. (2001). Multidirectional random wave transformation model based on ener‐

[14] Dally, W. R., Dean, R. G., Dalrymple, R. A. (1984). A model for breaker decay on

[15] Katayama, H., Goda, Y. (2002). Beach changes due to suspended sediment picked up

[16] Serizawa, M., Uda, T., San-nami, T., Furuike, K. (2003). Prediction of depth changes on x-y meshes by expanding contour-line change model, Ann. J. Coastal Eng. JSCE,

[17] Goda, Y. (1985). Random Seas and Design of Maritime Structures. University of To‐

[18] Uda, T., Yamamoto, K. (1991). Spit formation in lake and bay, Coastal Sediments '91,

[19] van den Berg, N., Falqués, A., Ribasz, F. (2011). Long-term evolution of nourished beaches under high angle wave conditions, J. Marine Systems, Vol. 88, Issue. 1, pp.

[20] Bird, E. (2000). Coastal Geomorphology: An Introduction, Wiley, England, p. 322.

[21] Davis, R. A., FitzGerald, D. M. (2004). Beaches and Coasts, Blackwell, Malden, p. 419. [22] Komar, P. D. (1998). Beach Processes and Sedimentation, Prentice Hall, New Jersey,

gy balance equation, Coastal Eng. J., JSCE, Vol. 43, No. 4, pp. 317-337.

Coasts 2013, Proc. 7th International Conf. pp. 9-16.

beaches, Proc. 19th ICCE, pp. 82-97.

50, pp. 476-480. (in Japanese)

kyo Press, Tokyo, p. 323.

Vol. 2, pp. 1651-1665.

102-112.

2nd ed., p. 544.

3155-3167.

450 Computational and Numerical Simulations

beaches backed by seawalls, Coastal Eng., Vol. 4, pp. 47-64.

by random breaking waves, Proc. 28th ICCE, pp. 2767-2779.

Determination of efficiency has become increasingly important in many areas of human activity. Approach to this problem is particularly interesting when there are no clear success parameters, and when the efficiency of using several different resources/inputs is measured for achieving several different outputs. In such measurements, we are always interested in determining the degree of efficiency of individual organisations, institutions, associations, etc. in relation to others acting under similar conditions. In doing so, the compared objects are presented through data on used resources/inputs and data on achieved outputs.

In forestry, the determination of efficiency of forestry companies is extremely complex because of multiple goals of forest management. The principle of sustainable development represents the management and use of forests and forest land in the way to preserve their biological diversity, productivity, regeneration capability, vitality and potential in order to enable forests to fulfil now and in future their key economic, ecological and social functions. The above stated makes the conditions of forest management increasingly demanding and imposes the necessity of continuous analyses of all relevant business performance indicators.

In the last few decades, forest management has been focused on multifunctional use and general benefits of forests. Due to multiple benefits and advantages offered by forests, as well as the non-market nature of a part of these outputs, the measurement of performance in forestry is highly demanding. In such conditions, it is pretty difficult to apply conventional economic methods, such as cost-benefit analysis, internal rate of return and others for determining business success. The right evaluation method must be selected in order to determine whether the resources are used efficiently.

© 2014 Šporčić and Landekić; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Taking into consideration multiple inputs and multiple outputs of forest management, in this paper Data Envelopment Analysis (DEA) was applied for determining the performance level of forest management units. DEA represents a methodology suitable for the efficiency analysis of numerous production units, but is not traditionally used in forestry. Although it was first applied in the forestry sector in 1986 [1], the number of papers based on measuring the performance by non-parametric techniques, such as DEA, is still very limited in forestry literature. The basic idea is to determine the performance through the efficiency level of individual DMUs1 based on the relationship between a complex input and a complex output.

