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NMŠ, Godište (Volume) 38: 67–77.
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Abstract – Nacrtak

Sustainable management of commercial forests can be achieved within the limits provided by an optimal, well-designed haul network with low-cost roads and skidding. In this study, a weighted-graph algorithm consisting of nodes (candidate log depots) and links (candidate forest roads) was used to optimize the haul network. The value of each link and node was calculated for thirty six candidate road in harvesting units of an Iranian forestry plan. The analysis of the nodes revealed different skidding costs because of different skidding and winching distances as well as number of logs. Total skidding cost for each node allowed identifying the least-cost depots and designing the links as a support to decisions on road network location. Road cost depends on the length and longitudinal gradient of links, side slope of terrain and unit cost of link construction. In general, the construction cost of each link increased by increasing the link length, side slope gradient and longitudinal gradient. According to our findings, the nodes and links constructed on low slope terrain are the least-costly. The information provided in this paper contributes to the development of knowledge about the usefulness of GIS-based weighted-graph algorithm in determining optimal road network in a forest. Total skidding cost is less for a log depot if there are more marked trees in the related cell. So, if the number of marked trees in the vicinity of the depot is higher and the distance to the depot is lower, the total skidding cost of the depot becomes lower.

Keywords: Weighted-graph, forest road, log depot, least-cost, optimization, GIS

1. Introduction – Uvod

The forest road network plays a critical role in providing both access to forest products and human mobility (Lee and Lee 1998, Stefanović et al. 2015). Forest road is important in harvesting operations, because it can affect total cost of forestry plans (Taiwo and Kumi 2013). Although the presence of road infrastructure network is essential for forest life, scarce literature is available on concurrent optimization of harvesting and road network layouts on steep terrain of Hyrcanian zone. In traditional optimization methods, the evaluation systems cannot be adapted to the needs of sustainable development of forest (Dahlin et al. 1992, Bin 2012, Galatioto et al. 2015). Therefore, nowadays, due to advances in computer sciences and remote sensing softwares, computer optimization models using Geographical Information System (GIS) are becoming practical (Sole and Valverde 2004, Jaafari et al. 2015).

Vector-based model and raster-based model are the two major models in GIS that represent spatial data for optimization algorithms. Vector-based model uses simple geometric designs such as nodes, links and polygons to represent spatial objects, while raster-based model quantizes an area into small discrete grid-cells. Digital elevation model (DEM) and digital terrain models (DTM) are cell format data sets. By using these models, different link patterns can be formulated to solve complex network theory. In a raster-based system, all cells are uniform and cells can represent a graph with nodes, links, polygons and surfaces. Liu and Dong (2008) used road network analysis algorithm with graph theory including corridor density, α circuitry index, β line-node ratio, and γ connectivity index. Watanabe (2010) used a proximity graph to analyze the road network patterns of major cities in the United States. Each link of proximity graphs on a digital map was compared with road links. Xie and Levinson (2007) attempted the graph theoretical analysis of transportation networks.

Networks can be classified into regular networks, random networks and complex network (Albert and Barabasi 2002). Regular networks, such as those used in the present study, have square lattices. A forest transportation network consists of the winching routes that collect felled and bucked trees from the entire cell (a portion of forest on a raster map) to a skidder on skid trail (Lockwood and Moore 1992). Then, timber is hauled on skid trails to a candidate log depot as a node and finally loaded and transported on the road as a link (Lu and Eriksson 2000). Epstein et al. (1994) made the planning software for optimizing the location of roads and log depots in forest operations. Some researchers used a GlS package for digitizing forest topographic maps and calculating distances from each raster cell to the nearest road on the digital terrain model. Besides, raster-based GIS data can be used to locate an optimal log depot in forest operation planning. This model found skid trails from stump to each candidate log depot and selected the best depot location with minimum total skidding and road costs (Liu and Sessions 1993, Tucek 1994, Contreras and Chung 2007). Naghdi and Mohammadi Limaei (2009) used linear programming model to reduce the skidding costs and to determine the optimal forest road network density.

