Network Planning of the Technological Chain for Timber Land Development

JAES JOURNAL OF APPLIED ENGINEERING SCIENCE www.engineeringscience.rs ISTRAŽIVANJA I PROJEKTOVANJA ZA PRIVREDU

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NETWORK PLANNING OF THE TECHNOLOGICAL CHAIN FOR TIMBER LAND DEVELOPMENT

Konstantin Rukomojnikov Aleksandr Mokhirev Albert Burgonutdinov Volga State University of Reshetnev Siberian State Perm National Research Technology, Institute of University of Science and Polytechnic University, Faculty Forest and Nature Technology, Lesosibirsk of Construction, Roads and Management, Forestry and Branch, Department Of bridges building department, chemical technologies, technology of logging and Perm, Russian Federation Yoshkar-Ola, Russian wood processing industries, Federation Lesosibirsk, Russian Federation

Olga Kunickaya Roman Voronov Igor Grigorev University Arctic state Petrozavodsk State University, University Arctic state agrotechnological University, Institute of Mathematics and agrotechnological University, Forestry and Land Information Technology, Forestry and Land Management Faculty, Department of Applied Management Faculty, Department of Technology Mathematics and Cybernetics, Department of Technology and equipment of the forest Petrozavodsk, Russian and equipment of the forest complex, Federation complex, Yakutsk, Russian Federation Yakutsk, Russian Federationv

Key words: logging, management decisions, wood removal, technological chain

Cite article: Konstantin, R., Aleksandr, M., Albert, B., Olga, K., Roman, V., & Igor, G. [2021]. Network planning of the technological chain for timber land development. Journal of Applied Engineering Science, 19(2), 407 - 414. DOI:10.5937/jaes0-28819

Online aceess of full paper is available at: www.engineeringscience.rs/browse-issues Journal of Applied Engineering Science Original Scientific Paper Istraživanja i projektovanja za privredu

doi:10.5937/jaes0-28819 Paper number: 19(2021)2, 807, 407-414

NETWORK PLANNING OF THE TECHNOLOGICAL CHAIN FOR TIMBER LAND DEVELOPMENT

Konstantin Rukomojnikov1, Aleksandr Mokhirev2*, Albert Burgonutdinov3, Olga Kunickaya4, Roman Voronov5, Igor Grigorev4 1Volga State University of Technology, Institute of Forest and Nature Management, Forestry and chemical technologies, Yoshkar-Ola, Russian Federation 2Reshetnev Siberian State University of Science and Technology, Lesosibirsk Branch, Department Of technology of logging and wood processing industries, Lesosibirsk, Russian Federation 3Perm National Research Polytechnic University, Faculty of Construction, Roads and bridges building department, Perm, Russian Federation 4University Arctic state agrotechnological University, Forestry and Land Management Faculty, Department of Technology and equipment of the forest complex Yakutsk, Russian Federation 5Petrozavodsk State University, Institute of Mathematics and Information Technology, Department of Applied Mathematics and Cybernetics, Petrozavodsk, Russian Federation

Making managerial decisions when choosing a variant of the technological chain for logging is complicated by the variety of natural and climatic conditions. The climatic features of the periods affect the productivity of technological machines and the cost of implementation. This research suggests using network planning to determine the technological chain of timber land development. The purpose of the research is construction of multi-purpose network models for planning the technological chain of logging operations in various production conditions of forestry enterprises operation. These models are aimed at making it possible to conduct calculations to increase the efficiency of labour, materials, funds, equipment distribution with the maximum reduction in the cost of logged products. As a result of the analysis of possible options for technological chains, several network models for the implementation of logging technological processes have been built.

