A Two-Stage DSS to Evaluate Optimal Locations for Bioenergy Facilities

: Research Highlights: A set of 128 potential bioenergy facility locations is established and evaluated based on the transport cost to select optimal locations. Background and Objectives: The identiﬁcation of optimal facility locations to process recovered forest biomass is an important decision in designing a bioenergy supply chain at the strategic planning level. The result of this analysis can a ﬀ ect supply chain costs and the overall e ﬃ ciency of the network, due to the low density and dispersed nature of forest biomass and the high costs associated with its logistics operations. In this study, we develop a two-stage decision support system to identify the optimal site locations for forest biomass conversion based on biomass availability, transport distance and cost. Materials and Methods: In the ﬁrst stage, a GIS-based analysis is designed to identify strategic locations of potential bioenergy sites. The second stage evaluates the most cost-e ﬀ ective locations individually using a transportation cost model, based on the results from stage one. The sensitivity of inputs, such as maximum allowable transport cost, the distance of transport and their relations to the proﬁt balance, and changes in fuel price are tested. The method is applied to a real case study in the state of Queensland, Australia. Results and Conclusions: The GIS analysis resulted in 128 strategic candidate locations being suggested for bioenergy conversion sites. The logistics analysis estimated the optimal cost and transportation distance of each one of the locations and ranked them according to the overall performance between capacities of 5 and 100 MW. An overview of the developed methodology.


Introduction
In Australia, native forests, timber plantations, and wood products absorbed 56.5 M tonnes of carbon dioxide in the year 2005, which reduced the total emissions by almost 10% [1]. Australia has 134 M hectares of forest, which is the seventh-largest reported forest area worldwide. Only one percent of this area is harvested for commercial timber and wood products [2]. The leftover material, forest biomass, can provide additional revenue streams for forest managers and supply a bioenergy market, while further contributing to climate change mitigation efforts [3]. Using forest biomass for bioenergy should be promoted to become an integrated part of forestry and a priority for all biomass utilization projects [4]. Sustainably sourced forest biomass can be combusted to generate heat, steam, and electricity [5,6]. However, this bioenergy trend receives little public attention and political support in Australia [7]. The bioenergy market represents only 4% of total energy production in Australia [8] and, of this, forest biomass is 25%, and bagasse or sugarcane residue is 29% [8,9]. With the lack Assessment Version One (BRAVO), was the first reference GIS-based DSS for bioenergy facility locations developed [25]. The BRAVO model was then altered by Voivontas et al. [20] to successfully implement the use of suitability and optimality analyses, in a GIS DSS, for locating facilities. The suitability analysis evaluated the centroids of administrative areas as potential facility locations. Shi et al. [16] converted remotely sensed biomass data for the supply of resources in a service-area model, using potential facility locations on a road network as demand points. Zhan et al. [38] established a delivery cost surface and treated every point of the surface as a potential location for energy conversion. Guilhermino et al. [39] applied a suitability analysis to different municipalities in a case study in Portugal to find the best location for energy conversion. Ranta [19] applied a resource location-allocation model according to supply resources from logging residues in Finland in a case study at the lowest cost possible. Frombo et al. [40] described an environmental DDS (EDDS) to minimize the overall cost in the planning of woody biomass logistics while taking into account the environmental impact. Freppaz et al. [42] applied a DSS to minimize the cost of transport and to maximize the capacity of six candidate facilities in a case study in Italy. Nord-Larsen and Talbot [41] estimated the total delivery cost of forest fuel resources in Denmark using a linear programming model depending on different supply-demand scenarios. Zhang et al. [27] applied a reduced transportation cost model to find the optimal location for biomass conversion and tested its sensitivity to changes in fuel price, biomass availability and transportation distance. Woo et al. [33] applied an MCA in combination with the lowest cost linear programming in order to find the best location to convert woody biomass in a case study in Tasmania. Each of these studies uses spatial components to visualize and calculate distances between supply points and candidate facilities. The spatial component is then combined with non-spatial data for transport, supply and demand quantities and other constraints in order to satisfy the objective function.
This paper presents a two-stage DSS approach that identifies the optimal location of forest biomass-to-bioenergy facilities based on available biomass, transport distance, and transport cost. The objectives of the DSS are (1) to identify strategic locations to convert forest biomass into bioenergy products based on biomass availability using an advanced GIS analysis, and (2) select the optimal bioenergy facility locations by reducing the distance and cost of transport using a transportation cost model. The state of Queensland, Australia, is used as a case example to demonstrate the developed DSS.
The rest of the article is organized as follows: Section 2 describes an outline of the two-stage DSS approach and briefly details the study area of Queensland, Australia. The results of the model implementation and sensitivity analysis are given in Section 3. Section 4 discusses the key findings. Finally, Section 5 presents concluding remarks and possible extensions for future studies.

