A Dynamical Model of the Industrial Economy of the Humber Region
Christopher J.K. Knight, Alexandra S. Penn, Rebecca B. Hoyle
AA Dynamical Model of the Industrial Economy of the HumberRegion.
Christopher J.K. Knight , Alexandra S. Penn , and Rebecca B. Hoyle ERIE, Department of Sociology, University of Surrey, Guildford, GU2 7XH, UK Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK Center for Environmental Strategy, University of Surrey, Guildford, GU2 7XH, UK
April 14, 2014
Abstract
The Humber region in the UK is a large and diverse industrial area centred around oilrefining, chemical industries and energy production. However there is currently a desireto see the region transition towards a more bio-based economy. New bio-related industriesare being situated in the region as a consequence of policy and economic incentives. Manyof these industries are connected through their supply chains, either directly, or by sharingcommon suppliers or customers and the growth or decline of one industry can hence haveimpacts on many others. Therefore an important question to consider is what effect thismovement towards bio-based industry will actually have on the regional economy as awhole. In this paper we develop a general abstract dynamical model for the metabolicinteractions of firms or industries. This dynamical model has been applied to the Humberregion in order to gain a deeper understanding of how the region may develop. The modelsuggests that the transition to a bio-based economy will occur with oil refining losing itsdominance to bioethanol production and biological chemical production, whilst anaerobicdigestion grows as a major source of electricity, in turn driving up the value of regionalwaste aggregators and arable farming in the overall economy.
The Humber region is a large diverse industrial area in the UK. It is centred around the portsof Grimsby, Immingham and Hull on the tidal estuary of the UK’s largest river system. Thisport complex is one of the largest and busiest in Europe. In fact the area surrounding theestuary contains 27% of the UK’s oil refining capacity and infrastructure for 20% of nationalgas landing [13]. The wider region has many diverse industries from farming, to energyproduction, to heavy industries. Many of these industries interact with one another, oftenvia the material supply of goods or services. This can range from the unexceptional use ofelectricity by almost all industries (in most instances procured from energy suppliers via thegrid), to industry-specific needs such as biomass for co-firing power plants. These interactionsform a complicated web representing the industrial economy of the Humber region. As wellas these physical, metabolic interactions there are also what we might call social interactions,both positive and negative. For instance, joint bidding for funding, competition for scarce,highly skilled workers, etc. We shall not dwell on such social interactions between firms inthis paper, however we extend our methods to take into account their effect in [8]. Insteadwe here seek to understand the metabolic interactions and how they influence the region asa whole. 1 a r X i v : . [ q -f i n . E C ] A p r bviously such an intricate network of relationships is not unique to the Humber region.In fact, any economy which has a regional component could be represented by a complicatedset of interconnections between constituent industries. However not all industrial economiesare as complicated as one another. For instance, consider local economies which are basedaround one major firm (a hub and spoke district [10]). Such economies are likely to have arelatively simple set of relationships between the industries present; either supplying the majorfirm or buying and using its products. Nor are intricate networks of relationships restrictedto ‘man made’ economies. Consider, for instance natural ecosystems, and the complexity ofvarious food webs made up of consumer-resource interactions [1, 5, 7].Unlike industrial districts, much research has been carried out on food webs and how tomodel them in a quantitative, whole system, manner. In contrast, modelling of industriestends to focus on the supply chains of individual firms [3, 4, 6] rather than modelling of allfirms within an economic or geographic district. This means, for instance, that competitioneffects for resources are not completely included. That is, competition may be included if twofirms supply a firm in the supply chain, but not if a competing firm does not supply (in someway) the firm that the supply chain is focussed on. This could have huge effects, for instanceif a competing firm (not in the supply chain) went out of business, this might mean that a firmin the supply chain doesn’t have enough business and so also fails, having a knock-on impacton the whole supply chain. Many of these models of supply chains are static, although someare dynamic, often using multi-agent approaches to simulate supply decisions [2, 14]. Due tothe lack of whole system (high level) dynamical models for interdependencies of firms in anindustrial district we draw inspiration from the field of ecological modelling.The archetype of whole system ecology models is the Lotka-Volterra model for preda-tor prey interactions, originally developed by Lotka in the 1920s, [9]. This is a dynamicalpopulation-based model with the change in population of each individual species being repre-sented by a differential equation. Each equation contains terms relating to population growth,for instance birth rates, which could be related to the availability of food, and hence to thepopulation of any prey species. Each equation also contains a term representing the decreasein population due to death. This term may be dependent on the size of predator popula-tions. The way that the growth and decay terms depend on the population sizes of otherspecies couples all of the equations together, creating a simple model of the complete foodweb. Variants of this basic Lotka-Volterra model have been applied to model many differentfood webs [11, 15], however, to our knowledge, no work has attempted to model the web ofindustrial firms in the same way. In this paper we seek to address this deficit by creating aLotka-Volterra type model for the interaction of industries. Instead of each equation mod-elling the size of a population of a particular species we instead create an equation for the‘size’ of each firm or industry. Where ‘size’ can be thought of as an abstract concept whichin some way represents the health and wealth of a firm. The coupling of these equations isthen via the ‘size’ of supplier and customer firms rather than prey and predator populations.This dynamical model of the interactions of industries in a economic or geographic districtwill be quite high level and general without going into many of the specifics considered whenmodelling individual supply chains. The idea behind the model is not to give intricate detailabout the system but rather represent it with a ‘broad brush’ in order to make statementson the scale of the whole system, and how it might respond to changes.In Section 3 we apply this model to the industrial economy of the Humber region to learnmore about the implications of the interconnected structure of the metabolic connectionsbetween industry types. In particular we investigate how the region may transition frombeing centred around fossil fuels to become a bio-based economy.2 A Dynamical Model of Metabolic Interactions
