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2007
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GIS-based accessibility analysis for network optimal location model

An application for bio-energy projects of the mineral Industry in the UK
SIG et analyse d’accessibilité pour la création d’un modèle de localisation optimale en réseau. Application aux projets de production de bioénergie de l’industrie minière au Royaume-Uni
Sylvie Dubuc

Résumés

Les analyses de localisation sont devenues partie intégrante des analyses spatiale et de la modélisation des SIG. Les modèles de localisation optimale sont souvent utilisés dans les processus de décision pour déterminer l’emplacement de services pour lequel l’accès des clients par rapport à la demande est maximisé dans un espace continu de possibilités. Mais que se passe-t-il si la demande potentielle est discrète et sa localisation prédéfinie, et que le model de localisation optimal est appliqué au choix de sites parmi un échantillon de sites potentiels ? Cette question est posée par l’industrie minière Britannique qui envisage la possibilité de restaurer certaines de leurs carrières épuisées en champs de production de plantes bio-fuel. Un petit nombre de carrières doivent être sélectionnées parmi l’ensemble des carrières à restaurer. Elles devront approvisionner une chaudière en bioénergie. Les carrières présentant la meilleure localisation pour être transformées en champ de production de bio-fuel sont celles dont la situation minimise les couts de transport de la biomasse produite vers le site de production d’énergie (chaudière).
Le cout de transport est estimé en fonction des mesures de distance et de temps de transport. Aussi, la fonction objective du modèle minimise la distance/le temps de transport entre le site de production d’énergie (la demande) et le(s) plus proche(s) site(s) de production de bio-fuel. Basée sur le critère du plus court chemin, la demande en plantes nécessaires pour alimenter la chaudière est successivement allouée aux carrières jusqu'à ce que la demande annuelle soit satisfaite. Le groupe de carrières ainsi sélectionné se caractérise par les meilleures localisations minimisant les couts de transport.
Plusieurs manières d’estimer le temps de transport ont été explorées et testées pour sélectionner les carrières. Une grande attention a été donnée à la construction de mesures d’accessibilité. D’abord basée sur la distance métrique, la longueur des routes a été utilisée pour déterminer le plus court chemin. Des distance-temps de transport multicritères ont ensuite été produites intégrant la longueur des routes, la vitesse de circulation en fonction du type de routes, le gradient de pente des routes dérivé d’un modèle d’élévation de terrain, ainsi que l’effet de frein des zones urbaines.
Les résultats des différentes modélisations sont comparés. Les résultats soulignent l’intérêt d’utiliser une mesure de temps de transport multicritère pour améliorer la précision des modèles d’accessibilités et de localisation. La méthode a été appliquée à une zone test dans le nord de l’Angleterre. Elle pourrait être appliquée à l’ensemble du Royaume-Uni sous réserve de quelques adaptations, présentées dans la méthodologie et discutées dans la conclusion.

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Notes de l’auteur

This research was supported by Cranfield University and RMC ltd Industry. I would like to thank Dr C.Sannier and Dr E.Brierley who initiated this project. I am very grateful to Tim Brewer (Cranfield-Silsoe) for his technical assistance. Further thanks go to the geography Department of King’s College London for supporting me in the production of this paper.

Texte intégral

Introduction

  • 1 The emissions of carbon dioxide should be reduced by 60% by the middle of the century in the UK, as (...)
  • 2 RMC Group (Ready-Mix Concrete product Ltd) is a leading international producer and supplier of mate (...)