Materials and Methods
The research applies a two-step DSS to optimize the location of bioenergy facilities. The first step of the DSS is a GIS-based analysis to identify strategic facility locations based on the availability of forest biomass and the suitability of a strategic location for bioenergy conversion. The second step is a transportation model analysis to identify optimal facility locations. An overview of the objects and attributes for strategic and optimal facility locations are presented in Figure 1.

GIS Analysis
GIS analysis is used to identify strategic locations to convert forest biomass to bioenergy products based on the availability of forest biomass. The method was previously described and tested by Van Holsbeeck and Srivastava [43] and consists of availability and suitability analyses. The availability analysis considers the following attributes, as outlined in Figure 1: forest area, type, log harvesting volumes, residue types, residue ratios, sustainability ratio, energy content, administrative area, and relative footprint. The estimated forest footprint and the available forest biomass are combined in an energy heatmap. The suitability analysis applies the Local Index of Spatial Autocorrelation (LISA) [44] on the heatmap as a technique to identify significant hotspots or clusters of high forest biomass energy in the forest. Centroids of significant highly forested areas are delineated and refined in an exclusion  The remainder of the locations are identified as strategic facility  locations due to their high forest biomass availability, proximity to the forest resource and road network  and can serve as a source of biomass demand points for the second stage (model analysis).

GIS Analysis
GIS analysis is used to identify strategic locations to convert forest biomass to bioenergy products based on the availability of forest biomass. The method was previously described and tested by Van Holsbeeck and Srivastava [43] and consists of availability and suitability analyses. The availability analysis considers the following attributes, as outlined in Figure 1: forest area, type, log harvesting volumes, residue types, residue ratios, sustainability ratio, energy content, administrative area, and relative footprint. The estimated forest footprint and the available forest biomass are combined in an energy heatmap. The suitability analysis applies the Local Index of Spatial Autocorrelation (LISA) [44] on the heatmap as a technique to identify significant hotspots or clusters of high forest biomass energy in the forest. Centroids of significant highly forested areas are delineated and refined in an exclusion analysis. The hotspots or clusters that are not located within 200-m proximity of the road network are eliminated form further analysis. The remainder of the locations are identified as strategic facility locations due to their high forest biomass availability, proximity to the forest resource and road network and can serve as a source of biomass demand points for the second stage (model analysis).

Transportation Model Analysis
The transportation cost model uses forest locations as a source of supply, the strategic facility locations (GIS analysis) as a source of demand, a set of transportation cost formulae and the one-way supply-demand distances to find the optimal facility location. The shortest path distance between forest and strategic locations is calculated by applying the Dijkstra algorithm [45]. To find the minimum cost associated with the shortest path for each forest and strategic facility location, a distance-dependent cost formula is developed for the transportation network.

Transportation Model Analysis
The transportation cost model uses forest locations as a source of supply, the strategic facility locations (GIS analysis) as a source of demand, a set of transportation cost formulae and the one-way supply-demand distances to find the optimal facility location. The shortest path distance between forest and strategic locations is calculated by applying the Dijkstra algorithm [45]. To find the minimum cost associated with the shortest path for each forest and strategic facility location, a distance-dependent cost formula is developed for the transportation network.

Transportation Cost Formula
The development of a transportation cost formula is based on a What-IF analysis in Microsoft Excel [46] and the formula is used to compute the cost of transportation. The analysis includes a range of parameters for tractor-trailer, operator, utilization, operation distance, speed, and fuel consumption, and operating cost based on experimental trucking data, adjusted to operations in Australia according to the National Heavy Vehicle Regulator (2019) [47]. The following parameters and values are used for the What-IF analysis: • Tractor-Trailer: A B-train vehicle with a gross weight of 62.50 tonnes; A maximum volume of 300 m 3 ; Forests 2020, 11, 968

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A tractor purchase price of AUD 300k and a trailer price of AUD 85k; A tractor salvage value of AUD 60k and a trailer value of AUD 8.5k; A 5 y tractor life and 10 y trailer life.
• Utilization: Two hundred and thirty operating days y −1 -1 shift day −1 ; A maximum 12-h shift −1 with 0 h of shift −1 overtime; An operational delay time of 5% and 95% available time. A loan interest rate equal to 10%; Registration costs of 8k AUD y −1 , 18k AUD y −1 insurance and 3k AUD y −1 miscellaneous costs; Profit and overhead costs equal to 8%; A weighted linear equation is established in correspondence with the parameters of the What-IF analysis described above, and is shown in Equation (1): where C T is the one-way transportation cost per unit (AUD MW −1 ), l ij is the one-way transportation distance (km) between nodes. The equation consists of two components: a fixed cost, and a variable (distance-dependent) cost. The fixed cost of 9150.77 AUD MW −1 covers the cost of salaries, maintenance, depreciation and interests, registration and insurance, and profit and overheads. The constant coefficient associated with the distance-dependent cost, 179.34 AUD MW −1 km −1 , corresponds to the average fuel cost of 1.42 AUD L −1 [48] and compensates both loaded and unloaded travel.