An industrial economy is made up of several different firms or industry types interacting invarious ways, in a spatially confined region. As an initial attempt to model the dynamics ofsuch a district of industrial types we shall only consider metabolic interactions, consisting ofthe trade in goods and services. Further, we shall make the model as simple as possible so thatmodifications to include social interactions [8] may be made and the model remain amenableto analysis. This means, among other things that the model shall concern only one good(locally), or equivalently make the assumption that all goods (sold within the district) areinterchangeable. Whilst this assumption is questionable in most instances, it hugely simplifiesthe modelling process and, more importantly, means that it is possible to find the data neededto initialise the model. It would be possible to make the model more complicated, howeverthis would be at the expense of the model’s usability. It must be remarked that the aim ofthe model is to express the general behaviour of the system as a whole, as such, the level ofassumptions made is appropriate.As no spatially confined industrial economy (an industrial district) is entirely closed therewill always be flows of materials and services into and out of the district. Similarly unless wemodel on the scale of the individual there will be transactions between entities in the modeland those which have not been modelled, for instance individual consumers. To accountfor this edge of the district we split the industry types into three categories signifying theirrelationship with what lies beyond the district. They are denoted ‘
Primary Suppliers ’ ( S ),‘ Intermediaries ’ ( I ) and ‘ End Consumers ’ ( C ). The distinction relates to the structural role ofeach firm, both the ‘primary suppliers’ and the ‘end consumers’ have some form of trade linkwith entities beyond those modelled in the local district. The rest of the firms are denoted as‘intermediaries’. The ‘primary suppliers’ are those firms who derive product from somewhereoutside of the network. For instance, if a local network is considered then any firm which buysmaterial from further afield is denoted as a ‘primary supplier’. Alternatively a firm whichmines for resources (as long as the resource itself is not modelled) is a ‘primary supplier’. ‘Endconsumers’ are those firms who sell product beyond the network, this can either be thought asglobal trade when considering a local network or as selling of product to individual customers(people or small firms not included in the model). It is important to recognise that a ‘primarysupplier’ may also buy from other firms in the network. Similarly ‘end consumers’ may supplyother nodes in the network. It is also possible for a firm (or industry) to be both a ‘primarysupplier’ and an ‘end consumer’, in this case the firm is called a hub of the network. Figure 1shows an example of a local metabolic network with labels denoting the type of each node.Note that every node must be connected (backward) to at least one supplier and connected(forward) to at least one consumer (a node with no outgoing connections to other nodes inthe network is automatically an ‘end consumer’, and one with no incoming connections fromother nodes in the network is automatically a ‘primary supplier’).With this distinction we can start formulating our model for the interactions of industriesin a region. We shall start by considering the industries denoted ‘intermediary’, the equationsfor industries of the other two classes can be easily derived from them. Each intermediary (bydefinition) will have suppliers and customers amongst the other firms (industries) that makeup the model. For a specific firm denoted ‘firm i ’ the set of firms which supply products orservices to it is denoted S i , and the set of firms which buy products or services from firm i is denoted C i . At its most basic our Lotka-Volterra type model says that each year a firm orindustry grows by the amount it sells its products and services for, less the amount it spentbuying the raw materials or services it needed, less overhead costs. However actually writing3 ICS SSS CCCC II
Primary SuppliersIntermediariesEnd Consumers
Figure 1: An example network with nodes marked as S: ‘primary Supplier’, I: ’Intermediary’,C: ‘end Consumer’.this basic model down proves to be fairly complicated.We denote the wealth/health/general utility of firm i by u i , and the worth of the productsor services sold to firm j by G ( u i , u j ). The worth of a product (or service) may be differentto those selling it and those buying it. The firm which sells the product is unlikely to sellit at cost price, meaning that their idea of value must take into account the profit that theymade in producing the product or offering the service. As our model only deals (locally) withone product any feedback loops may cause issues, leading to an exponential rise in the cost ofgoods as they circle round such a loop. To avoid this we assume that the value of the goods(as perceived by the buyer) is their actual material and production cost, whilst the value ofthe goods to the seller is the material and production cost of the product plus the profit theymake on it. This has the effect of renormalising everything at each time step and is similar toinflation adjusting the costs for each firm. Thus the cost to a firm i ’s utility of buying fromfirm j is G ( u j , u i ) and the gain to firm i ’s utility of selling to firm j is (1 + (cid:15) i ) G ( u i , u j ). Where (cid:15) i is the percentage profit that firm i makes. Finally, if we denote the percentage overheadcosts of firm i by d i then the basis of our model can be written:˙ u i = (1 + (cid:15) i ) (cid:88) j ∈ C i G ( u i , u j ) − (cid:88) j ∈ S i G ( u j , u i ) − d i u i . (1)This equation forms the basis of our model, and is almost complete for intermediary firms.The one major component still to add is the effect on the utility if a firm is not able to buyall of the materials or services it requires. This could affect the amount of its own producta firm is able to sell, however this soon gets very complicated and would require the use ofdelay equations. Instead we assume that the same amount of product (or service) is made butit costs more or is of lower quality. For instance, buying in the completed product from someexternal supplier at market rates to ensure the firm has enough product to sell in the shortterm. This would not change the worth of the product to the customer, but would certainlyaffect the worth to the supplier. We model this by imposing a multiplicative penalty term P i on the gain in utility given by the selling of product. This penalty is the actual supply ofmaterial and services over the total required supply. Thus our model for the health/wealthof a firm becomes˙ u i = (1 + (cid:15) i ) (cid:88) j ∈ C i G ( u i , u j ) P i − (cid:88) j ∈ S i G ( u j , u i ) − d i u i . (2)The details required to make (2) a complete model are expressions for the value of productsold between firms ( G ( u i , u j )) and the multiplicative penalty term ( P i ). There are different4ays to do this, including full market modelling in the case of the amount of product soldbetween firms. However we shall again choose a simpler option. We shall assume that thereis a fixed percentage of the utility that a firm requires in supplies, β i . That is β i u i is thetotal amount that firm i must ‘pay’ to buy all of the materials and services it needs when ithas grown to size u i . Similarly we assume that the value of the product each firm creates isproportional to its size u i . That is a firm with utility u i produces products with a value ρ i u i .A complete list of all the notation used in our model is given in Table 1. With this notationwe can express the penalty term (still for intermediary firms) as P i = (cid:80) j ∈ S i G ( u j , u i ) β i u i , the fraction of the required supply that a firm actually managed to procure. The expressionwe use for G ( u j , u i ) is more complicated as firm i is likely to have multiple suppliers and eachof them is likely to have multiple customers. If each firm that supplies firm i can meet alldemands for product placed upon them by all of their customers (they’re big enough) thenfirm i is able to buy the total amount of product it requires β i u i . We assume that the amountit buys from each of its suppliers is proportional to their size (utility). This expresses thedesire