Analysis of graph algorithm, including node and link characteristics of cells, is considered to improve strategic planning of forest road network (Anderson and Nelson 2004). Most existing optimization models for forest road planning do not work well as they assume that road construction costs are homogenous over the entire project area and neglect the total skidding costs for different candidate log depots at a raster cell size scale, whereas in this study construction cost of road and skidding cost of depot are separately calculated for each link and node. Log depots are temporary timber storage areas at forest road landings (Jourgholami et al. 2013). This study has shown the ability of application of computer techniques and methods in the analysis of the most important factors affecting the total logging costs and selection of optimum density of forest roads in the forest area. Moreover, attempts were made to complete and improve the proposed road network in a forest area taking into consideration various link patterns. This problem was mapped on a graph. The graph consists of a set of nodes and a set of road links between two nodes. The weight of a link represents road costs. Indeed, the objective of this research was to provide a weighted-graph algorithm so that planners could locate the least-cost road variant and log depot. Finally, comments are given on advantages, limitations and improvements of the presented optimization algorithm.

2. Materials and Methods – Materijal i metode

2.1 Creating a graph with nodes and links – Izrada grafikona s čvorovima i vezama

Bahramnia forest is located in Golestan province and in watershed number 85. This forest is divided into two districts. District I with an area of 1713.3 ha is extended from 36˚43´27˝ to 36˚45´6˝ N and 54˚21´26˝ to 54˚24´57˝ E. District II with an area of 1992 ha is located from 36˚42´30˝ to 36˚43´30˝ N and 54˚21´6˝ to 54˚23´30˝ E. The total length of forest roads in districts I and II is 30.3 and 28 km, respectively (21 km is located in timber compartments with an area of 995 ha). In our study area, single-tree selection method was applied in timber compartments at 10-year intervals. Two cycles of operations have already been done in district I. District II has not been harvested yet. The tree species of the case study are Parrotia persica, Carpinus betulus, Fagus orientalis, Quercus castaneifolia and Zelkova carpinifolia. The mean density of trees per hectare was 214.92 and the canopy cover was 75–85 % (Fig. 1).

Fig. 1 Study area located in northern forests of Iran

Slika 1. Područje istraživanja smješteno u sjevernim šumama u Iranu

In this study, portions of the forest, with trees marked for felling, were selected as harvesting units. A harvesting unit is an area to be harvested by ground-based skidding system and all logs hauled into depots by skidders. To produce the raster-base slope map of this area, the DEM of harvesting units was prepared from topography map and then the slope layer was produced by surface analysis tool. The slope layer of this portion was converted into raster format to use the cell size and cover it with a set of nodes and links. Each three cells on a vertical line were considered as a harvesting unit. Nodes as candidate log depots were placed on a regular grid and links that represented potential roads were projected to connect the nodes. Links with maximum length of 75 m were connected from a node to eight adjacent nodes (Fig. 2).

2.2 Total Skidding Cost (TSC) – Ukupni troškovi privlačenja (UTP)

The aim of the optimization algorithm used in this study was to create a graph with several candidate log depots within each harvesting unit. This algorithm can solve the haul network problem by minimizing the sum of road construction plus skidding costs. Depots were located on a slope less than 10 % for loading by crane. Candidate depots were arranged on a line in a harvesting unit. The distance between two lines was 150 meters. Indeed, this distance indicates the sum of winch cable length (50 m) and trees average length (25 m) at each side of the skid trail. The model calculates total skidding cost for a candidate depot k by adding up all the skidding costs from each cell to the candidate log depot k (Eq. 1) (Contreras and Chung 2007):

                        (1)

Where:

TSC_k total skidding cost for a candidate depot k, $

m total number of cells within the harvesting unit

SC_i skidding cost from the ith cell to log depot k.

The skidding cost for each cell is calculated using Eq. 2 (Contreras and Chung 2007):

                (2)

Where:

CT_i overall time consumption for a skidding cycle (min) from i^th cell to log depot

K is calculated using Eq. 3 (Mousavi 2012)

R represents the rental rate of a skidder which was 18.9 $ hr^-1,

N_i number of turns for skidding all timber from ith cell to log depot k.

The average timber volume per turn was 1.85 m³.

           (3)

Where:

X skidding distance, m

X_n number of logs

X_Wwinching distance, m

X_L log length, m.