Transportation Model
A linear transportation cost model is formulated with the aim of calculating the total transport cost between the available biomass supply points and each candidate facility location. Therefore, facilities are not competing for the biomass; thus, one facility can be present at any given time. The model consists of a set of m potential sites (forest nodes) where a set of n potential facilities (strategic locations) can be established whose demands can be satisfied from any available sites for procurement. The index set of all candidate forest sites is denoted by I, for I = {1, . . . , i} and the index set of all potential facilities is denoted by J, for J = {1, . . . , j}. For each potential facility j ∈ J a set of capacity levels is defined. Each forest site has a certain amount of biomass available Q i in (MW) and each facility has a given demand d j in (MW) supplied from m supply points. The unit transport cost between the source node and the destination node is represented by c ij in (AUD MW −1 ). The distance from the harvesting sites and the bioenergy facility is symbolized by l ij in (km), and is calculated between each demand point j and supply point i. For each demand point, the supply points are ranked based on the shortest distance. The available quantity of forest biomass Q i of the supply points is added until the demand d j of a facility j is fulfilled. When the condition is met, the demand of a facility is defined as displayed in Equation (2): The transportation cost for the jth demand point (TC j ) is the sum product of the transport cost (c ij ) for each of the m supply points and the amount of biomass Q i associated with that point. The unit cost for operating trucks c ij is found by using the cost formula in Equation (1). The total transport cost for demand point j is found in Equation (3).
The average transportation cost per unit of biomass (AUD MW −1 ) for the jth demand point, (ATCU j ), is calculated using Equation (4) by dividing the total transportation cost for the jth demand point (TC j ) by the total demand at demand point j (d j ). ATCU j is a normalized value from TC j to improve readability and is given by Equation (4): The total transportation distance for the jth demand point (TD j ) in km is the sum of the transport distance (l ij ) in km for each of the m demand points. The value of TD j is calculated according to Equation (5): Finally, the average transportation distance per unit of biomass (km MW −1 ) for a given facility site (ATDU j ), is calculated using Equation (6) by dividing the total transportation distance for the jth demand point (TD j ) by the total demand at demand point j (d j ).

Study Area and Data Management
To demonstrate the developed DSS, this study uses the state of Queensland, Australia. Queensland is the second largest state in the country, with a total forest area of 51 M ha [2]. An area of 20 M ha of state-owned native forest is commercially available for timber harvest, together with 1 M ha of private native forest and 216,000 ha of plantations [49,50]. The total timber volume processed in the financial year 2017-2018 equalled 3,153,000 m 3 [51]. The majority of harvest operation takes place in softwood plantations mostly located in southeast Queensland. Previous studies by the Australian government estimate a total annual production of 600,000 m 3 of forest harvest residues and 950,000 m 3 of sawmill residues [52]. There are 33 softwood sawmills and 61 hardwood sawmills in Queensland [50]. A densified fuel pellet production facility is located in southeast Queensland with a production capacity of 125,000 tonnes per year [53]. Most of these pellets are shipped for overseas energy production and consumption and do not contribute to the Australian renewable energy target. Twenty-three percent of the renewable energy in Queensland is derived from biomass resources (2% of the total energy produced in Queensland) [54]. In September 2018, a total of 49 bioenergy projects were in operation in Queensland, largely sourced by municipal waste (57%) and agricultural residue (27%) [8], while wood waste, or forest biomass, is an underutilized renewable energy feedstock in Queensland that only runs 6% of renewable energy projects [8].
For the GIS availability analysis, log harvest volume databases published by the Australian Bureau of Agriculture and Resource Economics and Sciences (ABARES) [55] and the Queensland Department of Agriculture and Fisheries [49] are combined with a range of conversion factors derived from the literature [43] and a mapping dataset [56][57][58][59][60]. The log harvest database for Queensland includes a range of species under the soft and hardwood plantations and soft-hardwood native forests. For the GIS suitability analysis, the Queensland road network and Australian Statistical Geography Standard are combined with LISA analysis [61,62]. The availability and suitability analysis are performed in ArcGIS Desktop Version 10.7 (ESRI Australia Pty. Ltd., Brisbane, QLD, Australia) [63].
For the model analysis, a total of 128 demand points or strategic facility locations, 80,920 forest supply points and the Queensland road network are combined to calculate the shortest path distance using the Origin-Destination Cost Matrix in ArcGIS [45,63]. The quantity Q i of forest biomass available in megawatts (MW) at each supply point is determined in the availability study using the data described in [43]. The results of the transportation cost model are analysed using What'sBest! Version 16.0 (LINDO Systems Inc., Chicago, IL, USA) [64].