to keep the largest of a firm’s suppliers as happy as possible - without totally alienatingany of the other suppliers. That is (if all of a firm’s suppliers are able to fulfil the entiredemand for product placed upon them) G ( u j , u i ) = β i u i u j (cid:80) k ∈ S i u k . If on the other hand one of firm i ’s suppliers (firm j say) is unable to fulfil the totaldemand placed upon it then it will, in total, supply the maximum amount that it can: ρ j u j .It will distribute this according to the demand placed on it by each of its customers. Weagain assume that it sells in proportion to the amount each customer requires (see above), inorder to retain the largest customers without alienating any of the smaller customers (notein our model we do not actually allow the customers or suppliers of firms to change, althoughthey can go out of business). That is G ( u j , u i ) = ρ j u j β i u i u j (cid:80) k ∈ Si u k (cid:80) l ∈ C j (cid:20) β l u l u j (cid:80) m ∈ Sl u m (cid:21) . Combining these two scenarios together gives: G ( u j , u i ) = β i u i u j (cid:80) k ∈ Si u k , if (cid:80) l ∈ C j (cid:20) β l u l u j (cid:80) m ∈ Sl u m (cid:21) ≤ ρ i u i ,ρ j u j β i u i u j (cid:80) k ∈ Si u k (cid:80) l ∈ Cj (cid:20) β l u l uj (cid:80) m ∈ Sl um (cid:21) , otherwise . (3)This completes the details of the model for intermediary firms. We now explain theamendments needed to cope with the ‘primary suppliers’ and ‘end consumers’. First ofall note that if the current model (2) were applied to an end consumer with no customersbeing modelled then there would be no growth term, u i would be monotonically decreasing.Similarly looking at a primary supplier the only negative term would be the overheads, eventhough products were being bought and paid for (just from outside the set of firms modelled).To counter this we add an extra term to the model containing the utility gain or loss from5xporting or importing, respectively, materials and products from outside the set of firmsmodelled. We denote this component of the model Λ i . The value of which depends on theclassification of the firm. If firm i is an intermediary firm then Λ i = 0. We assume that thesupply of a product from outside the district is essentially unlimited. That is, a firm whichis a supplier can buy what ever it requires from outside of the district, β i u i . If a firm buysall of its supplies from outside the district then using this makes sense, however if it buyssome of its supplies from inside the district it would end up buying supplies to the value of2 β i u i . If this is the case we make the value of β i half what it would otherwise be. Whilst thechoice of a half of the product being bought from within the district and half from outside ofthe firms modelled is fairly arbitrary, it is something which could easily be improved upon inlater iterations of the model if such detailed data is available.When considering ‘end consumers’ we make the assumption that the external market forthe products and services being created is bounded. The total maximum demand of theexternal market is for products with value M . If the total amount the district is trying to sellto the external market exceeds the market demand then each end consumer sells according totheir size. However, in complicated industrial districts it is possible (and indeed likely) thatthe goods being sold to the external market are not interchangeable. To account for this wesay that there are several external markets for different commodity types, each with a boundon the value of good which can be bought, M k . For instance it seems feasible that fuel couldbe treated as such a commodity type, with different fuel types competing in the externalmarket due to their similarities. A further complication arises if a firm supplies multipledistinct external markets, for instance if firm i is in k ∩ k . In this case, one must knowwhat proportion of the amount sold by firm i goes to market k and how much to market k . For simplicity we shall assume that firm i wants to sell the same amount of goods ineach external market (if in reality the proportion of goods sold to one external market fromfirm i is much smaller than that sold to other external markets then the sales to that marketfrom firm i could be ignored for the purpose of this model). In reality a firm with multiplemarkets may choose to reposition itself if one of those markets becomes unprofitable due toexcess competition, however to model this we would need to model the decisions of individualfirms, something we choose not to do in order to create a simple deterministic model of theinteractions of firms.If there is just one external market then the amount ‘end consumer’ i sells to the externalmarket is˜ G ( u i ) = (cid:40) ρ i u i , M > (cid:80) j ∈ C ρ j u j ,M u i (cid:80) j ∈ C u j , otherwise . Again if a firm is an ‘end consumer’ but also sells to other firms in the district then we make ρ i half of what it would otherwise be. If firm i is an ‘end consumer’ its utility needs to increaseby (1 + (cid:15) i ) ˜ G ( u i ). That is we haveΛ i = − β i u i , i a primary supplier , , i an intermediary , (1 + (cid:15) i ) ˜ G ( u i ) , i an end consumer , − β i u i + (1 + (cid:15) i ) ˜ G ( u i ) , i a primary supplier and an end consumer . However if there is more than one external market the expression for ˜ G ( u i ) is slightly morecomplicated. First of all we need a rescaled version of u , ˜ u , if firm i sells goods to n external6arkets then ˜ u i = u i /n . With this notation˜ G ( u i ) = (cid:88) k | i ∈ k (cid:40) ρ i ˜ u i , M k > (cid:80) j ∈ k ρ j ˜ u j ,M k ˜ u i (cid:80) j ∈ k ˜ u j , otherwise . Finally we must deal with the multiplicative penalty term due to lack of supply for ‘primarysuppliers’ and ‘end consumers’. As it is assumed that there is no limit to the amount ‘primarysuppliers’ (including hubs) can procure from outside the district, no penalty due to lack ofsupply will be imposed. In the case of an ‘end consumer’ (but not a hub) the penalty termwill be the same as for the intermediary firms. However the penalty is applied to the Λ i termas this is now the term which incorporates the benefits to the utility from selling products orservices. That is P i = (cid:40) , i a primary supplier , (cid:80) j ∈ Si G ( u j ,u i ) β i u i , otherwise . Thus our model for the metabolic interaction of firms or industries within a local districtis ˙ u i = (1 + (cid:15) i ) (cid:88) j ∈ C i G ( u i , u j ) P i − (cid:88) j ∈ S i G ( u j , u i ) + Λ i P i − d i u i , (4)with the notation detailed in Table 1. Symbol Definition Λ a The intrinsic growth rate (seen from a local perspective) of firm a . P i The penalty to firm i of not buying enough product. G ( a, b ) The worth of product a that is bought by firm b . β a The value of the material or services that a needs as a proportion of its wealth. ρ a The value of a ’s product or service as a proportion of its wealth. (cid:15) a The percentage profit made by firm a . d a Percentage upkeep costs of firm a . M k The maximum value of product type k which the district can sell externally.Table 1: List of Notation We shall use our abstract dynamical model of the interactions of firms or industries to learnmore about the intricacies of the Humber region. As we mentioned in the introduction theHumber region is made up of many distinct industry types. In [12] Penn et. al. devised amethod for creating a complete metabolic network of a system from an incomplete sample ofthe network using ‘network archetypes’, characteristic sets of input and output connectionsfor given industrial sectors. They were able to generate a network model of the Humber regionby using these archetypes to supplement data from a series of eighteen interviews which werenot originally designed to elicit complete network information. This model gives a staticimpression of the region and network analysis can be used to draw conclusions about nodes ofparticular importance or vulnerability wthin