Fig. 2 Graph created by links and nodes for a given harvesting unit

Slika 2. Grafikon izrađen pomoću veza i čvorišta za istraživanu sječinu

2.3 Total Road Cost (TRC) – Ukupni troškovi šumske ceste (UTŠC)

A set of links were created to connect a forest road from one depot back to the existing network. Once this new road is connected, it is added to the road network. Then the next depot is selected and connected to the road network. The procedure is repeated until all depots are connected. The total road cost for road candidate k is calculated using Eq. 4 (Contreras and Chung 2007):

                       (4)

Where:

TRC_k total road construction cost for road candidate k ($)

e total number of links for road k

RC_i construction cost of i^th link calculated using Eq. 5 (Contreras and Chung 2007):

               (5)

Where:

LD_i length of the link (m)

RC unit cost of road construction ($ m^-1) assumed to be 16.22 $ m^-1 in this study

LS_i longitudinal road gradient factor and SS_i is side slope factor (Table 1).

The road gradient must be less than 12 %.

Table 1 Road gradient and side slope factors (Contreras and Chung 2007)

Tablica 1. Faktori uzdužnoga nagiba šumske ceste i nagiba terena

Road gradient, % Uzdužni nagib šumske ceste, %	Road gradient factor Faktor uzdužnoga nagiba šumske ceste	Side slope, % Nagib terena %	Side slope factor Faktor nagiba terena
0–5	1.0	0–15	1.0
5–10	1.5	15–30	1.5
10–15	2.5	30–45	2.5
15–20	3.5	45–60	3.5

2.4 Optimization by graph analysis – Optimizacija grafičkom analizom

Total Harvesting Cost (THC) for candidate depot and road k was calculated using Eq. 6 and finally the least-cost variant was selected as the optimal depot and road location in the harvesting unit. Fig. 3 shows the procedure used to find the least-cost route from depots to the existing road in a flow chart.

           (6)

Fig.3 Diagram of the optimization algorithm used in the present study

Slika 3. Dijagram optimiziranoga algoritma uporabljena u istraživanju

3. Results – Rezultati

3.1 Total skidding cost for candidate depots – Ukupni troškovi privlačenja do predloženih mjesta pomoćnih stovarišta

Different distribution of marked trees in a harvesting unit has large effects on log depot location. In this study, two terminals have been located as log depots 9 and 10. Links and nodes were routed in zigzag shape to access terminal depots without considering curve design. Indeed, all links were assumed to be straight lines. The total skidding cost for a depot is limited by the overall time spent for a skidding cycle and the number of trips for skidding all timber. The skidding cycle time depends on log size, number of logs, winching and skidding distances. The influence of variables is not the same. Skidding cost in lower slope is less than that of higher side slope. Therefore, log depot location was shifted to lower slopes. Total skidding cost at four harvesting units in depots 1, 5, 7 and 9 were 72.80 $, 92.60 $, 65.75 $ and 29.23 $. These are the optimal log depot locations without considering road construction cost. Table 2 shows the skidding parameters of candidate log depots for locating the least-cost depot. Total skidding cost is less for a log depot having more marked trees in the related cell. So, if the number of marked trees in the vicinity of the depot is higher and the distance to the depot is lower, the total skidding cost of the depot becomes lower.

Table 2 Values of skidding time ( ), number of skidding turns ( ) and skidding cost from each cells to candidate depots ( ) as well as the total skidding cost for candidate depots in harvesting units ( )

Tablica 2. Vrijednosti vremena privlačenja (CT_i), broj turnusa privlačenja (N_i) i troškovi privlačenja od svake ćelije do predloženih mjesta pomoćnih stovarišta (SC_i) te ukupni troškovi privlačenja za predoložena mjesta pomoćnih stovarišta u sječini (TSC_k)

Skidding cycle time Vrijeme turnusa privlačenja	Candidate depots – Predložena mjesta pomoćnih stovarišta
	1	2	3	4	5	6	7	8	9	10
CT1, min	9.35	12.15	13.51	10.36	12.18	14.92	11.32	13.16	10.54	12.40
CT2, min	11.58	8.86	10.22	8.92	7.10	9.84	9.02	10.86	8.32	8.38
CT3, min	15.26	12.54	11.20	14.09	12.25	9.52	10.11	8.27	12.07	10.20
N1	12.00	12.00	12.00	12.00	12.00	12.00	7.00	7.00	3.00	3.00
N2	5.00	5.00	5.00	7.00	7.00	7.00	11.00	11.00	3.00	3.00
N3	4.00	4.00	4.00	8.00	8.00	8.00	3.00	3.00	3.00	3.00
SC1, $	35.34	45.92	51.09	39.18	46.05	56.40	24.95	29.02	9.96	11.72
SC2, $	18.24	13.95	16.10	19.67	15.66	21.70	31.24	37.64	7.86	7.92
SC3, $	19.22	15.79	14.11	35.51	30.88	23.99	9.56	7.81	11.40	9.64
TSCk, $	72.80	75.67	81.30	94.36	92.60	102.09	65.75	74.48	29.23	29.27