Sensitivity
The model analysis is based upon a number of assumptions and the establishment of a base case scenario which includes 100% availability of forest biomass and a fuel price of 1.42 AUD L −1 . The maximum transport distance and cost of the base case are established according to a reference scenario that includes a harvest cost of 48.25 AUD odt −1 , a stumpage cost of 0 AUD odt −1 , and a gate price of 64.80 AUD odt −1 . In reality, this might not always be the case, as fuel prices go up and down, all forest biomass might not be available and may find its way to alternative uses. Furthermore, other costs such as stumpage and harvesting costs might change as the intensity of forest biomass for bioenergy uses increases. With this in mind, the sensitivity of the transportation cost and distance and the optimal facility location should be tested against changes in these key parameters. The sensitivity analysis focused on the following three parameters: • A combination of the gate price, harvest and stumpage cost; • Biomass availability; • Fuel price.
Each of these parameters is tested separately for deviations from the base case scenario. The ATDU j and ATCU j from the different scenarios are compared to the reference base case. The combined effect of the gate price, harvest and stumpage cost does not affect the calculation of ATCU j and ATDU j according to Equations (4) and (6) but affects the maximum transportation distance by the incorporation of Equations (1) and (5). The availability of biomass and the cost of fuel directly impact the formulation of TC j in Equation (3), which is carried through into the calculation of ATCU j and ATDU j in Equations (4) and (6). The sensitivity analysis for biomass availability and fuel price is only tested on the ten best-performing facilities according to the model analysis of the base case.

Gate Price, Harvest and Stumpage Cost
As described earlier, the cost of transportation was defined by Equation (1), which corresponds to a relationship between distance and the attributes of transportation, e.g., trailer, operator, utilization. However, looking at feasible economic solutions, the cost of transport will be mostly limited by a profit margin that is defined by other costs in the supply chain. In order to be profitable, the price a contractor receives for the delivered biomass at the bioenergy facility (gate price) needs to outweigh the cost or spending that is associated with the delivery of biomass. These costs are inclusive of a stumpage cost or the price paid to the forest biomass grower, a harvest cost for the harvest of forest biomass, and a transport cost. Thus, resulting from those attributes, the maximum transport cost (TC max ) can be redefined according to Equation (7): When substituting Equation (1) into Equation (7), the maximum transport distance can be calculated according to Equation (8): Values for gate price, harvest cost, and stumpage cost can vary significantly based on the type of harvest system, forest type, type of forest biomass or tree species, the amount of biomass, equipment or even the deployment of biomass use in the area. A list of the used values is outlined in Appendix A.
The decision to include a low-cost scenario for the harvest cost is based on the motivation that the cost of the harvest, extraction and chipping of forest biomass can be reduced once more efficient supply chains are established or low-cost harvesting methods are applied in the case study area. On the other hand, a higher cost for harvest is included based on the motivation that infield chipping requires less machinery compared to typical extraction and roadside chipping operations but tends to have a higher cost of operation. The decision to include a moderate and high-cost scenario for stumpage cost is based on the growing interest in forest biomass. Increasing interest in biomass will add value to the material, which allows for landowners to create additional revenue. Increasing interest in forest biomass also justifies the reason for including a higher gate price scenario.
The effect of price and cost changes reflects on the maximum allowable transport cost and distance according to Equations (7) and (8). All possible combinations between gate price, harvest, and stumpage cost are tested in Equation (7). Only the positive values of TC max are allowed to secure a profitable supply chain. The remaining scenarios allow for the calculation of the maximum allowable transport distance (TD max ) in Equation (8). The maximum allowable capacity for the average facility is defined as the intersection between the average ATDU j of all facilities according to Equation (6) and TD max calculated in the remaining scenarios.

Biomass Availability
In the base case situation, the forest biomass quantities are calculated according to a previous study [43], and an assumption based on harvested log volumes in the state of Queensland. The estimated availability of the biomass already captures losses of biomass due to sustainable and technical restraints. However, it is unlikely that the remaining biomass will all be harvested and transported, or solely used for bioenergy purposes. Paper industries, horticulture or pellet exports will result in a reduction in forest biomass that will not be available for the Australian energy market [52]. To consider that less than 100% of the forest biomass will be converted to bioenergy in Queensland, several lower biomass availability scenarios are established and compared with the base case where 100% availability was used. The effect of reduced availabilities from 100% to 50% is tested on ATCU j and ATDU j with decrements of 10%. The reduced availability is defined as parameter Q i in Equations (2)   The distance factor in Equation (1) is established in correspondence with the average fuel price in 2019 for Queensland, Australia (1.42 AUD L −1 ) [48]. In order to evaluate the effect of fuel price on the total cost of transport, the minimum and maximum fuel prices for 2019 are compared against the average. The minimum fuel price for 2019 is 1.12 AUD L −1 which corresponds to an adjustment of Equation (1) according to the What-IF analysis in Microsoft Excel [46] and can be found in Equation (9): Similarly, a maximum fuel price of 1.73 AUD L −1 in 2019 results in Equation (10): Both Equations (9) and (10) will be used to substitute c ij in Equation (3) of the transportation model for the calculation of ATCU j and ATDU j . The sensitivity is only tested for the ten best-performing facilities and compared with the results of the base case in model analysis. The ATCU j and ATDU j are calculated for capacities ranging between 5 and 100 MW.