Key words: logging, management decisions, wood removal, technological chain

INTRODUCTION ating the sequence of technological process operations, not paying attention to the relationship between opera- This is expedient to divide technological process of log- tions at their initial stages. ging implementation for most enterprises in well forested areas into several periods [1]. The number and duration The scientists of Petrozavodsk State University together of periods are associated with the presence or absence with their colleagues from Finland suggest using differ- of waterways, the amount of rainfall, soil conditions of ent decision-making systems [7] GIS technologies and the area and a variety of other reasons. The technolog- simulation modelling [8, 9] to solve such problems. P. ical operations carried out in each period may vary de- V. Budnik in his works [10, 11] suggests using function- pending on the type of technological process adopted al-technological and probabilistic-statistical analysis to at the enterprise, the presence or absence of reload- improve technological chains. Network planning is also ing-and-sorting yards and banking grounds. The noted used in solving decision-making problems when choos- facts make it expedient to create multi-purpose network ing technological chains [12, 13, 14]. However, the sug- models of the technological chain for the implementation gested tools in most cases do not make it possible to of logging operations in large forestry enterprises. take into account the variety of natural and production conditions of the enterprise and the seasonality of the Such problems were addressed by many researchers logging process as well as analyse the likelihood of ac- using various mathematical tools [2, 3]. The authors of curate adherence to work completion dates in order to this research used graphic-analytical methods with cal- justify the need to adjust the organization of work and the endar year division into periods in previous works [4, 5] technological process of the enterprise. to improve technological chains. Methods of felling areas development and technological chains formation in dy- The implementation of the models suggested in the the- namic climatic conditions are also described in the publi- oretical researches of this article is carried out taking into cations of K. P. Rukomojnikov [6]. account the logging work volumes suggested at the early stages of planning in each period and is a consequent However, the suggested methods did not take into ac- structural link in the chain of use of the mathematical ap- count the fact that work at each operation cannot start paratus for the technological process optimization. until a sufficient operational stock of timber is created for this technological site. Thus, the model allows substanti-

*[email protected] 407 Konstantin Rukomojnikov, et al. - Network planning of the technological chain for timber land development

METHODOLOGY tation of transport operations of each period. On the suggested network models, these operations are highlighted As a result of the analysis of possible technological in bold circles and represent the starting and ending tops chains variants, several network models for the imple- of the graphs, as well as the tops showing the start and mentation of logging technological processes have been completion of timber talking out by road and waterways built. They are presented in Figure 1, 2, 3. The tops of in periods. When calculating the early and late terms network models, indicated as circles divided into sec- for the implementation of these operations, it should be tors, represent technological process operations. Names borne in mind that they characterize the boundary values of operations and their serial numbers are indicated in of the periods and must correspond to the earlier estab- the lower sectors of the circles. Operation is indicated lished dates for the start and completion of works in their by an arrow following the top, indicating the operation of relation. Thus, for example, operations on timber taking the logging technological process chain. The duration of out by waterways cannot start before the beginning of the technological operation is indicated above the arrow. the timber rafting period. The earliest calculated dates of the technological operation execution are determined in the left sectors. The RESEARCH OBJECTIVE latest calculated dates of the technological operations implementation, which do not change the planned date The objective of this research is to build multi-purpose for completion of the entire project for timber land devel- network models of the technological chain planning for opment in the analysed time interval under the model, logging operations in various industrial environments are indicated in the right sectors of circles. The late and of forestry enterprises operation, making it possible to early deadlines are equal for the initial and final event. perform calculations to increase the efficiency of labour, materials, funds, equipment distribution with a maximum Since it is enough to partially perform the previous oper- reduction in the cost price of logged products. ation to start the majority of operations of logging technological process, the previous technological operation The research was carried out in the production conditions shall be divided into several same technological opera- of logging enterprises of the Krasnoyarsk territory of Rus- tions, the numbers of which are marked with one or two sia. Large volumes of wood harvesting and long distanc- strokes above the corresponding operation number and es of wood transportation characterize enterprises. symbolic indicators of its duration and time of the start of All activities are presented in the models using the fol- implementation. lowing symbols: tfpi, trci – the duration of felling at timber The special features of the built network models include land followed by transportation to reloading-and-sorting fixed start and completion dates for each of their estimat- yard and banking ground respectively within the i-period, ed periods, which it is advisable to divide the whole year- days; tfi'– the duration of felling at timber land, ensuring ly technological process of the enterprise into due to the the start of work on timber taking within the i-period, days; obvious differences in the performance of the implemen- twrii, twrci – the duration of timber taking out from timber

Период 2= 100 Период 1= 68 138 138 138 150 Данные в клетках на крафе 1 Tewr2' Tlwr2' Teiw2' Tliw2' Tetr2' Tltr2' Tesc2' Tlsc2' примерно под эти данные. 7' 8' 9' 10' Они не нужны для теории. (Removal) (Removal) (Consumer) Они нужны лишь для примера расчета. (IW)