3.2 Total road cost for candidate roads – Ukupni troškovi predloženih šumskih cesta

36 access roads were analyzed considering their accessibility to a depot in each harvest units (Fig. 4). Each road was evaluated by calculating the construction cost of links that make a road. The present investigation takes account of the varying road construction cost over different kinds of terrain slope. Road cost depends on the length of links, longitudinal gradient of links, side slope of terrain and unit cost of link construction. Results show that, in general, the construction cost of each link increased by increasing the link length, side slope gradient and longitudinal gradient. Therefore, the construction cost of candidate roads 6, 12, 31 and 32 is higher than the cost of other candidate roads. These cases consider a road construction cost of 16139$, 16187$, 16686$ and 16637$, respectively. In addition, the construction cost of candidate roads 2, 8, 14 and 20 are the lowest (Table 3). These cases consider a road construction of 9435$, 9483$, 9848$ and 9896$, respectively. As shown in Table 2 and Table 3, total harvesting cost is relatively insensitive to skidding costs of depots in the study area. As the log depots are only located on slopes less than 15 %, the number of candidate depots for a given harvesting unit varies. As the depot spacing increases, fewer depots are present, and therefore the supplementary network (skid trail) length increases. As the log depots spacing increases, roads are able to avoid steep slope and the average longitudinal gradient is improved.

3.3 Total harvesting cost for candidate depots and roads – Ukupni troškovi privlačenja pri predloženim šumskim cestama i mjestima pomoćnih stovarišta

In this study, the total area of the selected harvesting units is 18 ha with a mean volume of 350 m³ logs. Some areas within the harvesting unit with the slope of more than 10 % have not been taken into consideration for locating log depots. In addition, the road gradient must be less than 9 % for safe truck driving according to the standard limit value. If the gradient is higher than 9 %, the link becomes unacceptable for road construction. The mean road gradient of optimal road is 4 % or 5 % less than the road gradient limit. Total harvesting cost is computed by adding total skidding cost to road construction cost. An optimal road candidate is the variant with the least total harvesting cost. So, road candidate 2 was chosen as the optimal variant (Table 4). Fig. 5 presents the optimal graph of road network as the least-cost candidate road. The weights of links in the network are determined according to construction cost. The lower the cost, the greater the chance that link will get routed. The total skidding cost of depots and construction cost of optimal road are 262.14$ and 17.73$ m^-1, respectively. Total length and total harvesting cost of the optimal graph are 532 m and 9697.14$, respectively. The analysis shows that the algorithm is feasible in selecting the optimal road according to the depots variable and construction cost.

Fig. 4 Different road network candidates developed by connecting log depots in harvesting units. Shaded grid cells represent different slope percentages (0–5 %, 5–10 % and 10–15 %)

Slika 4. Predloženo razvijanje šumske ceste dobivene povezivanjem mjesta pomoćnih stovarišta u sječinama; tamnije ćelije predstavljaju različite nagibe terena u postocima (0–5 %, 5–10 %, 10–15 %)

Table 3 Construction cost of links and total road construction cost attributes of 36 candidate roads examined in this research

Tablica 3. Troškovi izgradnje veza i ukupni troškovi izgradnje za 36 predloženih inačica šumskih cesta ispitanih u ovom istraživanju