GIS Analysis: Strategic Facility Locations
The total harvestable area of forest in Queensland is estimated to be 13.6 M ha, including both plantations and native forests. The total amount of forest biomass energy is estimated to be 732 MW. The amount of energy is produced annually in plantations and native forests combined and includes the production of pulp logs, sawmill residues and field residues. The total harvestable forest footprint and total biomass energy are aggregated in an energy heatmap and used as inputs for LISA in the suitability analysis. This results in 844 administrative area polygons with significantly high biomass energy. The centroids of the 844 locations act as potential locations for bioenergy facilities. In testing the proximity to the road network (200 m), only 131 locations are eligible. Three out of the 131 locations are located on Bribie Island and were excluded in further analysis due to connectivity issues. There are 128 strategic facility locations for bioenergy purposes in the state of Queensland. Table 1 presents the mean and standard deviation (Std Dev) of TC j , ATCU j , TD j and ATDU j values from 128 strategic locations over the different capacities. Potential demand levels from small capacity (5 MW) to high capacity (100 MW) for each location are tested. At each capacity level, we can determine what the average, minimum and maximum cost or distance per MW would be for transport if we were to open a facility.

Model Analysis: Optimal Facility Location
TC j and TD j values increase exponentially with increasing capacity. Normalizing the TC j and TD j values by the capacity creates a linear trend and smaller values for interpretation.
Because each strategic location is evaluated separately, locations for possible facilities can be ranked according to the ATCU j or ATDU j values. The location with the lowest ATDU j or ATCU j is considered the most optimal location. From the results shown in Figure 2, we can identify which of the 128 facility locations has the lowest ATCU j and ATDU j across all capacities (5-100 MW) based on hierarchy ranking. The labels of the 10 best facilities are shown. The dots represent 128 strategic locations, ranked by colour from lowest (green) to highest (red) ATCU j . In Figure 2a, the ATCU j value is averaged across all capacities for each facility. In Figure 2b, the ATCU j of a 5-MW facility is presented for each facility. Figure 2a indicates that the most optimal locations for energy conversion are located in the southeast (green) and other locations (red) are not feasible. However, looking at one particular small capacity (5 MW) in Figure 2b, it appears that some locations in the north can also be considered optimal in addition to the southeast. Location "476" is the best performing location with the lowest ATCU j and ATDU j across the range of capacities (Figure 3). The extent of the network to satisfy location "476" at a range of capacities is presented in Figure 3. As the most optimal location, the network connections are minimal but grow with increasing capacity. Table 1. Mean jth demand point (TC j ), average transportation cost per unit of biomass (AUD MW −1 ) for the jth demand point, (ATCU j ), total transportation distance for the jth demand point (TD j ), average transportation distance per unit of biomass (km MW −1 ) for a given facility site (ATDU j ) and SD values of 128 strategic locations for different capacities in Queensland.