1Following the European Directive restricting the emissions of carbon dioxide for industrial installations and non-renewable energy1, the United Kingdom government has adopted a policy to encourage renewable energy production, wherever it has the prospect of being economically and environmentally acceptable. Bio-energy is being recognised as one of the promising sources of energy to cut CO2 emissions as stated by the Biomass Task Force Report (2005). In April 2006, the UK Government (Johnson and Beckett, 2006) announced measures to encourage energy crop development. Feasibility studies are currently carried out to assess the potential of renewable energy sources, aimed to be used extensively in the near future. Further work on techniques for biomass combustion and their implementation have still to be established. Furthermore, the mining industry in the UK is held by law to convert quarries after exploitation, according to a variety of possible options (e.g. agriculture conversion, woodland, recreational space including green space, artificial lake). The mining company RMC Ltd 2focuses on the restoration of exhausted quarries of the mining industry for the production of Short Rotation Coppice (SRC) as energy source and their collection. A study has already been completed at Cranfiled University to assess the potential of using energy crops (e.g. SRC) for sustainable quarry restoration (Quinn et al, 2004). Restoring quarries to produce biomass energy is a potential solution for a sustainable mining industry in United Kingdom (UK) - and the whole of Europe.

2We present a methodology and the principal results of a feasibility study to identify, within a panel of quarries, those of best location for the production of energy crops with respect to their transport costs to a potential power station. Geographical Information Systems and road network analysis methods are used to develop accessibility measures applied on a pilot project area in the north of England. In the proposed model, the location of the power station is already defined. The potential sites eligible for the development of power stations (biomass boilers) in the UK, are under consideration by a research partner and do not fall into the scope of the project presented here. The eligible sites will be defined based on the location of current RMC plant locations and their characteristics, in addition to various technical considerations. This paper describes a network based method for building an optimal location model of quarry sites to be selected minimising the cost of transporting energy-crops. Because transport costs are a decisive element in the selection of clusters of potential quarries, we have put special emphasis on the accuracy of the travel time calculations. The model described was designed to meet the particular demands of RMC-Ltd with respect to accuracy, flexibility and adaptability at the UK level. This model was tested for the influence of a number of parameters involved in the travel time calculations (hereafter also called distance-time) and the results are described and discussed. We conclude that the optimal location model is principally fit for purpose and recommend measures for further improvements.

Background

Optimal location model

3Optimal locations were primarily modelled by Launhardt and Weber (Weber, 1909) to determine the optimal locations for industry plants, according to access to markets and raw materials within a continuous area of possibilities and in order to minimise the transport costs to serve a spatially distributed demand. Optimal location theory and modelling of facilities has seen important developments since the 1980s and allow analysing the spatial organisation of human activities (Carreras and Serra, 1997). The transport network often plays an important role in those models (Thomas, 2002). Within the large variety of location problems, reviewed by ReVelle et Eiselt (2005), one can distinguish between two types of models, those treating with d-dimensional space and those treating with networks. Network based measures are determined by summing the lengths of links or other criteria related to the length (e.g. distance-time, distance-cost). Better than coordinate based measures (like straight distance), it takes into account the heterogeneity of space between starting and ending points along the network (Smith, 2003). The characteristics of the transport infrastructures enable to model cost of travel accurately between locations, which is likely not to be uniform along the road network.

4Within network facility location problems, network-based plant and warehouse location studies have been developed since the 60s, which mainly emphasises the minimum distance location of facilities (called p-facilities) on a network of nodes, known as the p-median problems (Daskin, 1995; Thomas, 2002; Torsten and Densham, 2003; ReVelle et Eiselt, 2005). This has lead to the development of a variety of algorithms to address specific p-median problems (e.g. Kariv and Hakimi, 1979; Peters, 1996). More recently extensively used in retail location problems, the p-median model is typically applied for locating p facilities to serve demand, generally disperse (e.g. multiple points customer) in order to minimise the aggregate transportation cost (Daskin, 1995; Ghosh et al, 1995). Our problem is set differently. It may be seen as a particular case of p-median problem, conceptually relatively simple, where the demand is concentrated in one point already geographically identified (power station) rather than a multitude of points within a demand catchment’s area. The quarry sites (location of potential suppliers) can be assimilated to a group of eligible points (discrete problem), located on a network, and of which a few quarries are to be selected (p-facilities).

Measuring accessibility: distance, time, and cost

5A number of network optimal models are based on minimum distance or minimum cost criteria. Least cost path within a communication network may be based on a measure of distance of travel. For example, in a basic location-allocation model Torsten and Densham (2003) used the distance to calculate transport costs (length of links), assuming proportionality between distance and cost of access. Rather than metric distance, time of travel is now more and more used to find the least cost path between points on a network (Ghosh et al, 1995; Thomas, 2002; Brabyn and Barnet, 2004).