Link – Veza	$	Link – Veza	$	Link – Veza	$	Link – Veza	$	Link – Veza	$	Link – Veza	$
RC1–5	4157	RC1–4	3339	RC1–6	7605	RC1–5	4157	RC1–4	3339	RC1–6	7605
RC5–7	2475	RC4–7	2671	RC6–7	3500	RC5–8	3403	RC4–8	3975	RC6–8	3406
RC7–9	3425	RC7–9	3425	RC7–9	3425	RC8–9	5128	RC8–9	5128	RC8–9	5128
TRC1	10,057	TRC2	9435	TRC3	14,530	TRC4	12,688	TRC5	12,442	TRC6	16,139
RC1–5	4157	RC1–4	3339	RC1–6	7605	RC1–5	4157	RC1–4	3339	RC1–6	7605
RC5–7	2475	RC4–7	2671	RC6–7	3500	RC5–8	3403	RC4–8	3975	RC6–8	3406
RC7–10	3473	RC7–10	3473	RC7–10	3473	RC8–10	5176	RC8–10	5176	RC8–10	5176
TRC7	10,105	TRC8	9483	TRC9	14,578	TRC10	12,736	TRC11	12,490	TRC12	16,187
RC2–4	5184	RC2–5	3948	RC2–6	5178	RC2–4	5184	RC2–5	3948	RC2–6	5178
RC4–7	2671	RC5–7	2475	RC6–7	3500	RC4–8	3975	RC5–8	3403	RC6–8	3154
RC7–9	3425	RC7–9	3425	RC7–9	3425	RC8–9	5128	RC8–9	5128	RC8–9	4357
TRC13	11,280	TRC14	9848	TRC15	12,103	TRC16	14,287	TRC17	12,479	TRC18	12,689
RC2–4	5184	RC2–5	3948	RC2–6	5178	RC2–4	5184	RC2–5	3948	RC2–6	5178
RC4–7	2671	RC5–7	2475	RC6–7	3500	RC4–8	3975	RC5–8	3403	RC6–8	3154
RC7–10	3473	RC7–10	3473	RC7–10	3473	RC8–10	5176	RC8–10	5176	RC8–10	4405
TRC19	11,328	TRC20	9896	TRC21	12,151	TRC22	14,335	TRC23	12,527	TRC24	12,737
RC3–4	6707	RC3–4	6707	RC3–5	4564	RC3–5	4564	RC3–6	4567	RC3–6	4567
RC4–7	3498	RC4–7	3498	RC5–7	2475	RC5–7	2475	RC6–7	3500	RC6–7	3500
RC7–9	3425	RC7–10	3473	RC7–9	3425	RC7–10	3473	RC7–9	3425	RC7–10	3473
TRC25	13,630	TRC26	13,678	TRC27	10,464	TRC28	10,512	TRC29	11,492	TRC30	11,540
RC3–4	6707	RC3–4	6707	RC3–5	4564	RC3–5	4564	RC3–6	4567	RC3–6	4567
RC4–8	4802	RC4–8	4802	RC5–8	3403	RC5–8	3403	RC6–7	4458	RC6–7	4458
RC8–10	5176	RC8–9	5128	RC8–9	5128	RC8–10	5176	RC7–9	3425	RC7–10	3473
TRC31	16,686	TRC32	16,637	TRC33	13,095	TRC34	13,143	TRC35	12,450	TRC306	12,498

Table 4. Total harvesting cost ( used for analysis of 36 candidate roads

Tablica 4. Ukupni troškovi privlačenja (UTP) u analizi 36 predloženih inačica šumskih cesta

THCk	$	THCk	$	THCk	$
THC1	10,317.38	THC13	11,545.01	THC25	13,900.64
THC2	9697.14	THC14	10,111.25	THC26	13,948.68
THC3	14,799.87	THC15	12,375.74	THC27	10,732.88
THC4	12,957.11	THC16	14,560.74	THC28	10,780.92
THC5	12,712.87	THC17	12,750.98	THC29	11,770.37
THC6	16,417.60	THC18	12,970.47	THC30	11,818.41
THC7	10,365.42	THC19	11,593.05	THC31	16,964.37
THC8	9745.18	THC20	10,159.29	THC32	16,916.41
THC9	14,847.91	THC21	12,423.78	THC33	13,372.61
THC10	13,005.15	THC22	14,608.78	THC34	13,420.65
THC11	12,760.91	THC23	12,799.02	THC35	12,728.37
THC12	16,465.64	THC24	13,018.51	THC36	12,776.41

 

Fig. 5 Least–cost road selected as optimal variant in weighted–graph algorithm

Slika 5. Inačica šumske ceste s najmanjim troškovima odabrana kao optimalna varijanta dobivena ponderiranim grafičkim algoritmom