70 55 45 70 tlr2' tsic2 tf2' 68 twri2' 73 78 ttr2' 80 168 168 Tef2 Tlf2 Tewr2 Tlwr2 Teiw2 Tliw2 Tetr2 Tltr2 Tesc2 Tlsc2 Тe2! Тe2! 5 7 5 5 9 2 10 5 6 8 11 (Felling) (Removal) (IW) (Removal) (Consumer)

50 60 60 60 Tliw1' Tetr1' Tltr1' Tesc1' Tlsc1' 0 Tef1 Tlf1 Tewr1' Tlwr1' Teiw1' 2' 4' 5' 1 3' (Removal) (Removal) (Consumer) (Felling) (IW)

45 50 20 39 tf1' twri1' tiw1' ttr1' tsic1 5 5 10 15 16 Tewr1 Tlwr1 Teiw1 Tliw Tetr1 Tltr1 Tesc1 Tlsc1 2 4 5 5 3 5 1 5 (Removal) (IW) (Removal) (Consumer)

Figure 1: Network model of the technological chain for the implementation of two periods with the presence of an reloading-and-sorting yard without waterways

408 Istraživanja i projektovanja za privredu ISSN 1451-4117 Journal of Applied Engineering Science Vol. 19, No. 2, 2021 Konstantin Rukomojnikov, et al. - Network planning of the technological chain for timber land development

land to reloading-and-sorting yard and banking ground certain operations of the logging process chain are repre- respectively within the i-period, days; twrii', twrci'– the sented in the model by the following symbols: Тefi – early duration of timber taking out from timber land within the and late time of the start of timber felling of the i-period, i-period, ensuring the beginning of work in the reload- days; Тewri – early and late time of the start of timber taking-and-sorting yard and banking ground respectively, ing out of the i-period, days; Тeiwi – early and late time of days; tiwi, tcwi – the duration of the timber processing the start of work at the reloading-and-sorting yard within in the reloading-and-sorting yard and banking ground re- the i-period, days; Тetri – early and late time of the start of spectively within the i-period, days; tiwi', tcwi' – the dura- timber transportation from the reloading-and-sorting yard tion of the timber processing in the reloading-and-sorting within the i-period, days; Тesci – early and late time of the yard and banking ground respectively within the i-period, start of timber sale to the consumer within the i-period, ensuring the start of work on timber taking out (rafting), days; Тecwi – early and late time of the start of work at days; twrmi', twri' – the duration of timber taking out from the banking ground within the i-period, days; Тeri – early the reloading-and-sorting yard and rafting from the bank- and late time of the start of work on timber rafting within ing ground respectively within the i-period, ensuring the the i-period, days, (RSY) – reloading-and-sorting yard, beginning of work on the products sale, days; ttri, twri – the (BG) – banking ground. duration of timber taking out from the reloading-and-sort- Modified Bellman-Kalaba algorithm may be used to find ing yard and rafting from the banking ground respective- the late and early dates of the onset of events, as well as ly within the i-period, days; tsici, tscci – the duration of the maximum paths in a digraph. timber sale to the consumer from reloading-and-sorting When setting a task in a fuzzy natural production environ- yard and banking ground respectively within the i-period, ment, which fully corresponds to the technological pro- days, (RSY) - reloading-and-sorting yard. cess of logging operations of large forestry enterprises The early and late dates for the start of the execution of in well-forested areas, it is possible to display the initial