If we want to calculate an indicator of business performance which will reflect efficiency of the organizational unit we take into consideration the ratio of output and input. If we want to calculate a measure of efficiency that will consider more inputs and more outputs, it is necessary to make a selection of inputs and outputs that will be taken into the calculation, and it is necessary to join a certain weight to inputs and outputs in order to define a single measure

Nonparametric Model for Business Performance Evaluation in Forestry

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

453

Absolute measure of efficiency can be determined when we have explicitly defined relation‐ ship between inputs and outputs, or when we know the association that for every combination of inputs joins a specific set of possible outputs. If this relationship is known then, from the relation between really achieved and theoretically achievable outputs of each individual unit,

The concept of relative efficiency is used when it is not possible to define theoretically possible level of efficiency, and so the certain units are compared with those units whose business

DEA methodology does not require the pre-determined weight of inputs and outputs, and does not require any knowledge of the explicit links between inputs and outputs. Based on the known empirical data about the level of inputs and outputs for each unit DEA calculates its relative efficiency compared to other units. Observed unit reaches 100% relative efficiency (rating 1) if and only if compared with the other units it doesn't show inefficiency in the use

The story about DEA begins with the doctoral dissertation of Edward Rhodes, who has tried to evaluate the curriculum of public schools in Texas in the United States. At that time, it was a challenge to assess the relative efficiency of schools with multiple inputs and outputs, and without the usual information on prices and costs. As a result, the formulation of CCR

DEA was originally developed as a tool to measure the effectiveness of organizations working on non-profit basis (public schools and hospitals, military establishments), where it is not

was developed and the first DEA paper was published in the European Journal of

of any inputs or outputs. Specifically, for a unit is said to be relatively efficient if:

of efficiency for each organizational unit.

it is possible to determine their absolute efficiency.

**1.** it can not increase any of its outputs without -

**b.** reducing some of its remaining outputs

**b.** increasing some of its remaining inputs.

**2.1. Generally about Data Envelopment Analysis**

**2.** it can not reduce any of its inputs without **a.** reducing some of its outputs, or,

**a.** an increase of its inputs, or,

**2. Material and methods**

Operational Research in year 1978 [14].

model2

performance, given the state of manufacturing technology, is the best.

Data Envelopment Analysis, as the technique for measuring productivity and efficiency, is widely applied in many areas. It was used, for example, for making comparisons between organisations [2], companies [3], regions and countries [4]. For determining business perform‐ ance it was applied in banking [5], agriculture [6], wood industry [7], schooling [8], etc. In DEA bibliography [9] there are approximately 3,200 published DEA papers. However, in the area of management of renewable natural resources, it is still not sufficiently present. In forestry literature there is only a limited number of DEA papers [10 - 13], and it yet has to be introduced and accepted in forestry as a management tool at a strategic and operating level of decision making.

So, this paper assesses the efficiency of basic organizational units in the Croatian forestry, forest offices, by applying Data Envelopment Analysis (DEA), a nonparametric methodology for measuring relative efficiency of comparable decision making units with more inputs and outputs. The relative efficiency of compared forest offices is calculated in the paper with the most frequently used DEA models - CCR and BCC model. According to the aquired data, conducted calculations and analysis, the results of global technical efficiency (obtained by CCR model), local pure technical efficiency (obtained by BCC model) and scale efficiency were determined. The results also included the calculation of efficiency frontier, frequency of efficient units in reference set of inefficient units, determination of sources and values of inefficiencies, influence of the forest offices' structural characteristics on their efficiency and the average efficiency of forest offices grouped with respect to the forest administrations and regions they belong to. The research reveals DEA as a powerful multi criteria decision making tool and a possible, very valuable support in forest management.

### **1.1. Efficiency and the possibility to measure relative efficiency**

In the business analysis some indicators are calculated which represent the basis for evaluation and comparison of business performance (indicators of liquidity, profitability, cost-effective‐ ness, etc.). However, these indicators in the calculations take into account only some of the accounting issues, and so represent partial performance indicators. At the same time, multicriteria analysis of these partial indicators can't identify the best-performing unit, because it is unlikely that one of the units has all the observed simple indicators the best i.e. better than the other compared units.

<sup>1</sup> DMU (Decision Making Unit) is any production or non-production unit that uses certain inputs so as to achieve certain outputs.