6Work has been carried out to assess the distance-time of transport in the UK and has been applied to transport analysis and network-based location models. Studies on population accessibility to services have especially developed distance calculations for location models. For example, to analyse accessibility to General Practitioner (GP) surgeries for the remote rural population Lovett et al. (2002) have used different road speeds, based on national estimates published by the department of Environment, Transport and the Regions. Kelly et al. (2002) have proposed to introduce road speed estimations on the road network based on field analysis in the North of England. Much less common is the consideration of topographic variation in assessing time and cost of travel.

Topographic variation and least cost path model

7For Smith (2003) a two-dimensional surface is often insufficient to estimate the real distance of travel and to model the optimum path. Only few studies have integrated elevations of the terrain in path finding. As an improvement of the classic straight-line distance, Smith (2003) has developed an algorithm for path finding that takes into account the obstacles of the terrain (use of buffer and constraint) to find a path between two points in two-dimensional continuous space in a region with topographic variations. We therefore developed a measure to estimate the gradient slope values of the road. This measure has been used to improve the accuracy of travel time calculations and used in a least cost location model for quarries to produce energy crop for a power station. The transport cost was estimated from the time measures assuming proportionality between cost and time of travel. Several network-based measures are used (distance, time) to compute the least cost paths between locations and are compared. The kind of road, topographic variation and the slowing down effect of urban areas on the vehicle speed are criteria taken into account in the least cost path finding procedures. Precise distance-time assessment using multi-criteria measurements should improve transport and optimal location models. The methodology used in this project is explained and its application to our study area in North England is presented. In the future, the mining industry plans to apply the methodology described in this study to establish an optimal location model at the UK level. In order to perform this adaptation, recommendations are made at the end of the paper.

Data sources and study site

  • 3 The Urban areas in STRATEGI are based on the concentration of buildings and other structures, at th (...)

8This application was developed and tested on a sample area in the North of England (figure 1). The study area covers 20 by 40 Km and is located northwest of Manchester in a partly hilly area. It has a range of road types and the terrain elevations vary between 10 and 460 metres. Two contiguous Digital elevation models (DEM) have been ‘mosaiced’ into a single raster and used to define the spatial limits of the sample area. This application is designed to be applicable to the entire UK in the future. Whenever possible, data has been collected at the UK level. Ordnance Survey (OS) data product, STRATEGI Roads of UK was used to build the road network model of the study area. The information was contained in five shapefiles representing the following road types: motorway, primary road, A-road, B-road and minor road, characterised by various speed limitation. Speed restrictions and congestion effects that lower travel speed in urban areas were also considered. A land-use coverage produced by Ordnance Survey (OS Strategi data) with delimitation of urban areas3 was used to calculate a measure of time of travel on the road network. Elevation information of an OS Panorama Digital Terrain Model derived by contour lines of topographic maps (50 metres spatial resolution) was used to estimate the gradient slope of the roads. Geographic coordinates of quarries provided by the British Geological Survey (BGS) were used to create nodes at their location within the road model. Ten sites were presents in the study area.

Figure 1: The study area

Methodology

9A geographical Information System was used to locate the quarries of best location to be converted in energy-crop in order to minimize the transport cost to reach the closest potential power station site. In the location model tested on the pilot project area the demand of energy-crop is concentrated in one site and the potential supplier, are at discrete locations on the network, at quarry-nodes location. The objective was to model the potential supply, the demand and their interaction through a road network system in order to bring the supply to a demand site at the least cost. This accessibility analysis was then used to select the quarries of best location, minimising the transport cost when satisfying the demand in energy-crop required and taking into account the capacity of production of the quarries.