T T tlr2' T T ttr2' T T tsic2 tвп2 - соответственно, время валки на лесных участках первого и второго периода (без последующего сплава), дней.eiw2 liw2 etr2 ltr2 esc2 lsc2 tвс2 - соответственно, время валки на лесных участках первого и второго периода (с последующим сплавом),twri2 дней. 11 13 15 tсд2 - соответственно, время сплава древесины с берегового склада первого и второго периодов, дней (IW) Removal Consumer tсд' - соответственно, время сплава древесины с берегового склада первого и второго периодов, обеспечивающее начало работ по реализации древесины потребителю, дней tв2' - соответственно, время валки на лесных участках первого и второго периодов, обеспечивающее начало работT на вывозкеT древесины с TучастковT периода, днейT T T T tвб - соответственно, время вывозки леса с лесных участков первого и второго периода на береговой склад, днейewr2" lwr2" eiw2' etr2' ltr2' esc2' lsc2' tвп - соответственно, время вывозки леса с лесных участков первого и второго периода на промежуточный склад, дней tri2-tf2' 10' 11liw' 2' 13' 15' tвл2' - соответственно, время вывозки леса с лесных участков первого и второго периодов, обеспечивающее началоRemoval работ на промежуточном складе, дней tвл2' - соответственно, время вывозки леса с лесных участков первого и второго периодов, обеспечивающее начало работ на береговом складе,(IW дней) Removal Consumer tпс2 - соответственно, время обработки на промежуточном складе лесоматериалов, заготовленных в первый и второй периоды, дней tпс2' - соответственно, время обработки лесоматериалов на промежуточном складе вывозки древесины с лесных участков первогоT и второго периода, обеспечивающееT началоT работ по вывозкеТ древесиныТ с промежуточного склада, дней T T T tвл2' - соответственно,время вывозки древесины с промежуточного склада первого и второго периодов, обеспечивающееewr2' lwr начало2' работ по реализации продукции,ecw дней2' lcw2' er2' lr2' Тe2! Тl2! tвд2 - соответственно, время вывозки древесины с промежуточного efсклада2 первогоlf2 и второго периодов, дней tрп2 - соответственно, время реализации с промежуточного склада потребителю9 древесины первого trc2и второго-tf2' периода,10 "дней 12' 14' 17 Removal tрбп2 - соответственно, время реализации с берегового склада потребителюFelling древесины первого и второго периода, дней (CW) Rafting Тпв1 -соответственно раннее и позднее время начала валки леса в первом периоде,tf2' дн Валка Вывозка на ПС Вывозка на БС Тпвл1 -соответственно раннее и позднее время начала вывозки леса в первом периоде, дн T tcw2' T T124 дн 13000 5000 8000 Тппс1 -соответственно раннее и позднее время начала работ на промежуточном складе в первомT периоде,T twrc дн 2' T 31 дн 2000 1000 1000T T Тпвд1-соответственно раннее и позднее время начала вывозки древесины с промежуточногоewr склада2 lwr в первом2 периоде, дн ecw2 lcw2 er2 lr2 esc2' lsc2' 10 12 14 Тпрп1-соответственно раннее и позднее время начала реализации потребителю дрвесины в первом периоде, дн 16' Removal (CW) Rafting Consumer Тпбс1 -соответственно раннее и позднее время начала работ на береговом складе в первом периоде, дн Тпс1 -соответственно раннее и позднее время начала работ по сплаву дрвесины в первом периоде, дн T T tiw T T ttr1' T T tsic1 T T Тп2!- время завершения работ второго периода. Оно равно сумме дней расчетных периодов. eiw1 liw1 etr1 ltr1 esc1 lsc1 esc2 lsc2 Тррп2-раннее времяtwri начала1 работ второго3 периода, дн. Оно равно5 времени когда может7 быть начат второй этап теоретически. tscc2 Тр2!=Тп2! Removal Consumer (IW) 16 http://mas ter.cmc.m Consumer su.ru/files /setevoe_ planirovan T ie.doc.pdf T T T T T T T https://stu ewr1' lwr1' eiw1' liw1' etr1' ltr1' esc1' lsc1' dfile.net/ preview/5 597685/pa 2 ge:6/ tri1-tf1' ' 3' 5' 7' Removal (IW) Removal Consumer Т Т lf1 ef1 T T T T T T 1 ewr1" lwr1" ecw1' lcw1' er2' lr2' Felling trc1-tf1' 2" 4' 6' Removal (CW) Rafting twr1-twr1' T T twrc1' T T tcw1' T T twr1' T T T T ewr1 lwr1 ecw1 lcw1 er1 lr1 esc2 lsc2 esc2' lsc2' 6 2 4 8 8' tscc2 Removal (CW) Rafting Consumer Consumer

Figure 2: Network model of the technological chain for the implementation of two periods with the presence of a reloading-and-sorting yard (RSY) and a banking ground (BG) with timber rafting in the second period

Istraživanja i projektovanja za privredu ISSN 1451-4117 409 Journal of Applied Engineering Science Vol. 19, No. 2, 2021 Konstantin Rukomojnikov, et al. - Network planning of the technological chain for timber land development

Сетевая модель технологической цепочки реализации двух периодов с наличием промежуточного склада (ПС) и берегового склада (БС) Сетевая модель технологической цепочки реализации трех периодов с наличием промежуточного склада (ПС) и берегового склада (БС)

2 T T tiw2,857 T T ttr2' T T tsic2 1 eiw2 liw2 etr2 ltr2 esc2 lsc2 126 136 128 138 twri2 12911139 13 15 (IW) Removal Consumer