the system. With our dynamical model we seekto go beyond these purely structural results, and learn more about the possible future of thesystem. We do not run our dynamical model on Penn et. al.’s complete model of the Humber7egion due to the size of the network (seventy-six nodes) and the corresponding difficultyinvolved in finding the necessary data to initialise our dynamical model. Instead we use themodel of Penn et. al. to generate a condensed network representation of the Humber regioncomprising twenty-two interconnected nodes. This subset constitutes the the principal bio-based industries in the region and their main connections, direct and indirect, as determinedby number of mentions in interview transcripts and local knowledge on magnitude of materialsupplies. Importantly this network includes every stage in the possible bio-based economycycle from primary producers (agriculture), via processors of different kinds (food, biofuelsetc) to waste processors and recyclers (landfill, anaerobic digestion, composters etc).Figure 2 shows the network model for the metabolic interactions of the industries in theHumber region. The edges represent flow of material whilst the style of the edges represent
Food Processor Farming: LivestockRefineryComposter: Low GradeRefineryComposter: High GradeRefineryComposter: In-VesselRefineryWaste Aggregator: NationalRefineryWaste Aggregator: RegionalRefineryWaste Aggregator: LocalRefineryAnaerobic Digester RefineryChemical ProductionRefineryBiodiesel Production: WasteRefineryBiodiesel Production: Virgin RefineryFarming: ArableRefineryPower Plant: CoalRefineryPower Plant: Co FiredRefineryPower Plant: Biomass RefineryBioethanol ProductionRefineryBioprocessorRefineryWaste IncineratorRefineryLandfill: HazardousRefineryLandfill: Non-Hazardous RefineryRefinery
Figure 2: A condensed model of the industry interactions of the Humber region. Arrows showthe flow of material. Solid lines depict instances in which the flow of money is in the oppositedirection to the flow of material, whilst dashed lines represent instances where money andmaterial flow in the same direction (e.g. waste disposal).how the flow of material relates to the flow of money. In building our dynamical model offirm interaction we have implicitly assumed that the flow of material is opposite to the flowof money; that is you buy a material or product. These are represented by solid lines inthe figure. However in the Humber region there are several industries which deal with waste(for instance landfill sites), these industries are paid to take the waste from other industriesand dispose of it. In this case the material and the money both move in the same direction.These are the dashed lines in Figure 2. To allow the use of our dynamical model (4) on thisrepresentation of the region we must find a representation where the flow of money is oppositeto the flow of material or service. This is the key point, whilst the material may flow in thesame direction as the money this in fact represents a service flowing in the opposite direction.For instance, waste flows into the landfill, however if instead of the waste we consider theservice that the landfill is providing in taking waste from other industries then this flows in theopposite direction to the flow of money. Thus the network that we actually use to representthe Humber region in our dynamical model has all of the dashed arrows reversed. So, forinstance, landfill has lots of out going edges and no incoming edges, making it a primary8upplier. The classification of the other nodes in terms of their role with relation to firmsoutside the district is shown in Table 2.
Industry Type Category External Product
Refinery: Crude Oil Hub Fuel, ChemicalsFood Processor End Consumer FoodFarming: Arable Primary SupplierFarming: Livestock Primary SupplierPower Plant: Coal-Fired Hub ElectricityPower Plant: Co-Fired Hub ElectricityComposter: Low Grade Primary SupplierComposter: High Grade Primary SupplierComposter: In-Vessel Primary SupplierWaste Incinerator Hub ElectricityLandfill: Non-Hazardous Primary SupplierLandfill: Hazardous Primary SupplierWaste Aggregator: National IntermediaryWaste Aggregator: Large Regional IntermediaryWaste Aggregator: Small Local IntermediaryPower Plant: Biomass Hub ElectricityBiodiesel Production: Virgin Feedstock Primary SupplierAnaerobic Digester End Consumer ElectricityChemical Production: Biological Hub ChemicalsBioethanol Production: Virgin Feedstock Hub FuelBiodiesel Production: From Waste Hub FuelBioprocessor IntermediaryTable 2: Industry Classifications and External Market Products.In order to run the dynamical model (4) for industrial interactions on the network ofthe Humber region we first need to find initial values for the health/wealth ( u i ), as well asparameters; β i , ρ i , (cid:15) i and d i , for each of the industry types. We also need to classify theproduct types that are sold to the external market by the end consumers and hubs. Themajor commodities which the firms in our model export are; fuel, chemicals, electricity, andfood. The external markets that each firm supplies can be found in Table 2. For these fourdifferent external markets we must find values for the maximal demand, M k .Due to the fact that not all firms which would be classified as the same industry typeoperate in the same way, finding exact values for all of the parameters and initial conditionsis not possible. For instance consider arable farming - the economics will depend on whichcrop is grown as well as the size of the farm, and what method is used to grow the crop.Whilst the price the crop fetches will depend on the quality of the crop (which dependson the weather and on disease spread) and how many other farms have grown the samecrop. Instead we use average values, or values derived from an ‘archetype’ firm of a particularindustry. The values that we use for the parameters and initial conditions are given in Table 3and their derivation can be found in Appendix A. We take the total external market demand M to be the sum of the initial utilities over all end consumers, that is M = 13777 .
42. Forthe individual markets, e.g. fuel, we take the sum of the initial rescaled utilities, ˜ u i over allfirms supplying that market. So for instance the external market demand for chemicals M C is the initial utility of “chemical production: biological” plus half the initial utility of the9efinery, M C = 6573 .
33. The external market demand for fuel is M F l = 4870 .
58, the externalmarket demand for electricity is M E = 2308 .
54 and the external market demand for food is M F d = 24 . Industry Type u (0) β ρ (cid:15) d Refinery: Crude Oil 9445.45 0.228 0.493 0.027 0.007Food Processor 24.99 0.153 0.238 0.119 0.191Farming: Arable 0.11 0.061 0.444 0.507 0.066Farming: Livestock 0.28 0.105 0.465 0.184 0.029Power Plant: Coal-Fired 451.62 0.080 0.226 0.690 0.046Power Plant: Co-Fired 1627.35 0.080 0.227 0.714 0.038Composter: Low Grade 0.25 0 0.470 0.845 0.045Composter: High Grade 0.25 0 0.470 0.845 0.045Composter: In-Vessel 0.25 0 0.470 0.845 0.045Waste Incinerator 11.76 0 0.234 0.163 0.104Landfill: Non-Hazardous 4.97 0 0.444 0.484 0.140Landfill: Hazardous 2.55 0 0.444 0.502 0.136Waste Aggregator: National 1590.72 0 0.497 0.011 0.032Waste Aggregator: Large Regional 159.07 0 0.497 0.011 0.032Waste Aggregator: Small Local 1.59 0 0.497 0.011 0.032Power Plant: Biomass 209.21 0.167 0.239 0.106 0.030Biodiesel Production: Virgin Feedstock 37.57 0.138 0.484 0.073 0.048Anaerobic Digester 8.59 0 0.225 0.661 0.013Chemical Production: Biological 1850.60 0.173 0.229 0.241 0.056Bioethanol Production: Virgin Feedstock 120.87 0.084 0.223 0.570 0.019Biodiesel Production: From Waste 26.98 0.076 0.225 0.340 0.067Bioprocessor 199.61 0.383 0.470 0.148 0.014Table 3: The initial conditions and parameters needed in the dynamical model of the Humberregion (4). A detailed description of the method used to derive these values and the sourcesused can be found in Appendix A.