10Contrary to usual p-median problems, in this feasibility study the demand is located in the single point (P) rather than dispersed amount a multitude of individual demand points. Consequently, there is no need to identify the spatial extension of the demand catchment, and incidentally the group of demand points it includes, when allocating the demand to a particular facility (quarry). Therefore calculations to determine the best location of quarries to be restored for bio-energy production, within a set of eligible points (all quarries) are simplified. The calculation are decomposed and presented in the results. The model is based on the measures of accessibility between the quarry-nodes and the demand-node, the amount of demand and the potential supply in energy-crop of the quarries. Only one power station site was tested in the pilot project since the emphasis was mainly on the accessibility measures to be applied. However, the implantation of several power stations should be considered when the methodology would be applied to the whole UK, together with the full set of quarries to be restored over the UK. Consequently, the model developed here is made compatible with such future requirements and a location-allocation modelling is proposed. ArcInfo was chosen because it offers satisfactory tools to create a topological data structure to model the road network as well as network analysis modules with classical methods of path-finding and location-allocation modelling based on minimum distance (/cost) adapted to the problem addressed here. Several measures were calculated and used in a least cost path analysis. In addition to the metric distance on the road used to compute the shortest path between locations, 3 measures of time of travel involving more complex calculations were tested. The database created, including the layers, the features and their attributes are presented in Figure 2.

Creating a topological data structure

11A topological data structure of the road network was first created (Box 1). It was an important part of the data preparation, since the quality of the analysis relies on it. To perform a routing procedure based on the entire road network capabilities, the five road coverage, corresponding to various roads types and speed of travel, were appended in a single coverage. The extension and the limits of urban areas were also integrated within the road network model.

Box 1: Topological data structure in ARC/INFO

Box 1: Topological data structure in ARC/INFO

Figure 2: Raster, coverage and feature classes process flow chart

Least cost path analysis

12Network analysis techniques (Box 2) were used to model the road network and compute the least cost path between the origin node P (demand-node) and each destination node (Quarries). Dijkstra’s algorithm (Dijkstra, 1959) was used to compute the shortest path between the power station (P) node and the nodes corresponding to the quarries location, using minimum cost impedance item (measures of distance and time of travel). Applying dynamic segmentation model, four route-systems were created, each one based on one of the four minimum cost impedance items tested. The quarry-nodes were integrated within the road data structure to calculate directly the shortest path between P and each quarry. For each route-system, ten routes were computed, each one corresponding to the shortest path between one of the quarries (Qi) and the power station location (P).

Box 2: Least Cost Path analysis in ARC/INFO

Multi-criteria time of travel measures

13The same procedure was applied to calculate the minimum travel time to reach each quarry from the power station and back. 3 road travel times were tested: one based on Kelly et al. proposed measure, another using the values published by the Department of Transport (Department of Transport, 2004) and including whether or not the roads were inside an urban area. This second measure was then weighted by an estimation of the gradient slope of the road in a third measure.

14To produce a measure of distance-time of travel, we considered the values defined by Kelly et al. (2002), set for North West England and based on field-tests. We adopted these values to match with the 5 road types we distinguished. The values in table 1 are estimated average speeds, reflecting different degrees of traffic density, congestion, speed limit and other variable effects. Applied to our particular need, two limits of the measure used by Kelly et al. were found: First, a large part of the traffic was evaluated at rush hour. As crops are usually transported off-peak, the value of distance-time is likely to over-evaluate the real time of travel. Secondly, the measure was based on an average value of a variety of contexts and conditions on the roads, thereby eliminating the local effects of context in the path finding procedure. For those reasons, we have decided to build and test a new measure of time, based on the Transport Department average speed values for 2004, also used by Lovett et al. (2002), which enabled us to create a measure between urban and non urban areas. Distance-time2 item was created with a value of 60 miles per hour (mph) for all arcs outside urban areas and motorways within urban areas. Apart from motorways, arcs within urban areas were set at 33 mph.

Table : Average speeds for each main road

Source: An adaptation of Kelly et al., 2002.