8 15,67

Т T T T T T T T 23 ewr2' 155lwr2' eiw2' 149,0 155 etr2' ltr2' esc2' lsc2' 136 155 149,0 155 149,0 tfp2-tf2' 10' 11liw' 2' 13' 15' Removal (IW) Removal Consumer

136 155 144 155,0 T 152,2 155,0T T T T T T T 45 123,0 ewr2" lwr2" ecw2' lcw2' er2' lr2' Тe2! Тl2! 2ef2 lf2 11,5 11,5 18 trc2-tf2' 10" 12' 14' 17 9 Removal (CW) Rafting Felling tf2' 1 3 5,33 T T twrc2' T T 152,2tcw155,02' T T T T 124 124,0 126 137,0ewr2 lwr2 147 149,7ecw2 lcw2 er2 lr2 esc2' lsc2' 10 12 14 16' 2 Removal (CW) 1 Rafting Consumer

45 123,0 101 124,0 101 124 118 124 T 1,857 T T T T Т T T Т T T T ef1 lf1 etr1' esc2 lsc2 ewr1' lwr1' eiw1' liw1' ltr1' esc1' lsc1148' 152,1 tscc2 1 2' 3' 5' 7' 16 Felling Removal (IW) Removal Consumer Consumer 44 99 48 113

7,4 2 8,4 4 10 5 11 50 2,857 T T twri1' T T tiw1' T T ttr1' T T tsic1 1 2 1 155 155 ewr1 lwr1 eiw1 liw1 etr1 ltr1 esc1 lsc1 2 3 5 7 Removal (IW) Removal Consumer

2 25 twrc1' 124 124 125 128 twr2-twr2' T T tcw1 T T 23 twr2' T T T T 1 ecw67 1 lcw1 1 er2 lr2 esc1 lsc1 esc1' lsc1' 4 6 8 8' tfr1-tf1' (CW) Rafting 21,9 Consumer Consumer 99 tscc2 36 123,0 101 124,0 147 #### T T T T ewr1'' lwr1" ecw1 lcw1 - соответственно, время обработки лесоматериалов на промежуточном складе вывозки древесины с лесных участков первого и второго периода, обеспечивающее начало работ по вывозке древесины с промежуточного склада, дней 2'' 4' Removal (CW)

Figure 3: Network model of the technological chain for the implementation of two periods with the presence of a reloading-and-sorting yard (RSY) and a banking ground (BG)

data typical for the technological process implementation thousand m3 of timber in the banking ground in order to in the form of random durations of events with their vari- ensure timber rafting in the next period. In the second pe- ances and mathematical expectations. To ensure unin- riod, it is planned to transport 1 thousand m3 of timber by terrupted operation of the enterprise, the organization of land and 1 thousand m3 – by water. The calculation data work, which satisfies the suggested network models with are summarized in Table 1. a certain degree of probability, taking into account the in- Based on the initial data and suggested variant of the fluence of a number of random natural production factors network model of the technological chain for the imple- on the technological process, is required. mentation of two periods with the presence of a reloading-and-sorting yard (RSY) and a banking ground (BG) RESULTS AND DISCUSSION with timber rafting in the second stage, let us build a To demonstrate the variant of application of one of the network model (Figure 4). The calculated indicators of models, let us carry out the calculation using the suggest- the duration of work indicated in the initial data table are ed network model of the technological chain for the im- random variables characterized by their distribution law plementation of two periods of timber land development and characteristics of average values and variances. with the presence of a reloading-and-sorting yard and a Variances of random variables are not indicated in the banking ground. It is required to justify a rational plan for initial data table, but are previously known. The notations the timber land development. Two periods of timber tak- on the arcs of the network model, constructed to solve ing out are analysed: winter (124 days), winter-spring (31 the example of the suggested problem, demonstrate the day). In the first period, it is planned to lodge 13 thousand mathematical expectation of the operation duration (µ̅) 3 3 and their variances (σ ) separated by a semicolon. m transporting 5 thousand m of timber to the reload- 2 ing-and-sorting yard with their subsequent transportation The constructed model demonstrates that, based on the by land to the consumer, and transporting and storing 8 mathematical expectation of the suggested performance 410 Istraživanja i projektovanja za privredu ISSN 1451-4117 Journal of Applied Engineering Science Vol. 19, No. 2, 2021 Konstantin Rukomojnikov, et al. - Network planning of the technological chain for timber land development