4. Discussion – Rasprava

This study fills a knowledge gap in the application of computer road design in Iranian forestry and shows how weighted–graph algorithm can support decision makers in locating log depots and road network. Minimization of total costs of skidding and road construction was the traditional method to determine the optimal forest road density in a forest area (You et al. 2003, Chung et al. 2004, Żak and Węgliński 2014). This method is very similar to weighted–graph algorithm used in the present study. Ghaffarian and Sobhani (2007) calculated the optimum road density by minimizing the sum of road construction and skidding costs. In another study, they developed a skidding model by stepwise regression to predict the cost of skidding per cubic meter for 39 nodes. The harvesting volume and road construction cost for each node were computed by using NETWORK 2000 and shortest path algorithm (Ghaffarian and Sobhani 2008). In this study, we used 12 nodes and 96 links to produce a graph for the optimization algorithm. The total skidding cost for a node decreased by decreasing the overall time spent for a skidding cycle and the number of trips for skidding all timber. Moreover, road cost increased with increasing length of links, longitudinal gradient of links, terrain slope and unit cost of link construction. Ghaffarian et al. (2010) used the same cost for yarding and road segment per node and links. Rees (2004) calculated the least–cost paths by applying Dijkstra’s algorithm on a Digital Elevation Model. In this study, the total road construction cost was considered plus total skidding cost, as this factor was considered more important than other factors within the region.

A very big graph or network in the present algorithm is inefficient since a lot of calculations need to be repeated (Yongtaek and Hyunmyung 2005, Olsson 2007). In our study, links and nodes were routed in zigzag shape to access terminal depots without considering curve design. Therefore, it is necessary to develop a graph with the curvature design as used by Stückelberger et al. (2007). In this study, a weighted–graph algorithm consisting of nodes (depots) and links (roads) was used to optimize the haul network in the forest. Well–designed or optimal road network is a graph that includes the least–cost roads and skidding. The lower the cost, the greater is the chance that the link will get routed. Stückelberger et al. (2007) found that by considering various link patterns, road design elements and constraints, a designer can select cost–effective locations for road network in steep terrain on mountainous project areas. Liu and Sessions (1993) used an algorithm to find the least–cost road links by considering construction, maintenance and transport costs and various topographic conditions. Dahlin and Sallnas (1992) found the optimum road location by minimization of road transportation cost and road construction cost. They used a simulated annealing (SA) algorithm to optimize the road location. Locating roads within steep terrain can only be done if high node densities (30 nodes ha^–1) are used and obstacles are considered. In gentler terrain, node density can be reduced. Raster layers consist of a grid support accurate analysis of a graph (Dahlin and Sallnas 1992). Among 532 m of roads optimized by the weighted–graph algorithm in the study area, 432 m of roads were located within the slope terrain of 0–5 % and 100 m within 5–10 %. Our findings show that the optimization algorithm provides equal distribution of roads over the study area using short road length. The algorithm used in this research could provide engineers with good candidate choices for a forest road network plan.

In the present study, a weighted–graph algorithm has been developed to find the least–cost road network and log depots in harvesting units. The advantage of the model is that it can consider a wide range of data including skidding distance, number of logs and skidding turns, winching distance, skidder cost, log length, side slope, road gradient and road length, which may affect the total cost of skidding and road construction. The economic analysis carried out in this paper clearly illustrates the adequacy of application of the methodology used for opening of the forest area. Weighted–graph optimization algorithm requires many input parameters to determine the desired location of the road network and log depots. Therefore, other parameters can be added to the model in individual harvest units with their unique physiographic and vegetative conditions. The results of the analysis based on the weighted–graph on raster cells do not provide the understanding of nature, but this approach offers simplicity in implementation. Additional research needs to be done on refining links geometry in order to accurately evaluate longitudinal gradient and vehicle speed and to improve estimates of construction quantities. Moreover, algorithms such as Dijkstra should be integrated in weighted–graphs to produce better networks at lower cost.

5. References – Literatura

Albert, R., Barabási, L., 2002: Statistical mechanics of complex networks. Reviews of modern Physics 74: 47–97.

Anderson, A. E., Nelson, J., 2004: Projecting vector based road networks with shortest path algorithm. Canadian Journal of Forest Research 34: 1444–1457.

Bin, W., 2012: Forest road network sustainable development indicator system evaluate optimization support vector machine ant colony algorithm. PhD thesis, Central South University of Forestry Science and Technology, Forest Engineering Course, 200 p.

Contreras, M., Chung, W., 2007: A computer approach to finding an optimal log landing location and analyzing influencing factors for ground–based timber harvesting. Canadian Journal of Forest Research 37: 276–292.