(1 Mile = 1609.344 meters)

Distance-time weighted by the gradient slope of roads

15A weighting parameter was later added to this second measure of travel time to take into account the topographic variations in the calculation of the time of transport. The gradient slope of the arcs of the road coverage was calculated and used to weight the distance-time measure. For simplicity, we have considered the slow down effect to be proportional to the gradient slope and of the same proportion in descending and ascending sections. Further research and field observation would probably be necessary to calibrate the equation below more accurately. DEM elevation values were extracted at the nodes of the road coverage to calculate the percentage of slope between the first and ending node of each arc (Eq 1). By doing so, we model the elevation linearly between nodes. Even if this is likely not to be the case for a part of the arcs, this measure gives at least an approximation of the gradient slope and its fluctuation along the road network. Arcs have been classified according to their slope value (Table 2) and the time value of distance-time2 has been multiplied by the slope class value to produce a new distance-time impedance item in the AAT (Slopeweight).

16FTSlope= [(From-node* elevation)-(To-node* elevation)/ length of arc]*100 (Eq 1)

17* The road network is modelled by a succession of arcs linked to each other by nodes. Each arc is bounded by a starting node (from node) and an ending node (to-node).

Table : Classification of the slope gradient of the arcs of the road coverage

Demand in energy crop and potential production of the quarries

18The amount of crops provided by each quarries depends on its surface. As the surface of each quarry was unknown at the time of the study and as a simplification for the pilot-project, each quarry was defined by the same surface, corresponding to the average surface of all quarries. For the purpose of the feasibility study, the demand in energy at P was set to approximately 24000 GJ/yr. Quarries should produce short rotation willow coppice. Knowing that yields from short rotation willow coppice are around 10 oven dry tonne per hectare per year (od t/ ha/ yr) and each oven dry tonne yields approximately 18 GigaJoule (GJ), the equation (eq 2) below shows the annual possible energy from 3 quarries sites of average surface:

19Total energy: 3 x (46,2 ha x 10 od t/ ha/yr) x 18 GJ) = 24 948 GJ/yr. (Eq 2)

20As a result, the number of quarries to be restored (the p parameter) was set to 3 based on the idea that 3 quarries in a panel of 10 was a realistic prospect, given the average surface of quarries of 46.2 ha (RMC’s data for the UK) and the demand requested.

Selection of the quarries of best location

21Following the computation of the shortest path, it was necessary to determine which quarry locations allowed minimal transport costs in providing the amount of energy-crops required for the power station.

22A location-allocation procedure was used to assign quarry-nodes to P, until the demand in crops is satisfied. The quarry-nodes are characterised by an attribute ‘crops production’ (depending on their surface). The selection of quarries is based on the shortest path (i.e. the least cost path) and the allocation will cease when the total amount of crops requested by P is satisfied.

23Because the demand and supply parameters were simplified and the number of routes computed in the path-finding procedure was small (10 routes) it was possible to select the quarries of best location without running a full computed location-allocation model. It was possible to link the information of the initial Arc Attribute Table (AAT) of the road coverage to the computed shortest paths (creating an event table to locate features along the computed routes) and used to calculate the total length of the route for a return journey. Applied to a larger area, with a larger number of quarries, possibly several power station sites and quarries of various surfaces, a computed location-allocation modelling would be needed. For example, box 3 provides the instructions for the location-allocation modelling in Arc-Info.

Box 3: LOCATION-ALLOCATION modelling, using MINDISTANCE model, in ARC/INFO

Transport cost assessment

24Transport cost using a 100 m3 container lorry, including driver and fuel cost, was estimated £40 per hour and we allowed half an hour for loading and the same for un-loading. The amount of crop transported would be 13 oven dry tonnes (od.t) per load at a density of 130kg/m3 for dry material. The annual production of a quarry of 46.2 ha would be 462 oven dry tonnes. 36 travels are necessary to collect the annual production (e.g. 462 od.t /13 od.t = 35.54).

25Knowing the surface of each quarry (now available) and the minimum energy threshold necessary to guaranty the economic viability of the power-station equipment, it should be possible to create a more accurate model. Then the threshold could be converted into the minimum surface required to produce sufficient energy crops, which can be used as a constraint in the model. The path finding procedure must then be re-iterated until the cumulative surface of selected least cost quarries is superior or equal to the surface threshold calculated.