Table 1: Initial data to exemplify solution of the problem

Period winter winter Indicators -spring transportation to RSY BG RSY BG Initial data Average shift productivity of the logging team, m3/shift 100 Number of teams engaged in logging operations, pcs. 1 2 1 1 Average shift productivity of machines for timber transportation to warehouses, 25 40 20 25 m3/shift Number of vehicles for timber taking out to the warehouse, pcs 2 2 2 2 Average shift productivity during handling and processing operations in warehouses, 100 120 100 120 m3/shift Average shift productivity during timber transportation and rafting from the warehouse 44 0 30 350 to the consumer, m3/shift Number of vehicles for transportation to the consumer, pcs. 1 2 Average shift productivity during handling operations at the consumer’s warehouse, 100 0 100 300 m3/shift Calculated indicators Days required for felling, days 50 40 10 10 Days required for taking out, days 100 100 25 20 Days required for handling and processing operations at warehouses, days 50 66.7 10 8.3 Days required for transportation and rafting to the consumer, days 113.6 16.7 25.7 Days required for handling at consumer’s warehouses, days 50 3.3 30

Figure 4: Results of the calculation of the network model and justification of the schedule of the enterprise operation in two analysed periods Istraživanja i projektovanja za privredu ISSN 1451-4117 411 Journal of Applied Engineering Science Vol. 19, No. 2, 2021 Konstantin Rukomojnikov, et al. - Network planning of the technological chain for timber land development values indicated in the initial data for the problem, the the reliability of the suggested variant of operation, imple- variant of organizing the work and the vehicles and mech- mented on the network schedule. anisms selected there for may ensure the implementation To do this, we define critical paths in the implementation of the project, since this does not violate the deadlines of each period. We get that when implementing the first noted at the top of the graph: 6, 7', 10, 17. period, the critical path of this graph is a path character- In addition to the visual calculation of indicators of the ized by vertices: 1, 2, 3, 5, 7, 7', T (Figure 5), and when theoretical feasibility of the project based on the average implementing the second period, the most time-consum- values of the duration of operations (mathematical ex- ing path is: S, 6, 8, 8', 14, 14', 16, 17 (Figure 6). pectations), the analysis of the graph enables to evaluate The values marked on the vertices completing the graphs are indicated in days and mean that the lengths of the

critical paths of the first and second periods t̅ cr on aver-

age are t̅ cr1=117.6 and tcr2=28.2, which means that the obtained values do not exceed the duration of the periods indicated in the initial data. However, in each project of timber land development implemented in conditions of uncertainty, deviations of the lengths of critical paths from their found average value are possible. The magnitude of these deviations is most likely to happen at high values of the total variances of the durations of technological operations of the critical path. We determine the probability of the implementation of the first period in the allotted time for this (T). Considering the average length of critical paths using random values of with the normal law of their distribution, we obtain

æö_ æö_ ç ÷ ç ÷ çTt- cr ÷ Ptç cr T ÷ 05 . +× 05 . fç ÷ èøç ÷ ç o ÷ çèøcr ÷ Figure 5: Example of calculating the critical path of the first period

Figure 6: Example of calculating the critical path of the second period

412 Istraživanja i projektovanja za privredu ISSN 1451-4117 Journal of Applied Engineering Science Vol. 19, No. 2, 2021 Konstantin Rukomojnikov, et al. - Network planning of the technological chain for timber land development

æö_ ç ÷ çT- tcr ÷ f ç ÷ ç O ÷ where èøç cr ÷ is the tabular value of the Laplace probabil- schedules of operation may be easily converted to the ity integral; σcr root mean square deviation of the critical time scale applied to substantiate the efficiency of use of path length. material resources of a forestry enterprise. For the first period: ACKNOWLEDGEMENT o =å o2 =.5 60 cr1 ij(cr1) The reported study was funded by Russian Foundation For the second period: for Basic Research, Government of Krasnoyarsk Terri- tory, Krasnoyarsk Regional Fund of Science, to the re- o = o2 =.2 17 cr2å ij(cr2) search project: «Development of the fundamental prin- Then, the desired probability of implementation of the ciples of forest infrastructure design as a dynamically technological process operation on time for the first and changing system in the conditions of logging production second periods respectively will be equal to: », grant № 19-410-240005.