In this section we present the results that our dynamical model of firm (or industry type)interaction (4) gives when applied to the network model of the Humber region shown inFigure 2 with parameters initialised as shown in Table 3. To do this we have written matlabcode to run the system of differential equations (4) using the built in ode45 procedure toiterate the initial conditions. The output is shown in Figure 3, which plots how the utilityof the different industry types changes over time. Due to the difference in scales between themaximum utilities of the various industry types we show a zoomed in version as well, enablinga more detailed view of the behaviour of several industries to be seen.We point out that the dynamics of the various utilities are unlikely to be accurate forlong time scales due to the assumptions that were made in creating the dynamical model.10
50 100 150 200 250 300 350 400 450 50000.511.522.53 ! x 10 ! TimeHealth/ ! Wealth ! x 10 ! TimeHealth/ ! Wealth
RefineryFood ProcessorFarming: ArableFarming: LivestockPower Plant: CoalPower Plant: CoComposter: Low GradeComposter: High GradeComposter: In-VesselIncineratorLandfillLandfill: HazardousWaste Aggregator: NationalWaste Aggregator: RegionalWaste Aggregator: LocalPower Plant: BiomassBiodiesel Production: VirginAnaerobic DigesterChemical Production: Biological
Bioethanol Production: VirginBiodiesel Production: WasteBioprocessor
Figure 3: How the utility of various industry types changes over time according to our modelfor the interactions of industries (4) on the model of the structure of the Humber region,Figure 2, with the parameters as listed in Table 3.11or instance we assume that all products (sold locally) are interchangeable, which allowsindustries to die off entirely. This wouldn’t happen to the same extent in reality as manygoods are non-interchangeable. Another issue is the fact that new connections are not made,meaning that if all suppliers go out of business then so will the dependent industry. All ofthis means that the dynamics of the utilities of the various industries shown in Figure 3 areonly valid for short time scales, and in particular are unlikely to be valid much beyond whenthe first industry fails. From the output we shall take this point to be around time step 40(nominally 40 years although the real time period is likely to be shorter). Thus we analysethe output (in narrative form) of the model up until this point.Initially the utility of almost every industry type increases suggesting that the structureof the industries in the Humber region is viable, at least in the short term. The only industrytypes which show a decrease in utility initially are the national waste aggregator, the bio-processor, and the biomass power plant, all of which only decrease very slowly. Initially theutility of the food processor is almost static and only changes slowly over time, this is dueto the fact that it is the only industry type in the district which supplies the external foodmarket - a market (from the district perspective) which is substantially smaller than all ofthe other external markets. This substantially constrains the food processor meaning it willremain smaller than many other of the industry types in the district.The first interesting transition appears to occur at time 7, when the refinery reaches apeak and starts to decline drastically. This is caused by the limited external market for fueland chemicals. On the chemical side the refinery is being replaced by chemical productionfrom biological feedstocks, whilst on the fuel side it is being replaced by biodiesel production(primarialy from waste) and bioethanol production from virgin feedstock. It is particularlyinteresting to see the transition from an oil based economy to one centred on bioethanol(from virgin feedstock) and biodiesel (from waste) production in such a short time-scale asthe Humber region is currently trying to shift its economy in this direction, away from anoil-centric economy towards a bio-based economy, see [13] and references therein. However,in the slightly longer term we see that biodiesel production starts decreasing, again beingreplaced by bioethanol production. In a similar time frame as this decrease in biodieselproduction the model suggests that the district will have over estimated the demand of theexternal market for both fuel and chemicals, resulting in a sharp decrease in their productionuntil an equilibrium is reached.Another transition that we can see in Figure 3 is in the source of electricity. After theinitial increase in all forms of electricity generation (with the exception of biomass powerplants), both coal-firing and co-firing power plants start to decrease with electricity insteadbeing produced by anaerobic digestion. The reason such a transition appears possible is thatthere is an increase in the amount of waste in the system, with landfills and waste aggregatorsgrowing, eventually landfills start decreasing again with the waste instead going to the wasteaggregators (both national and regional). As anaerobic digestion increases it takes more andmore waste away from landfill, effectively becoming the dominant form of waste disposal inthe region. The increase in anaerobic digestion leads to an increase in the amount of digestatethat is available for farmers (arable) to use, meaning that they can grow their crops morecheaply and thus leading to an increase in their utility. There is also a feedback effect here,in that an increase in arable farming leads to more goods which can be used in the anaerobicdigestion process.In summary it appears that in the short term the dominant industry of the Humber regionwill transition from refineries to bio-ethanol production (from virgin feedstock) and biologicalchemical production. As the production of electricity changes these industries are replaced12n their dominance in the district by anaerobic digestion, and the associated regional wasteaggeregator.