Chung, W., Sessions, J., Heinimann, H., 2004: An application of heuristic network algorithm to cable logging layout design. International Journal Forest Engineering 15: 11–24.

Dahlin, B., Sallnas, O., 1992: Designing a forest road network using the simulated annealing algorithm. InProc: Computer supported planning of roads and harvesting workshop. Feldafing, Germany. pp. 36– 41.

Epstein, R., Weintraub, A., Sapunar, P., Sessions, J., Sessions, J. B., 1994: PLANEX software for operational planning. International Seminar on Forest Operations under Mountainous Conditions, July 24–27, 1994, Harbin, P.R. of China.

Galatioto, F., Huang, Y., Parry, T., Bird, R., Bell, M., 2015: Traffic modeling in system boundary expansion of road pavement life cycle assessment. Transportation Research Part D: Transport and Environ 36: 65–75.

Ghaffarian, M. R., Sobhani, H., 2007: Optimization of an existing forest road network using Network 2000. Croatian Journ al of Forest Engineering 28: 185–193.

Ghaffarian, M.R., Sobhani, H., 2008: Optimum road spacing of ground based skidding operations in Nowshahr, Iran. Caspian Journal of Environmental Science 6: 105–112.

Ghaffarian, M. R., Stampfer, K., Sessions, J., Durston, T., Kuehmaier, M., Kanzian, C. H., 2010: Road network optimization using heuristic and linear programming. Journal of Forest Science 56: 137–145.

Jaafari, A., Najafi, A., Rezaeian, J., Sattarian, A., Ghajar, I., 2015: Planning road networks in landslide–prone areas: A case study from the northern forests of Iran. Land Use Policy 47: 198–208.

Jourgholami, M., Abdi, E., Chung, W., 2013: Decision making in forest road planning considering both skidding and road costs: a case study in the Hyrcanian Forest in Iran. iForest 6: 59–64.

Lee, K., Lee, H., 1998: A new algorithm for graph–theoretic nodal accessibility measurement. Geographical Analysis 30: 1–14.

Liu, S., Dong, Y., 2008: Characterizing the hierarchy of road network and its landscape effect with graph theory. The 7th International Symposium on Operations Research and Its Applications (ISORA’08), Lijiang, China, October 31–Novemver 3, 2008, pp. 152–159.

Liu, K., Sessions, J., 1993: Preliminary planning of road systems using digital terrain models. International Journal Forest Engineering 4:27–32.

Lockwood, C., Moore, T., 1992: Harvest scheduling with spatial constraints: a simulated annealing approach. Canadian Journal of Forest Research 23:468–478.

Lu, F., Eriksson, L. O., 2000: Formation of harvest units with genetic algorithms. Forest Ecology and Management 130:57–67.

Mousavi, R., 2012: Time consumption, productivity, and cost analysis of skidding in the Hyrcanian forest in Iran. Journal of Forestry Research 23: 691–697.

Naghdi, R., Mohammadi Limaei, S., 2009: Optimal forest road density based on skidding and road construction costs in Iranian Caspian forests. Caspian Journal of Environmental Science7: 79–86.

Olsson, L., 2007: Optimal upgrading of forest road networks: Scenario analysis vs. stochastic modeling. Forest Policy and Economics 9: 1071–1078.

Rees, W. G., 2004: Least–cost paths in mountainous terrain. Computers & Geosciences 30: 203–209.

Stefanović, B., Stojnić, D., Danilović, M., 2015: Multi–criteria forest road network planning in fire–prone environment: a case study in Serbia. Journal of Environmental Planning and Management 1–16.

Stückelberger, J., Heinimann, H. R., Chung, W., 2007: Improved road network design models with the consideration of various link patterns and road design elements. Canadian Journal of Forest Research 37: 2281–2298.

Sole, R. V., Valverde, S., 2004: Information theory of complex networks: On Evolution and Architectural Constraints. Lecture Notes Physics 650: 189–207.

Taiwo, A., Kumi, F., 2013: An appraisal of road condition effect on rural transportation in Sekyere central district of the Ashanti Region of Ghana. Journal of Transportation Technologies 3: 266–271.

Tucek, J., 1994: Using the GIS environment for opening–up of forest. International Seminar on Forest Operations under Mountainous Conditions, July 24–27, 1994, Harbin, P.R. of China.