Results and discussion

26Data management and processing have been used to set the main characteristics of the road network according to our objectives. Figure 3 shows the road network of the sample area displayed by type of road, urban areas and elevation of the terrain, the location of the potential power station site tested (P) and the location of quarries (Qi). These feature layers have been used to calculate several travel time measures to compute routes.

Figure 3: The road Network of the pilot sample area

Least cost path using several distance measures

27Least cost path analysis has been applied to define the best route between each quarry and the power station. Ten routes were computed to find the minimum impedance path for each one. Five impedance items were calculated and used to compute the path of five route-systems (Table 3).

Table : Distance measures used in Pathfinding

28Computed routes were mapped for each route-system (Figure 4). Figure 4-a shows the routes of the Route-length route-system, using the length of the arcs as impedance item. The routes computed are the shortest ones expressed in metric distance. Although they are the shortest ones, they are not necessarily the quickest ones using one or the others distance-time of travel (figure 4-b,c,d). For example, the shortest path to link the quarries Q8 and Q9 to the power station P is not the quickest when distance-time measure is used (Figure 4-b). The Path using the motorway was quicker than the conjunction of primary road and minor road, used in Routelength route-system. This scenario seems realistic.

Figure 4: The least cost path computed between quarries (Q1-10) and power station (P),for the 4 route-systems

29There is also a clear difference in Path design between route-systems using different distance-time computations. Distance-time and distance-time2 gave a significantly different value (Tables 4 and 5) and the best routes computed take different paths. The distance-time, calculated by Kelly et al. (2002) has the advantage of making a distinction in speed of travel between types of roads. But it has the inconvenience of not taking into account the local contrast in velocity due to the mixing of urban and non-urban areas. Distance-time2, calculated from the average speed value of the Transport Department, emphasises the contrast in speed travel between urban and non-urban areas. The change in route path using distance-time2 (Figure 4-c) compared to distance-time (Figure 4-b) shows the urban effect on time of transportation.

30It is worth noting that the major elevation cannot be avoided, as there is only one road that joins the power station site in the relatively hilly part of the study area. As consequence there were a limited number of possible paths to reach the power station for a part of the journey. However, weighting the time of travel by the gradient of slope, using distance-slope rather than distance-time2, has intruded some changes in the path of routes 1, 2, 6 and 8 in order to avoid some relatively high elevations.

31As an example of the sensibility of the path to the distance item chosen, let’s see the change in Path 1 depending on the distance type used (Figure 5). Selecting a path using metric distance will preferentially select B-roads, while using distance-time impedance item will favour the selection of primary roads. No difference is made between the types of road (B-road, primary road) when using distance-time2, but differences are made between urban and non-urban areas. As the possible roads are partly crossing urban areas and non-urban areas in similar proportion in this area, the shortest path appears also to be the quickest one in this case. When introducing slope weighting to the distance-time2 (distance-slope), the path computed changes, avoiding elevated areas crossed by the B-road. In this case the primary road, located in a flat low elevation area, is preferred.

Figure 5: Path of route 1 according to several impedance items

Distance calculation and cluster of quarries

  • 4 With quarries of various surfaces, the total number of quarries selected would depend on the cumula (...)
  • 5 A similar procedure could have been done automatically, see Box 3.

32A cluster of 3 quarries is required to provide the power station ‘P’ with sufficient energy crop4. For each route-system a solution has been provided (scenario). To do so, the measures of distance and time of travel calculated for each route (Tables 4 and 5) have been used to classify routes, from 1 for the best path to 10, as shown in table 6. The quarries with the routes classed 1 to 3 were selected5. The composition of the cluster for each scenario is highlight in table 5 and shown in figures 6, 7 and 8. The order of classification of the routes changes when using different impedance items, such as metric distance, distance-time and distance-time2 (table 6). The cluster of quarries selected remains the same if distance-time2 is used alone or weighted by the slope effect (Distance-slope). Applied in a relatively flat area (like most of England) gradient slope weighting is therefore likely not to be a main criterion. However, it can create enough contrast to make a noticeable change in the optimal path design.