In this paper we have developed a simple dynamical model describing how different firms orindustries interact via their supply chains. The combination of the supply chains of variousindustries forms an interconnected web of such metabolic interactions. The model that wehave developed acts on this network of metabolic connections, following the impact of anincrease or decrease of an industry’s wealth/health on other industries and their consequentialimpact on each other.This dynamical model could be used in many different scenarios to explore how differentindustrial districts or regions might function, and to investigate the possible future of the dis-trict. This could be especially useful if a major transition in focus of the district is occurring,or is expected to occur in the near future. We applied our model to the Humber region inthe UK, a major source of UK energy production traditionally from fossil fuels and also of oilrefining capacity. The region is currently undergoing a transition towards a bio-based econ-omy. Using a (roughly) parametrised version of the dynamical model we were indeed able tosee the development and transition to a bio-based economy. The outcomes of the model seemto make sense within the wider context of the Humber region and are what is hoped for in atransition from fossil fuel based economy to a bio-based economy. The oil refinery is replaced(in dominance) by bioethanol production from virgin feedstock, biodiesel production fromwaste, and chemical production from biological feedstocks. On the power generation side, theuse of both coal and co-firing power plants increase before being replaced by electricity gen-erated from waste through anaerobic digestion. Such an increase in anaerobic digestion maywell require more waste material than can be provided easily, which could lead to an increasein the use of raw materials from arable farmers. However the excess digestate such anaerobicdigestion produces would enable cheaper enrichment of soil for arable farming. The fact thatthese outcomes seem to be desirable suggests that the current structure and make-up of theHumber region is adequate to the political desire to transition to a bio-based economy.However, even though the the dynamical output of our model makes sense we must stillsound a note of caution. The dynamical model assumes that all goods are interchangeable(locally) and the parameter values used are only rough estimates. There are also majoraspects of the industrial district that are not modelled at all. The most obvious (and probablyinfluential) of which is the social aspect of the district. It is simply not true that the onlyway that firms or industries influence each other is through supply and demand metabolicinteractions. There are many different forms of social interaction, such as joint bidding forfunding, competition for scarce highly skilled workers, and joint training. Each of these formsof social relationship potentially detailing its own network of relations between the firms orindustries in a district. It does, however, seem possible to divide the social relationships intotwo broad classifications; those which are mutually beneficial, and those which are detrimentalin some way to the firms involved. We explore this issue further in [8], extending the dynamicalmodel presented here to incorporate these social interactions.
Acknowledgements
This work was supported by the Engineering and Physical Sciences Research Council [grantnumber EP/H021450/1] (Evolution and Resilience of Industrial Ecosystems ERIE). We would13ike to thank D. Avitabile for useful discussions during our initial model development, andF. Schiller, A. Yang and E. York for their help in finding some of the sources used inparametrising the model for the Humber region.
References [1] J. Bascompte, C.J. Meli´an and E. Sala Interaction Strength Combinations and theOverfishing of a Marine Food Web, PNAS 102(15), pp. 5443-5447, 2005.[2] H. Baumgaertal, S. Brueckner, V. Parunak, R. Vanderbok, J. Wilke, Agent Models ofSupply Network Dynamics, The Practice of Supply Chain Management, 2001[3] T.Y. Choi and Y. Hong, Unveiling the Structure of Supply Networks: Case Studies inHonda, Acura, and DaimlerChrysler, Journal of Operations Management 20(5), pp. 469-493, 2002.[4] C. D’Apice, R. Manzo and B. Piccoli, Modelling Supply Networks with Partial Differen-tial Equations, Quart. Appl. Math. 67, pp. 419-440, 2009.[5] C.S. Elton, Animal Ecology, Sidgwick and Jackson, London, 1927.[6] C. Harland, R. Brenchley and H. Walker, Risk in Supply Networks, Journal of Purchasingand Supply Management 9(2), pp. 51-62, 2003.[7] H.W. Hunt, D.C. Coleman, E.R. Ingham, R.E. Ingham, E.T. Elliott, J.C. Moore,S.L. Rose, C.P.P. Reid and C.R. Morley, The Detrital Food Web in a Shortgrass Prairie,Biology and Fertility of Soils 3 (1-2), pp. 57-68, 1987[8] C.J.K. Knight, A.S. Penn and R.B. Hoyle, Comparing the Effects of Mutualism andCompetition on Industrial Districts, In writing, 2013.[9] A.J. Lotka, Elements of Physical Biology, Williams and Wilkins, 1925.[10] A. Markusen, Sticky Places in Slippery Space: A Typology of Industrial Districts,Economic Geography 72(3), pp. 293-313, 1996.[11] W.W. Murdoch, C.J. Briggs and R.M. Nisbet, Consumer-Resource Dynamics, Mono-graphs in Population Biology 36, Princeton University Press, 2003.[12] A.S. Penn, P.D. Jensen, A. Woodward, L. Basson, F. Schiller and A. Druckman, Sketch-ing a Network Portrait of the Humber Region, Forthcoming in Complexity, 2013.[13] A.S. Penn, C.J.K. Knight, D.J.B. Lloyd, D. Avitable, K. Kok, F. Schiller, A. Woodward,A. Druckman and L. Basson, Participatory Development and Analysis of a Fuzzy Cog-nitive Map of the Establishment of a Bio-based Economy in the Humber Region, PLoSONE 8(11), 2013.[14] J.M. Swaminathan, S.F. Smith and N.M. Sadeh, Modelling Supply Chain Dynamics: AMultiagent Approach, Decision Sciences 29(3) pp. 607-632, 1998.[15] P. Turchin, Complex Population Dynamics, A Theoretical/Empirical Synthesis, Mono-graphs in Population Biology 35, Princeton University Press, 2003.14
Derivation of Parameter Values Used.
This section contains the derivation of the parameter values found in Table 3, along with thesources of the data used in the derivation. As there are 111 separate parameter values whichneed evidencing it should not be a surprise that we used a multitude of sources of data. As weonly require rough numbers for the parameters many of these sources are web pages. It wasfairly easy to find data for some of the industry types, where for instance we could access fullaccounts for an archetype company, however in other instances it was harder or impossibleto find the specific data required. For instance we ended up using the same data for all threetypes of composter, and the regional and local waste aggregators were based on nationalwaste aggregators with an attempt at appropriate scaling applied. With all of these issues,along with the fact that some data sources had to be inflation and currency adjusted, wemust emphasise that the data in Table 3 should only be viewed as giving approximate ordersof magnitude for the parameters, and any conclusions drawn should be carefully analysed.In order to find the necessary parameter values we found four pieces of data for eachindustry type in 2013 GBP: the total revenue in a year, the amount spent on materials in ayear, the amount spent on overheads in a year, and the amount spent on production in theyear, see Table 4. (Note that the amount spent on material in a year can be negative if theindustry is paid to take that material, for instance landfill.) We used these pieces of data
