Measuring the performance and returns to scale of forest management plans using data envelopment analysis approach (Case study; Iranian Caspian forests)

[Research]

Measuring the performance and returns to scale of forest management plans using data envelopment analysis approach (Case study; Iranian Caspian forests)

M. Zadmirzaei¹, S. Mohammadi Limaei¹*, L. Olsson², A. Amirteimoori³

1- Department of Forestry, Faculty of Natural Resources, University of Guilan, Sowmeh Sara, Iran.

2- Department of Information and Communication Systems, Faculty of Science, Technology and Media, Mid Sweden University, Sundsvall, Sweden.

3- Department of Applied Mathematics, Faculty of Science, Islamic Azad University - Rasht branch, Rasht, Iran.

* Corresponding author’s E-mail: limaei@guilan.ac.ir

ABSTRACT

The aim of this study was to assess the relative efficiency of the Iranian forest management plans using the non-parametric method – Data Envelopment Analysis (DEA) as a well-known and robust technique for measuring the relative efficiency of organizations. The relative efficiency of forest management plans was calculated using the most frequency DEA models such as global technical efficiency (CCR), local pure technical efficiency (BCC) and Scale Efficiency (SE) on 12 units in Guilan Province, Iran. According to the results of CCR and BCC models, the efficiency averaged 0.83 and 0.93, respectively. The results of SE discussed a worrying aspect of these units efficiency; namely, there were only 3 efficient forest management plans (Shafaroud, Nav and Fiyab). However, the Scale Efficiency Index (SEI) brings out some interesting points; there were approximately 58% (7 units out of 12) under Increasing Returns to Scale (IRS). Therefore, the managers of forest management plans should  focus more on the plans under IRS, so that they will have the opportunity to become more efficient through growth, otherwise managers will not be able to promote their overall productivity.

INTRODUCTION

Efficiency and productivity measurement in organizations has received a great deal of attention both in research and in practice. It means that determining the efficiency has become increasingly important in many areas of human activity. In forestry, the determination of efficiency of forest management plans is very complicated because of multiple goals of forest management, i.e. in the last few decades, forest management has been focused on multifunction usage (economic, ecological and social functions) and general benefits of forests. Owing to the multiple benefits and advantages offered by the forest as well as the non-market nature of part of these outputs, measuring the efficiency in forestry is highly demanding (Sˇporčić et al. 2009). 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.  A well-documented method in the operations research is Data Envelopment Analysis (DEA) that was originally introduced by Charnes et al. (1978) in the form of mathematical programming, based on an earlier work of Farrell (1957). Afterwards, In the DEA literature, many authors have extended techniques to measure the relative performances of operational units in different conditions. DEA utilizes linear programming (LP) to evaluate the relative performance of a set of homogeneous decision making units (DMUs) with multiple incommensurate inputs and outputs without requiring a specified functional form.

The LP can be formulated in many ways and is a transformation of the original fractional programming problem, see section 2.1.2: Output Maximization and Input Minimization DEA Programs on page 42 of Ramanathan (2003) as well as section 2.5: Data Envelopment Analysis on page 29 of Subhash (2004). Indeed, attempts to understand the relationship between the technology of a DMU, its efficiency and environment, and the measurement of Returns to Scale (RTS) are not new to DEA. But one of the key properties of the production structure is the scale of operations.

It receives particular interest because the existence of economies or diseconomies of scale may have different implications for the market structure and conduct. Hence, the economic concept of RTS has also been widely studied within the framework of DEA to answer a critical quest in any study of productive efficiency; whether the underlying technology exhibits increasing, constant, or decreasing returns to scale.

The economic concept of RTS is extremely important in forestry as well, because forests are rare recourses and also have multifunction (marketable and non-marketable) uses in which monitored by forest management plans. So, in a rational insight, assessing the performance of these plans to propose appropriate solutions for improving their performance and scale efficiency state is really vital.

In general, two main categories have been followed for treating RTS in DEA: first, RTS measurement using BCC-DEA models; this type of research efforts includes Banker & Thrall (1992), Tone (1996), Golany & Yu (1997), Sueyoshi (1999), Cooper et al. (2000), Tone & Sahoo (2003); the second, RTS measurement developed by Färe, Grosskopf & Lovell (FGL-DEA model) who used a quantitative measurement of scale elasticity.

In fact, this type of research can be traced to the efforts of Färe et al. (1983, 1985, and 1994). Noteworthy, the alternative measurements provided by the FGL-DEA approach is an important one because this approach identifies RTS through the ratios of a series of relative efficiencies obtained from different DEA models with radial measure, which has different constraints (Färe et al. (1983). These ratios are developed from the model pairs that differ only in conditions of the convexity and sub-convexity that are satisfied (Banker et al. 2004). Despite that DEA has been applied in a wide range of applications, there are few studies in forestry by this non-parametric approach. For instance, Kao & Yang (1992) used the DEA efficiency results to appraise three alternatives proposed by the Taiwan Forestry Bureau for reorganizing the 13 forest districts considered in their earlier study (Kao & Yang 1991). The efficiency of 19 public Forestry Boards in Finland was evaluated using DEA (Viitala & Hanninen 1998).

The efficiency of the Croatian forestry organization was evaluated by non-parametric models (Sporcic et al. 2009), their research revealed DEA as a powerful multi criteria decision making tool for support in forest management. The DEA model was used to measure the productive efficiency of forest enterprises in the Mediterranean Region of Turkey (Korkmaz 2011).

DEA was first used to assess the efficiency of Iranian forest industries by Mohammadi Limaei (2013). He investigated the efficiency of 14 Iranian forest management units.