33Our results suggest that it is advantageous to integrate measurements of travel speed based on the type of roads. Each measure translates the effect of one important factor of travel speed and lead to different results. This supports the idea that a realistic measure requires a multi-criteria time of travel calculation combining all the criteria tested in this study. It should take into account the slow down effect of urban area as well as the type of roads and the gradient slope of the roads.

Table : Distance and travel time measured on path using length of route and distance-time* impedance item.

*Distance-time is calculated from Kelly et al measurements [4], with a distinction between speed value by type of road

Table : Travel time measured on path using distance-time2*, alone and weighted by the gradient slope

*Distance-time2 is calculated from the values published by the Department of Transport [3], with a distinction between urban and non-urban areas travel speed.

34

Table : Classification of routes according to their distance/time of travel

Table : Classification of routes according to their distance/time of travel

Figure 6: Scenario A. Cluster of quarries selected from route-length path finding

Figure 6: Scenario A. Cluster of quarries selected from route-length path finding

Figure 7: Scenario B. Cluster of quarries selected from route-time path finding

Figure 7: Scenario B. Cluster of quarries selected from route-time path finding

Figure 8: Scenarios C and D. Cluster of quarries selected from route-time2 and route-slope path finding.

Minimum transport cost calculation

35The transport cost for a return journey was calculated based on the time of transport on the routes computed (Tables 4 and 5). The annual transport cost to collect the energy crop for scenarios B, C, D, is shown in table 7.

Table : Annual transport cost per scenario

Example: Cluster b annual travel cost for oven dry crops = 36 x [(CostQ10 + CostQ7 + CostQ8) / 3]

*Transport cost has not been calculated for path computed using metric distance (Cluster A)

36We have defined and tested the methodology to compute the least cost path between a set of quarries and a potential power station location. Then a cluster of quarries of best location was selected, which minimises the transport cost of crops between quarries and a power station. This method can be used to test several potential power station locations. A location-allocation modelling should be applied to select an adequate cluster of quarries that minimise the transport to each power station.

Conclusions and future work

37We have established a methodology to help the decision making process of RMC Ltd who aims to convert quarries into energy crop fields and to produce biomass energy at suitable power stations. Because transport costs play a decisive role in the feasibility or profitability of such an undertaking, the methodology was designed to measure distances as accurately as possible. The quarries of best location to be restored into energy-crop fields were determined by a location model taking into account several accessibility measures. It is reasonable to assume that time of travel estimates reflect travel costs sufficiently well, because transport costs will depend mainly on driver wages, lorry wear and petrol costs. The optimal location model proposed different clusters of quarries to be selected, depending on which distance measure was incorporated in the calculations on the road network. Whereas our methodology has the inconvenience to be time-consuming, it has the clear advantage of providing more precise results than a model based on straight-line distance. Network analysis and shortest path computing provide a suitable method to measure the transport cost based on distance and time of travel. If the transport cost is well estimated, it is possible to compute an accurate least-cost path between each quarry and each potential power station and hence select the most suitable cluster of quarries associated to a particular power station. Any applied model is only as good as it reflects reality. We therefore considered multiple parameters for distance/time calculations, such as slow down effects in urban areas, the type of roads used as well as topological heterogeneities (slopes) for a better travel time estimation. Although the latter did not significantly change the selection of quarries in the trial area, the slope parameter may play a more decisive role in more mountainous regions. Because RMC Ltd plans to extend this model to the entire UK, integrating the slope parameter is likely to be important in mountainous regions like Scotland. Here, integrating the topography in the time travel calculation may ultimately proof cost efficient.

38We tested the relative importance of the parameters individually in a test region in the north of England. We observed that integrating the type of roads to find the best path had the largest impact on the choice of quarries, followed by the effects of urban/non urban areas and slope. Taken together, our results show that accurate travel-time and hence transport cost estimations requires the integration of several criteria and that the criteria chosen are suitable to improve the accessibility measurement. Importantly, the outlined methodology should be sufficiently flexible to be adapted to different regions. However, to make this optimal location model fully operational, further development is required with respect to: calibrating the parameters, integration of more parameters and testing their accumulative effects. Also, optimisation of the gradient slope measure and adaptations to extend the model more generally at UK level are envisaged.