Industry Type Revenue Material Cost Overheads Production Cost
Refinery: Crude Oil 4787.96 4311.51 69.2 276.78Food Processor 13.28 3.826 4.76 3.12Farming: Arable 0.071 0.013 0.007 0.015Farming: Livestock 0.152 0.058 0.008 0.058Power Plant: Coal-Fired 344.7 72.67 20.55 13.7Power Plant: Co-Fired 1265.04 259.56 61.65 41.1Composter: Low Grade 0.151 -0.062 0.011 0.022Composter: High Grade 0.151 -0.062 0.011 0.022Composter: In-Vessel 0.151 -0.062 0.011 0.022Waste Incinerator 4.106 -2.296 1.22 4.14Landfill: Non-Hazardous 0 -3.28 0.695 0.998Landfill: Hazardous 0 -1.7 0.3475 0.499Waste Aggregator: National 143.55 -656.35 51.08 739.74Waste Aggregator: Large Regional 14.355 -65.635 5.108 73.974Waste Aggregator: Small Local 0.14355 -0.65635 0.05108 0.73974Power Plant: Biomass 110.48 70 6.23 22.5Biodiesel Production: Virgin Feedstock 19.5 10.37 1.8 5.9Anaerobic Digester 4.37 -2.05 0.114 2.06Chemical Production: Biological 1051.9 638.9 104.1 55.7Bioethanol Production: Virgin Feedstock 84.5 20.33 2.24 13.8Biodiesel Production: From Waste 16.25 4.11 1.8 4.82Bioprocessor 107.76 76.5 2.78 12.57Table 4: The data used to derive the initial conditions and parameters needed in the dynamicalmodel of the Humber region (4). Values are millions of 2013 GBP.to derive the parameters used in the modes. For the wealth/health of a firm ( u i ) we usedthe sum of the revenue, the absolute value of the material cost, the overhead cost and the15roduction cost. For the percentage spent on material ( β ) we used 0 if the total materialcost was zero, otherwise we used the cost of materials over u i . This was further divided bytwo if the industry was a primary supplier and bought material from within the district. Forthe percentage profit ( (cid:15) ) we used the value of goods and services (revenue + | material cost | ifmaterial cost is negative, or revenue otherwise) less the cost of material bought (zero if totalmaterial cost was negative) less overheads less production costs all over the value of goodsand services. For ρ we used the value of goods and services over u i (1 + (cid:15) i ). This is furtherdivided by two if the industry is an end consumer and also sells to firms in the district. Notethat the ρ term has been divided by (1 + (cid:15) i ) to recover the actual ‘worth’ of the productbefore profit was included. Finally for the total external demand of the market ( M ) we usethe sum over all end consumers of u i .We now give separate details of the data sources for each of the industry types. Forcurrency conversion we use the following factors throughout: $1= £ £ e A.1 Refinery: Crude Oil
We base our analysis for a refinery on the Total Lindsay oil refinery [1] which produces 10million tonnes per year, that is 73.3 million barrels a year, [2]. We use spot prices to find theaverage price of crude oil [3], between 2007 and 2012 these spot prices were (USD/barrel);80.14, 104.84, 66.19, 83.76, 105.20 and 102.84. This gives an average cost per barrel of $90.50or £ . × . M = 4 , . M .The gross margin (that is sales - cost of materials) per barrel is given in [4, Table 3]. Theygive average gross margins for 2001 to 2005 (USD/barrel); 8.60, 6.89, 8.36, 8.05 and 9.87.Thus the average gross margin is $8.35/barrel, or equivalently £ .
82 + 6 . × . M = 4 , . M . [4, Table 3] also gives the average netmargins (gross margins less overheads less production costs). From 2001 to 2005 they were(USD/barrel); 2.99, 0.21 2.18, 2.56 and 3.51, which gives and average net margin of $2.29 or £ £ . − £ .
78 = £ .
72. Now, [5, p. 101], “Fixed costs can represent up to 80% of the totalcost of processing every tonne of crude” . We shall use the fixed costs as the production costs,that is £ £ . M gives the values presented in Table 4. A.2 Food Processor
We base our analysis of food processors on Cadbury, as suitable data was available, and thenscale the resulting figures to better represent an average food processor. We use data from the2009 annual financial report as this is the last financial report before Cadbury was boughtout and amalgamated by Kraft Foods. Specifically the data is from stock exchange RNSannouncement 2009 (annual financial report) [6]. This document reports Revenue (sales)of £ , M , underlying profits of £ M , trade payable of £ , M , distribution cost of £ M , marketing costs of £ M , and administrative costs of £ , M .We use the trade payable figure as the cost of materials, and the combination of distribu-tion, marketing and administrative costs for the overheads ( £ , M ). For the productioncosts we use the sales less profits less materials less overheads ( £ , M ). Finally we needto scale these figures to represent a more average food processor. The average firm revenue inthe food processing sector is £ . M ( £ . M inflation adjusted) [7, Table 2.1]. Dividingthe figures from Cadbury by 5384 / . ≈ . .3 Farming: Arable There are many different arable crops grown in the UK, however the vast majority of the cropproduces is cereals, and of this the largest crop is wheat [8]. As such we shall base our analysisof arable farming on growing wheat. We also use the fact that the average UK farm size is57 hectares [9]. From [10, Table 4.4] we learn approximate costs and revenue per hectare;the returns (sales) are £ , /ha ( £ ,
254 inflation adjusted), the cost of agrochemicals is £ /ha ( £ .
58 inflation adjusted), and total variable costs of £ /ha ( £ .
57 inflationadjusted).In order to provide an estimate for the amount spent on materials we shall use the amountspent on agrochemicals and the amount spent on seed. [11] gives the cost of seed as £ /ha ( £ .
47 inflation adjusted), which gives a materials cost of £ . /ha . For the overheadswe shall use the fuel costs, [12, Table 4] gives the amount of different fuels that are used ingrowing cereals per hectare. We use spot prices (taken in mid September 2013) for these fuelsto calculate a total fuel cost per hectare of £ .
71, see Table 5.
Fuel Type Amount (per ha.) Unit Cost
Road fuel 11 L 142.47pRed Diesel 115.6 L 69.5pLPG 2 Kg ( ≈ £ .
57, material costs of £ .
05, andoverheads of £ .
71, the production costs must be the difference (variable costs less materialcosts less overheads) which gives a figure of £ . /ha . Multiplying all of these figures bythe 57 hectare average farm size gives the values used in Table 4. A.4 Farming: Livestock
Like arable farming, livestock farming is diverse in the UK, however unlike arable farming itis not dominated by one crop. We choose to focus on dairy farming and base our analysison that as [12] also provides data on fuel use for dairy farming, giving a total fuel cost (perhectare) of £ .
