THE ANALYSIS AND ASSESSMENT OF PRODUCTIVITY IN THE PROCESSING OF BEECH LOGS ON THE EXAMPLE OF THE SELECTED PRODUCTION SYSTEM IN SERBIA BY APPLYING STATISTICAL MODELING

: This paper presents the results of the study of the influence of the selected factors on the productivity of the processing of beech logs on the example of the selected producer of sawn timber in Serbia by applying statistical modeling. The analysis covered three basic factors that have an impact on productivity: the length, middle diameter and number of cuts on the logs of beech that were processed during the observed period. The research was carried out on a sample of 105 logs, and it contained various sizes of middle diameters, lengths and number of cuts. The research aimed to review the functional dependence of selected factors and productivity in order to reach appropriate conclusions, provide expert recommendations and measures to increase productivity and make appropriate forecasts of possible productivity values. In order to examine the functional dependence of the selected variables, statistical modeling was performed in SPSS, v.20 and MS Excel software packages, where the selected dependent variable is the number of logs processed in one hour, and as an independent variable the volume was taken into consideration (which contains the middle diameter and the length of the logs) and the number of cuts. Statistically obtained parameters showed a significant influence of the volume and number of cuts on the change of the number of logs which are processed in one hour. In the obtained regression model the correlation coefficient R is 0.994, while the coefficient of determination R 2 = 0.988. Since in sawmill processing productivity is most often expressed as the volume of processed logs in the unit of time, a transformed form of the equation shows the dependence of the volume on the number of logs and the number of cuts. By setting the hypothesis and by interpreting the statistical indicators, it has been found that the impact of the analyzed factors is very high, but that, in addition to them, productivity is influenced by technical and organizational factors.


THE ANALYSIS AND ASSESSMENT OF PRODUCTIVITY IN THE PROCESSING OF BEECH LOGS ON THE EXAMPLE OF THE SELECTED PRODUCTION SYSTEM IN SERBIA BY APPLYING STATISTICAL MODELING
M. Sc. Aleksandra Lazarevic, professional associate, University of Belgrade -Faculty of Forestry (aleksandra.lazarevic@sfb.bg.ac.rs) Dr Slobodanka Mitrovic, full professor, University of Belgrade -Faculty of Forestry Miljan Kalem, Graduate engineer of forestry, professional associate, University of Belgrade -Faculty of Forestry Abstract: This paper presents the results of the study of the influence of the selected factors on the productivity of the processing of beech logs on the example of the selected producer of sawn timber in Serbia by applying statistical modeling. The analysis covered three basic factors that have an impact on productivity: the length, middle diameter and number of cuts on the logs of beech that were processed during the observed period. The research was carried out on a sample of 105 logs, and it contained various sizes of middle diameters, lengths and number of cuts. The research aimed to review the functional dependence of selected factors and productivity in order to reach appropriate conclusions, provide expert recommendations and measures to increase productivity and make appropriate forecasts of possible productivity values. In order to examine the functional dependence of the selected variables, statistical modeling was performed in SPSS, v.20 and MS Excel software packages, where the selected dependent variable is the number of logs processed in one hour, and as an independent variable the volume was taken into consideration (which contains the middle diameter and the length of the logs) and the number of cuts. Statistically obtained parameters showed a significant influence of the volume and number of cuts on the change of the number of logs which are processed in one hour. In the obtained regression model the correlation coefficient R is 0.994, while the coefficient of determination R 2 = 0.988. Since in sawmill processing productivity is most often expressed as the volume of processed logs in the unit of time, a transformed form of the equation shows the dependence of the volume on the number of logs and the number of cuts. By setting the hypothesis and by interpreting the statistical indicators, it has been found that the impact of the analyzed factors is very high, but that, in addition to them, productivity is influenced by technical and organizational factors.
Key words: productivity, logs, volume, number of cuts, correlations, regression