æö_ ç ÷ REFERENCES Ptç cr1 ×124÷ =.+. 0 5 0 5 f 1 . 136 =. 0 69 èøç ÷ 1. Mokhirev A.P., Pozdnyakova M.O., Medvedev S.O., æö_ ç ÷ Mammatov V.O. (2018) Assessment of Availability Ptç cr 2 ×31÷ =.+. 0 5 0 5 f 1 . 296 =. 0 70 èøç ÷ of Wood Resources Using Geographic Information and Analytical Systems (The Krasnoyarsk Territory Obviously, in order to increase the likelihood of deliv- as a Case Study). Journal of Applied Engineering ering the logged volume of wood to the consumer, it is Science. Vol. 16. Pp. 313-319. DOI: 10.5937/jaes16- necessary to take measures to reduce the time spent for 16908 critical path operations of the first and second periods of the enterprise operation. In particular, in the first period 2. Sokolov A.P., Osipov E.V. (2017) Imitational model- priority attention shall be focused on the activation of the ing of the production process of wood harvesting us- process of timber taking out from the reloading-and-sorting Petri nets. Lesotechnicheskiy zhurnal. Vol. 7. No. ing yard to the consumer’s warehouse; and in the second 3 (27). Pp. 307-314. period – on timber rafting from the banking ground to the 3. Shegelman I. R., Shchegoleva L. V., Ponomarev consumer’s warehouse. Another variant of the decision, A. Yu. (2005) Mathematical model of selection of adopted on the basis of the network model may be a through-flow processes of harvesting, transportation change in the contractual relationship with the consumer and processing of wood raw materials. Izv. spblta. to reduce the planned volume of timber supply from the No. 172. pp. 32-37. reloading-and-sorting yard in the first period and increase 4. Mokhirev A.P., Rukomojnikov K.P. (2019) Graph- them in the next period. ic-analytical modelling of technological chain of logging operations in dynamic natural and production CONCLUSION conditions. IOP Conf. Series: Earth and Environ- Thus, the calculations enable to determine the probabil- mental Science 316 pp. 012-039 DOI:10.1088/1755- ity of completing the set of technological operations of 1315/316/1/012039 the enterprise exactly within the deadline. The number of 5. Rukomojnikov K. P., Mokhirev A. P. (2019) Valida- logging teams, timber removal machines, handling and tion of the Logging Operations Scheme through the processing equipment in reloading-and-sorting yards, Creation of Dynamical Model of the Enterprise Func- banking grounds, consumer’s warehouses etc. has been tioning. Forestry Journal. no. 4, pp. 94–107. DOI: substantiated. It is possible to achieve reduction of the 10.17238/issn0536-1036.2019.4.94 need for material resources of the enterprise by shifting 6. Rukomojnikov K.P. (2015) Justification of methods non-critical operations of the technological process within and parameters of rational technologies for quarter- their full reserve of time, identified on the basis of calcu- ly development of forest areas. Volga. state technol. lations in the presented models. UN-T. Yoshkar-Ola, p. 22. Application of one or a set of several interconnected net- 7. GerasimovYu., Sokolov A., Fjeld D. (2013) Improving work models enables to choose a rational system for the Cut-to-length Operations Management in Russian functioning of the forestry enterprise for any number of Logging Companies Using a New Decision Support periods, distribute production capacities, determine the System. Baltic Forestry. Vol. 19, no. 1(36). Pp. 89- start and end terms, justify the time intervals required 105 for individual operations, the maximum allowable delays 8. Sokolov A. P., Gerasimov Y. Y., Seliverstov A. А. without introducing additional time restrictions for the im- (2009) Methodology for optimizing the fleet of vehi- plementation of model elements. Application of the data cles for the removal of assortment based on simula- obtained makes it possible to perform calculations with tion in the GIS environment. Scientific notes of Petr- the construction of the calendar schedule for the proj- SU. No11(105). pp. 72-77. ect of timber land development. Subsequently, the built

Istraživanja i projektovanja za privredu ISSN 1451-4117 413 Journal of Applied Engineering Science Vol. 19, No. 2, 2021 Konstantin Rukomojnikov, et al. - Network planning of the technological chain for timber land development

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Paper submitted: 13.10.2020. Paper accepted: 29.12.2020. This is an open access article distributed under the CC BY 4.0 terms and conditions.

414 Istraživanja i projektovanja za privredu ISSN 1451-4117 Journal of Applied Engineering Science Vol. 19, No. 2, 2021