Therefore, due to the important role of forests to include multiple usage (economic, ecological and social functions) this study is conducted to estimate the relative efficiency and returns to scale of some forest management plans in the north of Iran to disseminate the necessary information for manager of forest management plans until they will be able to adjust the units operating scale and become more efficient through growth.

The DEA method is, therefore, well suited to be used in this case study.

MATERIALS AND METHODS

DEA models

Conventionality DEA is defined as a linear programming methodology (Lin & Wang 2014) which allows to assess the performance of multiple DMUs when the production process presents a structure of multiple inputs and outputs (Tone & Tsutsui 2014; Oral et al. 2014). In this matter, there are many DEA models with their pros and cons, thus, with respect to this paper goals, the most frequently applied DEA model is used as follows.

CCR model

Charnes et al. (1987) formulated a DEA model, referred to as CCR (Charnes, Cooper & Rhodes), with Constant Returns to Scale (CRS) assumption (Model 1)). A CRS assumption implies that all DMUs would be able to increase their output by a similar proportion, given an increase in the rate of their inputs, no matter what their scales are. The efficiency score resulting from a CCR model is called the global technical efficiency.

                                                                            (1)

where: = amount of input i used by unit j,

 = amount of output r is produced by unit j,

 = a small non-Archimedean quantity which prohibits any inputs/outputs factor to be ignored.

Due to the input-oriented nature of this model, the objective function tries to reduce input amounts (θ) by fixing output levels. In fact, θ is a real decision variable and λ is a non- negative vector of decision variable that in this sample to choose each allowable vector (λj) for making an upper limit for outputs and a lower limit for inputs of  DMU0.  Hence the optimal θ, denoted by θ*, is not greater than 1 (Cooper et al. 2007).

Definition 1.A decision maker is fully efficient if and only if both (optimal solution problem) and (slack input and output variables).  

BCC model

The CCR model (1) can be modified to accommodate Variable Returns to Scale (VRS). This model was introduced by (Banker et al. 1984), referred to as BCC, and requires a convexity constraint (2) added to the CCR model (1). Noteworthy, the convexity of the production possibility set is a maintained hypothesis in DEA because the convexity ensures that when two or more input–output combinations are known to be feasible, any weighted average of the input bundles can produce a similarly weighted average of the corresponding output bundles (Subhash 2004). Therefore, in this model, each DMU against other DMUs in the same scale range as well as the efficiency score provided by a BCC model is called local pure technical efficiency.

                                                                              (2)

Definition 2. The definition of efficient decision maker is the same as definition 1.

SE model

The scale efficiency (SE) of a DMU can be calculated based on its global technical efficiency and local pure technical efficiency resulting from CCR and BCC models, respectively (3). SE represents the inefficiency of a DMU which is merely due to its scale of operations. This model can be formulated in the following form (Cooper et al. 2007).

Definition 3. A decision maker is fully efficient if and only if both (optimal solution problem).

                                    (3)

SEI/ FGL model

Färe et al. (1985) introduced the following “scale efficiency index” (SEI) method or FGL model, which is based on Non-Increasing Returns to Scale (NIRS), to determine the nature of local RTS for DMU_o (Tone & Sahoo, 2005):

                                                            (4)

In fact, they proposed a method by changing from (Model 2) to (Model 4) and these following steps: .

If, then DMU_o exhibits CRS and also is fully efficient by SE; otherwise if, then DMU_o exhibits IRS if, and DMU_o exhibits NIRS if.

 Case study

The area of natural forest in Iran is approximately 12.4 million hectares, equal to 7.5% of the total area of Iran. Of this, approximately 1.9 million hectares are commercial forests called Iranian Caspian, Hyrcanian or Northern forests which is controlled by forest management plans.

In  this research, according to forestry experts’ idea, two inputs (plantation cost and stock before  executing  the forest management plan,  called  stock 1) and two outputs (harvesting revenue and stock after executing the  plan,   called  stock 2) were considered. At least 12 forest management plans had to select using rule of thumb in DEA approach. Hence, the number of DMU should follow:

 where n = number of DMUs, m = number of inputs, and s = number of outputs. Afterwards, we assume that this (or other) degrees of freedom conditions are satisfied and that there is no trouble from this quarter (Cooper et al. 2011).  It should be noted that the length of the planning horizon includes 10 years. Hence, in this case, the average data of a ten-year period were considered. Moreover, the monetary data were adjusted by the Consumer Price Index (CPI) of Iran in the base year 2011 (Table 1).

RESULTS

The results of global technical efficiency (CCR) and local pure technical efficiency (BCC) are meaningfully different; the number of efficient units by CCR is 3 and by BCC is 6 and also the efficiency averages for CCR and BCC are 0.83 and 0.93, respectively (Table 2).  The results of BCC and FGL models indicate that most of forest management plans 58% (7 out of 12) are under IRS.

Also, this comparative approach shows that two forest management plans are under NIRS and the rest of them are under CRS as well as they are fully efficient (score 1) by SE model (Table 3).

The results of the scale efficiency (SE) model show the distance between the boundary fixed and variable returns to scale (CCR and BCC) in which based on this model there is a considerable distance between them, i.e. there are only 3 (Shafaroud, Nav and Fiyab) efficient forest management plans (Fig. 1).

Fig. l. The result of SE model.

Table 1. Mean values of input and output data of forest management plans used in DEA models.

In this study, we used GAMS software for model analyses.

Table 2. Results of CCR and BCC models.

Table 3. Results of RTS.

                                    ^{* Under CRS and also fully efficient by SE model.}

ANALYSES AND DISCUSSION