INTRODUCTION
In the conditions of pronounced competition and high demand for wood raw materials on the one hand and limited forest resources and activities that are being implemented in the direction of mitigation of climate change on the other, wood processing companies are making great efforts to fully and rationally use timber raw materials (S retenović, Glavonjic, 2014). The constant change of demand by consumers, the strengthening of competition, the increase in prices of basic raw materials and the lack of qualified labor are just some of the problems that companies in Serbian wood industry face on a daily basis. In order for a company to survive and develop in such business conditions it must be aware of all its good and bad sides and be flexible and ready for everyday changes that the environment imposes. For this reason, the assessment of production parameters is a very important factor in the analysis of a company's assessment. The parameters by which the enterprise expresses its productive capabilities are, most often, productivity and cost-effectiveness. According to Čufar et al. 2012, beech can be used to obtain at least 250 products, but the processing of each of them is not always justified in terms of efficiency and economy. Similarly, in this paper, emphasis is placed on one of the parameters of performances of the production process, which is productivity.
Productivity is an expression of the production capability of a company, that is, from the economic point of view, most often rational use of the labor force. Productivity expresses the ability of a company to produce a certain amount of products of satisfactory quality in the shortest period of time, with the lowest amount of labor force consumed. There are many factors that affect productivity that can be divided into two basic groups. These are objective and subjective factors. Objective factors are those that affect the company from within the environment and the company does not have any impact on them. Some of these factors are technological discoveries, new scientific achievements, natural conditions and measures of the social community. All these factors affect the business of a company to a greater or lesser extent. Those factors which were analyzed in this paper, and which every company can and should influence in order to survive in the market are subjective factors. The first group of subjective factors are human factors that include the structure of the workforce, work experience, personnel policy and others. The second group of subjective factors are the organizational factors. In addition to the above factors, according to Eliasson L. (2011), the quality of raw materials and other characteristics, has a great influence on the productivity and efficiency of production of which the most important are discussed in this paper on the example of the selected production system.

OBJECT AND AIM OF THE STUDY
The main research object in this paper is the processing of beech logs in the selected production system in Serbia. The main objective of the study was to investigate and analyze the impact of the following factors on beech logs on the productivity of their processing in the selected production system: the length and the pitch diameter of the logs and the number of cuts. The specific goal of the study was to make certain conclusions and, in this regard, define appropriate recommendations and measures of importance for improving the efficiency of production in the selected production system.

MATERIAL AND METHODS
For the purpose of carrying out the research in this paper, the following scientific methods of research were used: analysis, induction, deduction, and methods of statistical analysis. In addition, the techniques of field research were used: interviews and recordings. Statistical data processing was performed in the statistical program SPSS, v.20.0 and MS Excel. The basic statistical tools that are most commonly used for analysis and projections of behavior of certain economic phenomena are based on regression and correlation analysis as indispensable methods. The coefficient of determination (R 2 ), the coefficient of correlation (R), t-statistics of the obtained parameter estimates and F-statistics were used to estimate the significance of individual elements of the obtained regression models of trend (Rankovic, 2012). The statistical significance threshold in all cases was α = 0.05 (the level of permissible error is equal to or less than 5%) (R a n kovi ć , 2012). In this paper, the analysis method was used to analyze the collected data on the processing of beech logs. The induction method was used to draw certain conclusions on the processing of beech logs, as well as for assessing the indicators of productivity. The method of deduction was used to explain the facts and make conclusions based on the data obtained from the mentioned statistical packages.
Data collection was peformed in a production system located in Kraljevo. The results of the recordings were recorded in the already prepared recording sheets. Upon completion of the recording, all data were subjected to logical control first and then entered into the listed statistical packages in which their processing was performed. The length of logs ranged from 2.0 m to 5.8 m, while the mean diameters ranged from 23 cm to 78 cm. The number of cuts on the observed logs ranged from 6 to 26 per log, depending on the previously described characteristics of the logs. The logs were processed using three types of sawing: "sharp", "prism" and "circularly individual". Depending on the characteristics of the logs, the appropriate sawing method was selected. The sample on which the recording took place in the selected time period was 105 logs.
The sawmill in Kraljevo, where the recording was performed, is currently the largest manufacturing system for the processing of beech logs in Serbia with an annual capacity of about 30,000m 3 , or daily capacity with slightly more than 100m 3 . The production system employs over 400 workers and processes only beech logs. The recording was performed for 16 hours on the same machine, log band saw -brand Rulmak RM-1200, operated by one worker in the course of four days. On other machines, the technological process of processing was carried out by workers whose work process depended on the efficiency of work on band saw logs, which is of great importance when measuring productivity. Productivity was recorded only in the first phase of work on the line for two-phase processing. Collective data on the values of individual parameters obtained during the recording are shown in Table 1 The volume of logs was obtained using the formula: where: ds -pitch diameter of the log [m] l -log length [m] π -Ludolf's number rounded to two decimals (3.14).
The obtained values rounded up to two decimals, i.e. to the same number of decimals that it is rounded off according to the old JUS standards that are still applied in practice in Serbia and in the specific production system.
The processing of collected data was performed in the SPSS software packages, v.20.0. and MS Excel, in which regression and correlation analysis is combined as a unique methodological tool. One of such packages was used in Potkány et al. 2013. In these statistical packages, the shape and degree of dependence between the productivity of processing beech logs and the selected factors are determined. For the purposes of this study, the possibilities of calculating the parameters of the double linear regression and their statistical evaluation were used.
Parameters of the equations that are calculated are subjected to the estimation of statistical significance or significance, through their standard errors and corresponding t -statistics. According to B o j o v i ć S., M i t ro v i ć S., 2010, the obtained models were statistically estimated through the assessment and analysis of the coefficient of determination (R 2 ) and the coefficient of correlation (R). The correlation coefficient (R) was used as an element on the basis of which the level of interconnection of dependent and independent variables was evaluated.