Gate Price, Harvest and Stumpage Cost
The maximum transport cost is calculated for the base case (Scenario 1) as shown in Table 2. The base case scenario includes a stumpage cost of 0 AUD odt −1 , a harvest cost of 48.25 AUD odt −1 , and a gate price of 64.80 AUD odt −1 . The maximum transport cost is 16.55 AUD odt −1 or converted to 25,200 AUD MW −1 . The maximum transportation distance is 89 km and is the return distance from the facility to the forest. Table 2. Estimated maximum transport cost (TC max ) and maximum allowable transport distance (TD max ) values for a range of scenarios based on changes in gate price, stumpage and harvest costs.  Different combinations among gate price, harvest and stumpage cost are summarized in Table 2. Only the positive values of TC max in Equation (7) are allowed to secure a profitable supply chain.
Negative TC max values are removed from Table 2. The remaining scenarios allow for the calculation of TD max in Equation (8) and are presented in Table 2. We notice that only one scenario (10) with a stumpage cost of 28.27 AUD odt −1 remains. This means that combinations between this stumpage cost and other harvest costs and gate prices resulted in a negative value for TC max . We also notice that none of the high harvest costs (77.16 AUD odt −1 ) are presented in the table, which means that these costs outweigh the price received for biomass and result in a loss in the supply chain.
In Figure 4, the maximum transport cost calculated in Table 2 for the base case scenario is compared to the mean of ATCU j values (J = 128) from the foregoing analysis (Table 1). For further comparison, the mean ATCU j of the ten (J = 10) best strategic locations ( Figure 2) for each capacity is added to Figure 4. From the graph, it appears that, based on the calculated average, the 10 best locations remain under the maximum transport cost threshold (y = 25,200). Only at capacities above 90 MW does the curve exceed TC max . On the other hand, the mean of all strategic locations exceeds TC max at every capacity. This indicates that the average facility location in Queensland would not be profitable. However, in Table 3, the number of locations with ATCU j under TC max are calculated and more detail indicates that, especially at lower capacities, a large set of locations can be feasible.   The maximum allowable capacity for a facility can be defined as the intersection between the average ATDUj of all strategic locations according to Equation (6) and TDmax calculated in the remaining scenarios (Table 2). In Figure 5, the mean ATDUj of all strategic locations is compared to the TDmax of the ten best scenarios. The dotted line y = 89 is the TDmax value of the base case scenario in Table 2. The point of intersection is at y = 89; x = 6, meaning that, based on the maximum return travel distance of 89 km MW −1 , we could supply the average location in Queensland with up to 6 MW of forest biomass energy (CAPmax). With an increasing or decreasing gate price, stumpage or harvest cost, this maximum allowable capacity changes. Different values for TDmax in Table 2 are presented in Figure 5 (TDmax = y) and responding CAPmax values are indicated. Notice that at a maximum transport distance of 4 km (scenario 7), a negative capacity was retrieved and therefore this scenario  The maximum allowable capacity for a facility can be defined as the intersection between the average ATDU j of all strategic locations according to Equation (6) and TD max calculated in the remaining scenarios (Table 2). In Figure 5, the mean ATDU j of all strategic locations is compared to the TD max of the ten best scenarios. The dotted line y = 89 is the TD max value of the base case scenario in Table 2.
The point of intersection is at y = 89; x = 6, meaning that, based on the maximum return travel distance of 89 km MW −1 , we could supply the average location in Queensland with up to 6 MW of forest biomass energy (CAP max ). With an increasing or decreasing gate price, stumpage or harvest cost, this maximum allowable capacity changes. Different values for TD max in Table 2 are presented in Figure 5 (TD max = y) and responding CAP max values are indicated. Notice that at a maximum transport distance of 4 km (scenario 7), a negative capacity was retrieved and therefore this scenario cannot be sustained. For scenario 5, we find a maximum capacity of 0 MW, which also indicates that there is not enough supply within this distance cut-off to satisfy a facility. Table 4 presents the percentage of strategic locations (j) that fall under the maximum allowable transport distance (TD max ) for each scenario and the range of capacities. From the table, we can see that 99% of locations can be supplied with 5 MW if we were able to transport biomass over a total distance of 302 km in scenario 3. This percentage drops with increasing capacity and decreasing distance and becomes 0% when the maximum transport distance is reduced to 4 km and capacities are over 5 MW. Despite this, 1% of the locations are able to produce 5 MW of energy under a maximum transport distance of 4 km.

Biomass Availability
The effect of reduced availabilities from 100% to 50% is tested on the mean ATCU j and ATDU j of the 10 best strategic locations with a decrement of 10%. For the sake of simplicity, the mean ATCU j and ATDU j are only calculated for capacities of 5, 10, 15 and 20 MW and are presented in Figure 6. For example, the ATCU j of location "476" at 20 MW and 100% availability is 20,300 AUD MW −1 and increases to 21,200 AUD MW −1 at the same capacity with only 50% of the biomass available. For location "801" the ATDU j is 3.73 km MW −1 at 100% biomass availability and 5 MW capacity and increases to 5.99 km MW −1 at the same capacity with only 50% of the biomass available. From the foregoing analysis and according to Figure 2, location "476" is the overall best performing location on different capacities (5-100 MW). However, according to Table 5, location "801" is the most optimal at 100% biomass availability and low capacities (5-20 MW). With decreasing biomass availability, however, longer distances will need to be covered to satisfy the potential demand of the facility. At reduced biomass availability and increasing capacity, locations "125" and "476" become more favourable (Table 5). Table 5. Optimal locations at a range of capacities and reduced biomass availability. 100%  801  801  801  801  90%  801  801  801  125  80%  801  801  801  125  70%  801  801  801  476  60%  801  801  125  476  50%  801  801  476  476 3.

Fuel Price
The ATCUj of the ten best facilities is calculated accordingly for the low and high fuel scenario (Equations (9) and (10)) and compared with the average fuel price in Figure 7. For example, the ATCUj of location "476" at 20 MW and average fuel price is 20,300 AUD MW −1 and increases to 20,700 AUD MW −1 with a high fuel price and drops to 19,800 AUD MW −1 with a low fuel price. At a low capacity (5 MW), both the high and low fuel prices result in a 1% change in the ATCUj value. At a high capacity From the foregoing analysis and according to Figure 2, location "476" is the overall best performing location on different capacities (5-100 MW). However, according to Table 5, location "801" is the most optimal at 100% biomass availability and low capacities (5-20 MW). With decreasing biomass availability, however, longer distances will need to be covered to satisfy the potential demand of the facility. At reduced biomass availability and increasing capacity, locations "125" and "476" become more favourable (Table 5).

Fuel Price
The ATCU j of the ten best facilities is calculated accordingly for the low and high fuel scenario (Equations (9) and (10)) and compared with the average fuel price in Figure 7. For example, the ATCU j of location "476" at 20 MW and average fuel price is 20,300 AUD MW −1 and increases to 20,700 AUD MW −1 with a high fuel price and drops to 19,800 AUD MW −1 with a low fuel price. At a low capacity (5 MW), both the high and low fuel prices result in a 1% change in the ATCU j value. At a high capacity (100 MW) this results in a 7% decrement of ATCU j for low fuel price and a 6% increment of ATCU j for the high fuel price.