Watanabe, D., 2010: A study on analyzing the grid road network patterns using relative neighborhood graph. The Ninth International Symposium on Operations Research and Its Applications (ISORA’10), Chengdu–Jiuzhaigou, China, August 19–23, 2010, pp. 112–119.

Yongtaek, L., Hyunmyung, K., 2005: A shortest path algorithm for real road network based on path overlap. Journal of the Eastern Asia Society for Transportation Studies 6: 1426–1438.

Yu, C., Lee, J., Munro-Stasiuk, M. J., 2003: Extensions to least–cost path algorithms for roadway planning. International Journal of Geographical Science 17: 361–376.

Xie, F., Levinson, D., 2007: Measuring the structure of road networks. Geographical Analysis39:336–356.

Żak, J., Węgliński, S., 2014: The selection of the logistics center location based on MCDM/A methodology. Transportation Research Procedia 3: 555–564.

 

Određivanje najpovoljnijih mjesta pomoćnih stovarišta i najpovoljnijega pružanja šumske ceste ponderiranim grafičkim algoritmom optimizacije

Sažetak

Održivo i ekonomski isplativo gospodarenje šumskim ekosustavima može se postići isključivo u slučaju uspostave optimalne šumske transportne mreže na terenu pri kojem su troškovi izgradnje i održavanja primarne i sekundarne šumske prometne infrastrukture svedeni na minimum. U ovom istraživanju korišten je ponderirani grafički algoritam koji je pomoću čvorova (prijedlog mjesta pomoćnih stovarišta) i veza (inačica šumske ceste) optimizirao šumski transportni sustav. Vrijednosti svakoga čvora i veze izračunavane su za svih 36 inačica šumskih cesta u istraživanoj sječini. Analizirajući vrijednosti čvorova (mjesta pomoćnih stovarišta) ustanovljeno je kako ukupni troškovi privlačenja variraju u ovisnosti o vrijednostima duljine privitlavanja i privlačenja te o broju privučenih trupaca. Ukupni troškovi privlačenja izračunati za svaki čvor omogućili su određivanje mjesta pomoćnih stovarišta kod kojih su troškovi privlačenja najniži te nadalje određivanje veza koje će poslije služiti pri odlučivanju o optimalnom horizontalnom pružanju šumske ceste. Troškovi vezani uz šumsku cestu ovise o duljini i uzdužnom nagibu veza, poprečnom nagibu terena i jediničnim troškovima izgradnje pojedine veze. Općenito se može reći da troškovi izgradnje svake veze rastu povećanjem duljine veze, poprečnoga nagiba terena i uzdužnoga nagiba. Rezultati ovoga istraživanja pokazuju da su čvorovi i veze konstruirani na padinama blažih nagiba najjefitinije, a ujedno i ekonomski najopravdanije inačice. Rezultati dobiveni ovim istraživanjem uvelike doprinose razumijevanju svih pogodnosti koje, na GIS-u temeljen, ponderirani grafički algoritam pruža pri određivanju optimalnoga šumskoga transportnoga sustava. Ukupni troškovi privlačenja manji su na pomoćnim stovarištima u čijem gravitacijskom području postoji veća doznačena masa odnosno više doznačenih stabala. Dakle, ako je broj doznačenih stabala u blizini mjesta pomoćnih stovarišta veći, a udaljenost do pomoćnoga stovarišta manja, ukupni troškovi privlačenja promatranoga pomoćnoga stovarišta postaju manji.

Ključne riječi: ponderirani grafikon, šumska cesta, pomoćno stovarište, minimalni troškovi, optimizacija, GIS

 

Authors’ addresses – Adrese autorâ:

Assist. prof. Aidin Parsakhoo, PhD.

e-mail: Aidinparsakhoo@yahoo.com

Gorgan University of Agricultural Sciences and Natural Resources

Faculty of Forest Science

Department of Forestry

Gorgan, P.O. Box 386

IRAN

Assoc. prof. Majid Lotfalian *

e-mail: mlotfalian@sanru.ac.ir

University of Agricultural Sciences and Natural Resources of Sari

Faculty of Natural Resources

Department of Forestry

Sari, P.O. Box 737

IRAN

Corresponding author – Glavni autor *

Received (Primljeno): February 21, 2017.

Accepted (Prihvaćeno): May 15, 2017.

Proffesional paper – Stručni rad