RESULTS
The first step in the field research was to record the number of logs that are processed in one hour, their volume and the number of cuts on each individual log. In this way, the starting basis for obtaining the functional dependence of the number of logs processed in one hour in relation to the volume and number of cuts was created.
The zero hypothesis in this case assumed that there is no interdependence between the linear composite of the variables and the numbers of pieces of processed logs.
H0 -There is no interdependence between the linear composite of the variable and the number of pieces of processed logs.
H1 -There is an interdependence between the linear composite of the variable and the number of pieces of processed logs.
The functional dependence of the number of logs and linear composites is shown by a linear equation: The basic parameters of this model are: On the basis of the obtained parameters, the equations have the following form: y = 0.657 · x 1 + 0.045 · x 2 The deviation of the actual number of logs from the regression values in time is shown in Graph 1.
The value of the correlation coefficient R (R = 0.994) and its statistical significance show that the number of logs is to a large extent associated with the linear composite of the variables. The determination coefficient R 2 is 0.988, which further shows (1) (2) that the number of processed beech logs in the selected production system can be significantly explained by changes in volume and number of cuts on logs. This means that 98.8% of the total number of logs can be explained through these two variables. The value of the regression parameter a with volume amounted to 0.657, while the regression parameter that is related to the number of cuts is 0.045. Observing these values, as well as the values and significance of t statistics for the volume and number of cuts, it can be concluded that the parameters analyzed are directly related to the number of logs being processed. This is confirmed by the graphic display.
Considering that in sawmill processing the productivity is most often expressed as the volume of processed logs in the unit of time, the equation number (2) has to be transformed into a form that shows the dependence of the volume of the individual logs in the unit of time on the number of logs processed in the same unit of time and number of cuts.
On the basis of transformation of equation number (2), the following equation is obtained: where is: y -productivity by volume [m 3 / h] x 1 -number of logs [pcs] x 2 -number of cuts [pcs].
Equation (3) shows the functional dependence of the volume of processed logs on the number of logs and the number of cuts. As can be seen by equation (3), the productivity expressed through the volume of processed logs is directly proportional to the number of logs that are processed, and inversely proportional to the number of cuts. In a particular case, if the number of logs is increased by 1, and the number of cuts is reduced by 1, the productivity of log processing in the observed production system would be increased by 1.59 m 3 /h.