39In the future the accuracy of our travel-time estimations have to be judged against actual travel times in a field study, for example by measuring the travel time of a lorry between quarries and to the power station in the trial area. This will be an important test to gauge the accuracy of our accessibility measures. Also, it can provide data on how the different parameters used should be weighted in the model. If sufficiently accurate, no further parameters should be required to be integrated. If further optimisation is needed, we consider also integrating a measure for sinuosity. However, it is likely that the gradient slope parameter somewhat reflects sinuosity, given that most sinuosity is usually found in mountainous regions. This correlation has to my knowledge not been systematically investigated and may proof useful in applications were travel times are the defining criteria for optimal location models. The gradient slope parameter we use could be improved. Because we consider differences in elevations between nodes to estimate gradient slopes, possible local differences between two nodes were not taken into account. It remains to be tested if the gradient slope estimations are sufficiently accurate. Lorry travel times, especially when loaded, are effected in mountainous regions, but it remains to be assessed to what extend this effects travel costs (for example petrol use and lorry usage as well as travel time). Another important factor to consider in choosing the best cluster for quarry restoration is quarry specific, i.e. the productivity of a quarry in terms of energy crop. This information should be integrated into the optimal location model as soon as available.

40The optimisation and finalisation of the described optimal location model should involve: the possible addition of more parameters to better estimate travel times; the weighted combination of the parameters used and assessment of their cooperative effects on estimated travel times; and finally the application of the optimal location model at the UK level. The latter will be facilitated by the automation of the described procedures (i.e. writing script to allow path-finding reiterative procedures, using loops). Location-allocation modelling (see Box 3) should be used to allocate each power station site to quarries and select the quarries of best location.

41The described optimal location model is adjusted to the special needs of the mining industry where potential locations are fixed and travel costs decisive. We have therefore aimed to estimate travel times, considered to be directly proportional to travel costs, as accurately as possible and using a network based approach. Whereas we think that a network based approach offers advantages with respect to data amounts to be handled and higher accuracy in measuring distances, a d-dimensional space approach may provide different advantages, e.g. a more accurate estimate of the downhill –uphill sections of a route. We hope that this paper contributes to the understanding of the underlying challenges of accurate travel time simulations, widening of the applications of optimal location models and discussions of the best methods to particular questions.

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Notes

1 The emissions of carbon dioxide should be reduced by 60% by the middle of the century in the UK, as stated by the Government in the 2003 Energy White Paper (Energy White Paper: Our energy future – creating a low carbon economy, DTI, February 2003, CM 5761)

2 RMC Group (Ready-Mix Concrete product Ltd) is a leading international producer and supplier of materials, products and services used essentially in the construction industry.

3 The Urban areas in STRATEGI are based on the concentration of buildings and other structures, at the time of digitisation of the dataset. It does not take into account the number of people living in the area.

4 With quarries of various surfaces, the total number of quarries selected would depend on the cumulative surface of the quarries selected in order to minimise the transport time/cost.

5 A similar procedure could have been done automatically, see Box 3.

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Titre Box 1: Topological data structure in ARC/INFO
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Titre Table : Classification of routes according to their distance/time of travel
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Titre Figure 6: Scenario A. Cluster of quarries selected from route-length path finding
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Titre Figure 7: Scenario B. Cluster of quarries selected from route-time path finding
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Sylvie Dubuc, « GIS-based accessibility analysis for network optimal location model », Cybergeo: European Journal of Geography [En ligne], Systèmes, Modélisation, Géostatistiques, document 407, mis en ligne le 26 novembre 2007, consulté le 24 janvier 2022. URL : http://journals.openedition.org/cybergeo/12653 ; DOI : https://doi.org/10.4000/cybergeo.12653

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Auteur

Sylvie Dubuc

Research Fellow
Sylvie.dubuc@socres.ox.ac.uk
United Kingdom

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