Discussion
This research combines GIS methods with a transportation cost model to find the optimal location of forest biomass-to-bioenergy facilities. In considering the development of a profitable bioenergy facility that can sustainably produce bioenergy from forest biomass: (i) there has to be enough biomass to supply the bioenergy facility, and (ii) the biomass has to be sourced within a sensible distance at the lowest possible cost. The two-stage DSS helps to address this biomass logistics problem and this research demonstrates the method in the large study region of Queensland, Australia. The spatial component preceding the transportation cost model indicated that 732 MW of forest biomass is available per year and identified 128 strategic locations to covert this biomass into energy products. Similar quantities for biomass availability can be found in the Australian literature for the state of Queensland [65][66][67] and are roughly converted to one million dry tonnes of forest biomass. Each of the strategic locations served as inputs for the transportation cost model and further location optimization. In the literature [19,20,27], GIS-based methods have been used numerous times to assess biomass and to identify locations for biomass conversion, but seldom have they been applied to such a large-scale extent. Since the transportation of biomass is an overwhelming contributor to biomass supply chain costs [25], further refinement of strategic locations based on transport cost and distance provides a more optimal solution to the facility location problem.
By calculating the average transportation cost and distance of the strategic locations retrieved from the GIS analysis, this research can identify the most optimal location for a forest biomass-tobioenergy facility if we were to establish one. A similar approach was applied to finding the optimal location to convert forest biomass to biofuel by Zhang et al. [27]. The most optimal location for a facility would be the facility with the lowest transport cost and distance at the required capacity.

Discussion
This research combines GIS methods with a transportation cost model to find the optimal location of forest biomass-to-bioenergy facilities. In considering the development of a profitable bioenergy facility that can sustainably produce bioenergy from forest biomass: (i) there has to be enough biomass to supply the bioenergy facility, and (ii) the biomass has to be sourced within a sensible distance at the lowest possible cost. The two-stage DSS helps to address this biomass logistics problem and this research demonstrates the method in the large study region of Queensland, Australia. The spatial component preceding the transportation cost model indicated that 732 MW of forest biomass is available per year and identified 128 strategic locations to covert this biomass into energy products. Similar quantities for biomass availability can be found in the Australian literature for the state of Queensland [65][66][67] and are roughly converted to one million dry tonnes of forest biomass. Each of the strategic locations served as inputs for the transportation cost model and further location optimization. In the literature [19,20,27], GIS-based methods have been used numerous times to assess biomass and to identify locations for biomass conversion, but seldom have they been applied to such a large-scale extent. Since the transportation of biomass is an overwhelming contributor to biomass supply chain costs [25], further refinement of strategic locations based on transport cost and distance provides a more optimal solution to the facility location problem.
By calculating the average transportation cost and distance of the strategic locations retrieved from the GIS analysis, this research can identify the most optimal location for a forest biomass-to-bioenergy facility if we were to establish one. A similar approach was applied to finding the optimal location to convert forest biomass to biofuel by Zhang et al. [27]. The most optimal location for a facility would be the facility with the lowest transport cost and distance at the required capacity. However, understanding that one facility is necessary to capture the entire supply over large areas such as Queensland is complex and a challenging task. Even though the rationale of the transportation cost model is to minimize the cost of transport, our additional motivation is to maximize the capacity within the study area. In the ideal scenario, the cost of supply is kept minimal and the biomass that is produced within the forest is utilized to the greatest possible extent by the bioenergy facility. The combination of GIS and a transportation cost model allows us to tackle this problem. The ATCU j that is calculated for each facility at a range of capacities is low when either the cost of transport is minimal, or the supplied capacity is great (AUD MW −1 ). Thus, the ATCU j value is an indicator of the optimal facility location problem. For comparison, the study by Zhang et al. [27] found a total cost value of USD 4.32 M for a facility using 635,000 tonnes (50% moisture) of forest biomass. The ATCU j value from their result converts to 31,100 AUD MW −1 for the best facility. In our research, location "476" was found to be the best performing across a range of capacities and has an ATCU j value of 22,300 AUD MW −1 , which is located in the most biomass-dense area of the study region.
To understand the effect of price and cost changes in the biomass supply, the results of the transportation cost model were compared to the maximum cost and distance of the biomass supply chain. Values for gate price, harvest cost, and stumpage cost can vary significantly based on the type of harvest system, forest type, type of forest biomass or tree species, amount of biomass, equipment or even the deployment of biomass used in the area. The cost of harvest, stumpage and the gate price of forest biomass are not included as integral parts of the transportation model; however, they are incorporated as constraining elements to secure the profit of the forest biomass market. According to different cost price scenarios in relation to sensitivity, the maximum allowable transport cost and distance will vary and are independent of the capacity. This research estimated that the maximum allowable transport cost is 25,200 AUD MW −1 and the maximum allowable transport distance is an 89 km MW return journey. We found one other research example in Australia that indicated a range of costs between 48.32 AUD odt −1 and 63.25 AUD odt −1 for hardwood chips for delivering biomass residues over a transport distance of 90 km [68]. When converted, the 89-km maximum allowable transport distance in this research corresponds to a maximum transport cost of 16.55 AUD odt −1 . When we convert and add the cost of harvest (48.35 AUD odt −1 ) to the transport cost we receive a comparable value of 64.80 AUD odt −1 . The point of intersection between the 89-km maximum allowable transport distance and the average transportation distance per megawatt according to the transportation analysis is at a capacity of 6 MW. Thus, under the circumstance of the base case scenario, the average facility in Queensland becomes less profitable beyond this capacity when keeping in mind that this is based on the average of the best and worst performing locations. The introduction of a maximum allowable transport costs creates a benchmark for the strategic facility locations from the transportation cost model. When the benchmark cost or distance is exceeded, the strategic location can be rejected as an optimal solution.
To examine the sensitivity of decisions to changes in biomass availability and the cost of fuel, the transportation cost model was also executed by changing these parameters. The biomass availability can suffer considerable losses due to alternative uses; hence, this research investigated 10% decrements of biomass availability. By reducing the availability of biomass supply, the preference of location shifts. With less biomass available, more biomass needs to be collected from additional forest locations. This affects the result of the transportation cost model by increasing the cost due to increased transport distances or reducing the supplied capacity. The optimal facility location is therefore characterized by an increasing ATCU j value. On average, for a 5-MW facility, a reduction of 10% in the biomass availability resulted in an ATCU j increase of 90 AUD MW −1 . The cost of fuel can change significantly throughout the year. Cyclical changes in fuel price, sometimes up to 20%, are not uncommon and have a significant impact on the cost of transport and the fleet. Changes in fuel prices do not interfere at a capacity level of a facility or the supply of biomass to a facility. However, changes in fuel price will affect the ATCU j value from the transportation cost model and simultaneously impact the maximum allowable transportation distance. Changes in the ATCU j value up to 7% were recorded in this study based on changes in fuel price. Similar to the results found in Zhang et al. [27], a change in fuel price did not affect the optimal location, as opposed to changes in biomass availability.
There are several possible opportunities for future research to extend and enhance the developed DSS. One of the key opportunities is to take the single-facility transportation problem to a multi-facility optimization scenario, thereby focusing on utilizing as much of the forest biomass as possible throughout the study area by selecting multiple optimal locations for the conversion of biomass. It is important to consider that each potential facility can be supplied with biomass from within its service area at the lowest possible cost without competition between these facilities. Such models can reinforce the decision on the number of facilities and required capacity needed in the study area to maximize the demand, while minimizing the cost. Often, there will be limits to a capacity of a facility, so it is worth considering a minimum and maximum capacity level based on the technology and biomass resource. When optimizing the supply chain, research should consider economic, environmental and social aspects to come up with the best possible scenario. Depending on the geographical location, interruptions of the forest biomass supply occur annually due to spring/breeding season, snow or fire seasons. It is therefore recommended to improve the knowledge of biomass availability by simulating the annual harvesting cycles and biomass storage solutions.