DISCUSSION
The displayed results clearly show the high impact of the selected factors on the productivity of beech log processing in the selected production system. In addition to the linear model, a step-bystep model was developed in which the results obtained were worse and they were not shown in this research paper. However, since the effect of all three variables was observed together, it was confirmed that their impact on the processing time is high. Observing the linear regression of the dependent variable and the linear composite of independent variables, it was confirmed that the linear composite explains 99.4% of the total number of logs that are processed in one hour. It is therefore concluded that the zero hypothesis is contradicted and that there is a linear connection between the particular linear composite and the dependent variable in the manufacturing system in which the recording was performed. Based on the above, the following is a forecast of a possible production if the analyzed factors are aligned with the real possibilities of the manufacturing system. In practice, different situations are possible in terms of increasing the number of logs and the number of cuts that are processed in one hour, increasing the number of logs, reducing the number of cuts, reducing the number of logs, and increasing the number cuts and reducing both the number of logs and the number of cuts. For all these combinations according to the equation (3) from the aspect of productivity it is the most advantageous for the production system to increase the number of logs that are processed in one hour, and to reduce the number of cuts. In this sense, in Table 2 the results of modeling this option for 5 cases are presented.
In case the number of logs per hour is increased by 1 and the number of cuts is reduced by 1 in relation to their mean values from Table 1, one could expect that the average productivity per hour would be 5.45m 3 , which is 1.72m 3 or by 46.01% higher than the average value of sliced logs from Table 1. If the number of logs per hour is increased by 5, and the number of cuts decreased by 5, one could expect that the productivity increase would be more than three times compared to the mean value measured during real-time recording in the selected production system. It best shows how much the measured productivity can change in real terms and that appropriate measures need to be taken to improve it and raise it to a higher level.
Graph 2 shows a proportional increase in productivity, increasing the number of pieces of processed logs for n + 1, ..., n + 5 and reducing the number of cuts for n -1, ..., n -5. In this regard, and based on the results of the research and the performed analysis, one of the measures for increasing the productivity in the observed production system is sorting logs by classes and thicknesses before processing, which will be processed in one working time. Insufficient number of conveyors and their incorrect installation in production can be cited as a key organizational problem of the observed production that directly affects productivity. Improvements in the transport system to a large extent would contribute to the increase in the number of logs that could be processed in one hour. In addition to the faster and easier manipulation of processing objects, their application would greatly facilitate the workload of the worker, reduce his fatigue and thereby contribute to the increase in the overall productivity of his work.
According to Loh and Koh (2004), in the past few years companies have focused on improving technology and reducing the number of employees due bad economic conditions. This fact indicates that the problem that arises in the world exists in Serbia as well. Global changes in business have an impact primarily on the company efficiency and attempts to find optimal business solutions (Hernaus, 2009). Compared to the above, a similar situation exists in the company where the recording was performed. One of the differences is that selected company does not invest great resources in the technological modernization in order to bring overall productivity and efficiency to a satisfactory level. The productivity level of the selected production system is very low compared to similar production systems in the developed European countries. The lagging behind of wood processing enterprises (without furniture) in Serbia, for companies in developed European countries, when it comes to investments in technological modernization, are best illustrated by the following examples (Glavonjić B. 2017): total investments in the procurement of machines and equipment per company in wood processing in Germany in 2015 amounted to 56,745.2 EUR, in Slovakia 7,703 EUR, and in Serbia 3,259.3 EUR. For this and other reasons, average productivity in the production of sawn wood in 2015 in Serbia was 139.6 m 3 /worker, and in Germany 1.129.8 m 3 /worker, which is 8.1 times more than in Serbia. If the competitiveness of Serbia in the international market is to be improved, investments in technological modernization are inevitable in the selected, as well as other companies in the wood processing of Serbia.

CONCLUSIONS
Due to an insufficient supply of wood raw materials to the market, a selected company is forced to purchase logs of various dimensions and variable quality from different forest estates. This is one of the reasons why productivity in the observed production system varies greatly.
Procurement and processing of raw materials of poor quality directly affect productivity. In addition to the low percentage of exploitation of logs of poorer quality, the quality of the obtained assortments is problematic, which leads to the situation that the processing of such logs is at the limit of cost-effectiveness. In addition to this factor, another objective factor which greatly influences the operations of companies in the wood processing industry in Serbia is the relationship among sawmills and their "fight" on the market for each cubic meter of timber raw materials. Technological obsolescence is also one of the big problems of the production system in which the research was carried out. Many machines are over 30 years old, so the manipulation of logs takes place manually which also has a negative impact on productivity. Moreover, the influence of other objective and subjective factors on productivity is very pronounced, most often in the negative sense.
The results of the performed statistical modeling and related projections of possible productiv-Graph 2. Productivity increase by increasing the number of logs and reducing the number of cuts ity clearly show that, in addition to technological modernization, important factors of productivity are the average diameter and the number of cuts. The obtained functional dependencies of productivity and these factors clearly indicate the need to procure logs of a larger average diameter as much as possible, and that when making the foundations of sowing, it is necessary to try to obtain as much wood as possible with as few cuts as possible. Therefore, they represent two important elements for productivity growth, not only in the selected production system, but also more widely.