If we want to calculate an indicator of business performance which will reflect efficiency of the organizational unit we take into consideration the ratio of output and input. If we want to calculate a measure of efficiency that will consider more inputs and more outputs, it is necessary to make a selection of inputs and outputs that will be taken into the calculation, and it is necessary to join a certain weight to inputs and outputs in order to define a single measure of efficiency for each organizational unit.

Absolute measure of efficiency can be determined when we have explicitly defined relation‐ ship between inputs and outputs, or when we know the association that for every combination of inputs joins a specific set of possible outputs. If this relationship is known then, from the relation between really achieved and theoretically achievable outputs of each individual unit, it is possible to determine their absolute efficiency.

The concept of relative efficiency is used when it is not possible to define theoretically possible level of efficiency, and so the certain units are compared with those units whose business performance, given the state of manufacturing technology, is the best.

DEA methodology does not require the pre-determined weight of inputs and outputs, and does not require any knowledge of the explicit links between inputs and outputs. Based on the known empirical data about the level of inputs and outputs for each unit DEA calculates its relative efficiency compared to other units. Observed unit reaches 100% relative efficiency (rating 1) if and only if compared with the other units it doesn't show inefficiency in the use of any inputs or outputs. Specifically, for a unit is said to be relatively efficient if:

	- **a.** an increase of its inputs, or,

Taking into consideration multiple inputs and multiple outputs of forest management, in this paper Data Envelopment Analysis (DEA) was applied for determining the performance level of forest management units. DEA represents a methodology suitable for the efficiency analysis of numerous production units, but is not traditionally used in forestry. Although it was first applied in the forestry sector in 1986 [1], the number of papers based on measuring the performance by non-parametric techniques, such as DEA, is still very limited in forestry literature. The basic idea is to determine the performance through the efficiency level of individual DMUs1 based on the relationship between a complex input and a complex output.

Data Envelopment Analysis, as the technique for measuring productivity and efficiency, is widely applied in many areas. It was used, for example, for making comparisons between organisations [2], companies [3], regions and countries [4]. For determining business perform‐ ance it was applied in banking [5], agriculture [6], wood industry [7], schooling [8], etc. In DEA bibliography [9] there are approximately 3,200 published DEA papers. However, in the area of management of renewable natural resources, it is still not sufficiently present. In forestry literature there is only a limited number of DEA papers [10 - 13], and it yet has to be introduced and accepted in forestry as a management tool at a strategic and operating level of decision

So, this paper assesses the efficiency of basic organizational units in the Croatian forestry, forest offices, by applying Data Envelopment Analysis (DEA), a nonparametric methodology for measuring relative efficiency of comparable decision making units with more inputs and outputs. The relative efficiency of compared forest offices is calculated in the paper with the most frequently used DEA models - CCR and BCC model. According to the aquired data, conducted calculations and analysis, the results of global technical efficiency (obtained by CCR model), local pure technical efficiency (obtained by BCC model) and scale efficiency were determined. The results also included the calculation of efficiency frontier, frequency of efficient units in reference set of inefficient units, determination of sources and values of inefficiencies, influence of the forest offices' structural characteristics on their efficiency and the average efficiency of forest offices grouped with respect to the forest administrations and regions they belong to. The research reveals DEA as a powerful multi criteria decision making

In the business analysis some indicators are calculated which represent the basis for evaluation and comparison of business performance (indicators of liquidity, profitability, cost-effective‐ ness, etc.). However, these indicators in the calculations take into account only some of the accounting issues, and so represent partial performance indicators. At the same time, multicriteria analysis of these partial indicators can't identify the best-performing unit, because it is unlikely that one of the units has all the observed simple indicators the best i.e. better than the

1 DMU (Decision Making Unit) is any production or non-production unit that uses certain inputs so as to achieve certain

tool and a possible, very valuable support in forest management.

**1.1. Efficiency and the possibility to measure relative efficiency**

making.

452 Computational and Numerical Simulations

other compared units.

outputs.

	- **a.** reducing some of its outputs, or,
	- **b.** increasing some of its remaining inputs.