Conclusions
This paper demonstrated the use of a two-stage decision support system that finds the optimal location of forest biomass-to-bioenergy facilities based on available biomass, transport distance, and transport cost in the study area of Queensland. In stage 1, the method identified 128 strategic locations using a GIS approach. In stage 2, the optimal location for forest biomass-to-bioenergy conversion was based upon reduced transport costs. The influence of fuel price, biomass availability, and cost and pricing of the biomass supply chain was evaluated through a series of sensitivity analyses.
From the case study, we can conclude that: • Location "476" was identified to be the optimal location for bioenergy production from forest biomass across a range of facility capacities.

•
The ATCU j of the average facility in Queensland ranges from 33,700 AUD MW −1 at 5 MW capacity to 79,400 AUD MW −1 at 100 MW with an ATDU j of 86 km MW −1 at 5 MW and 341 km MW −1 at 100 MW.

•
The sensitivity analysis showed that fuel prices and biomass availability have an influence on the transport cost. Biomass availability also influences the selection of the optimal facility location. At the lowest capacity level and 100% biomass availability, location "801" was the optimal location; with increasing capacity or reduced availability, location "476" was the optimal site. • The sensitivity analysis also showed that changes in the biomass price and the costs of the supply chain have an impact on the maximum allowable transport distance and cost. In the base case, the maximum allowable transport distance for a facility in Queensland is 89 km MW −1 and the maximum allowable transport cost is 25,200 AUD MW −1 .
The use of a two-stage DSS for the selection of an optimal facility location has been demonstrated. Additionally, the method evaluated every other possible location and created an average performance scenario for the case area, which enables future planning, investigation and investment from a strategic perspective. The single-facility transportation cost model can be extended to optimization methods that allow for multiple facilities to coexist. The method can potentially be extended to other regions and biomass scenarios.