52, see Table 6. As for arable farming we use this fuel cost as the overheads.The average dairy farm in the UK has a herd size of 86 cows, and an average density of two
Fuel Type Amount (per ha.) Unit Cost
Road fuel 13.7 L 142.47pRed Diesel 147.9 L 69.5pLPG 0.7 Kg ( ≈ ,
300 litres of milk a year. With a spotprice for milk at farm gate (taken in mid September 2013) of 28 . p/L we have an average17airy farm revenue of 6300 × × . £ , . p/L whilst [14] states ”feed costs represent[] 40 to 60 percent of thecost of producing milk”. We take the average of 50% of total production costs being spent onfeed (materials), meaning that material costs and the production costs (excluding materials)in Table 4 are both same; 0 . × . × ×
86 = £ , . A.5 Anaerobic Digester
We base our analysis of Anaerobic digestion on GWE Biogass Ltd which converts 50,000tonnes of waste a year to biogas which is the converted to 2MW of electricity [15]. If weassume that the plant operates for the equivalent of 300 complete days a year it generates14.4 GWh of electricity. Further [16] gives that the mass of sludge (digestate) out is 80%to 90% of the mass in. Using the figure of 80% gives that the plant produces 40 ,
000 tonnesof sludge a year. Schiller [17] suggests that digestate has a value of £ /tonne , giving arevenue from digestate of £ M . From [18] we can calculate the price the firm gets from saleof electricity, Table A-4 gives a basic price of e . /M W h and Table A-8 gives an additionalprice for electricity support (to incentivise production of electricity from ‘green’ sources) of e . /M W h . This gives a total gain of e . /M W h ( £ . /M W h inflation adjusted).Meaning that the revenue from selling electricity is £ . M per year. So the total revenue(sales) is £ . M .The price for materials is negative. The anaerobic digester uses waste from other industriesas its source material. If it didn’t use this material then the industry would have to pay forits disposal, (traditionally through landfill or incineration). Schiller [17] suggests a price of £ /tonne to dispose of waste. As GWE biogas use 50,000 tonnes of waste a year theirmaterial costs are − £ . M .Finally the overheads and production costs. [19, Table 4] gives the overheads for an anaer-obic digestion plant with 70,000 tonne capacity as e K ( £ . K inflation adjusted). Asimple scaling for the difference in capacity gives an approximation of the overheads for GWEbiogas as £ . K . For the production costs we use the OPEX costs as given in [18, p. 36],a value of e . /tonne ( £ . /tonne inflation adjusted). Multiplying this by the 50,000tonne capacity gives the value used in Table 4. A.6 Power Plant: Coal-Fired
We base our analysis of coal-fired power plants on a 900MW capacity plant running for 7880hours (full time equivalent) a year. Our analysis is based on these specifics as this forms oneof the cases studied in [20]. In [20] different technologies are considered as well as differentcoal types. We shall average the data over these technological and coal type differences toarrive at the values used. The technologies used are described as subcritical, supercritical andultra supercritical, whilst the three coal types analysed are Bituminous, Lignite and PRB.Now, [20, Appendix A] gives the annual production of electricity (in TWh) across these 9scenarios as 6.53, 6.47, 6.60, 6.54, 6.48, 6.61, 6.54, 6.49 and 6.61. Thus the average electricitygeneration is 6 . T W h . We assume that this electricity is sold at the same basic price(no subsidies) as that generated by anaerobic digestion, i.e. e . /M W h ( £ . /M W h inflation adjusted), this gives the sales figure for coal-fired power plants.In order to calculate the material cost, we need to know how much coal is burned andthe cost of that coal. The cost of coal to the gate is given in [20, Appendix A] as $39.55,$17.90 and $23.47 per tonne depending on type and quality. This gives an average priceof $26 . /tonne ( £ . /tonne inflation adjusted). Further [21] says that a 100MW power18lant uses 53.8 Tonnes of coal an hour. Assuming no efficiencies of scale this means that a900MW power plant uses 484.2 tonnes of coal an hour. The annual material cost is thus givenby £ . × . × £ . M .[20, Appendix A] also gives values for fixed and variable costs. We use the variablecosts for the overheads and the fixed costs for production costs. So for overheads we takethe average of 27.33, 38.51, 20.03, 27.64, 38.99, 20.24, 28.35, 40.06 and 20.71 ($M), which is$29 . M ( £ . M inflation adjusted). For the production costs we take the average of 19.07,19.43 and 19.61 ($M), which is $19 . M ( £ . M inflation adjusted). A.7 Power Plant: Biomass
We base our analysis of a biomass-fired power plant on the proposed Drax Heron plant, whichwould burn 1.4 million tonnes of biomass a year to produce 290MW of electricity [22]. Againto calculate the revenue we shall use the same basic price for electricity generated as for theanaerobic digester, namely e . /M W h ( £ . /M W h inflation adjusted). There used tobe an additional subsidy linked to how much biomass was burnt [23], but that has recentlybeen repealed. Thus, assuming that the power plant operates for 7200 (full time equivalent)hours a year the revenue from electricity generation is £ . M . To calculate the materialcost we just need a price for biomass. We use the value for wood chips of £ /tonne givenin [24], meaning that the total material cost is £ M .To calculate the production costs we note that [24] gives annual operating costs of 2% ofcapital costs and annual maintenance costs of 2.5% of capital costs. The 250MW power plantthat they use in their analysis had a capital cost of £ M . Scaling with no economies of scalegives a capital cost for a 290MW plant of £ M ( £ M inflation adjusted). However it islikely that economies of scale should be taken in to effect, as a result we shall use a capital costof £ M . We use the annual operating and maintenance costs as a proxy for the productioncosts giving a production cost of £ . M . Finally, we need a value for the overheads. Wewere unable to find specific data for biomass burning power plants, so instead we use datafor coal-burning power plants given in [20, Appendix A]. As for the coal-firing power plantwe use the total variable costs averaged over the three technology types and the three coaltypes. The smallest plant that they analyse is 400MW, for this size plant the values givenin [20, Appendix A] are 11.6, 17.5, 8.9, 11.2, 16.9, 8.6, 11.0, 16.6 and 8.5 ($ M ). This gives anaverage value of $12 . M ( £ . M inflation adjusted). We need to adjust this to the capacityof the Drax Heron plant, a simple scaling would give £ . M/ ×
290 = £ . £ . M . Thedifference in capacity between the plants leading to these two figure is 500MW, and theclosest of the figures comes from a plant which is 110MW larger than the plant we consider,therefore the overheads are given by 6 . − / × (6 . − . £ . M . A.8 Power Plant: Co-Fired
The analysis of co-firing power plants (coal and bio-mass) is based on Drax, [25], which has acapacity of 3960 MW and generates 24
T W h of electricity each year. Using the same sellingprice of electricity as both the coal-firing and biomass firing plants (the same as the anaerobicdigester’s unsubsidised price) of £ . /M W h gives revenue of £ , . M .As the plant burns both biomass and coal calculating the cost of materials requires knowl-edge of how much of each fuel is used each year. From [25] we have that Drax consumes 9.1M tonnes of coal a year and 1.725 M tonnes of biomass (a 660MW plant full burning biomass19equires 2.3 M tonnes of biomass a year, whilst Drax co-fires 12.5% biomass). Using thesame cost for coal as for the coal-firing power plant ( £ . /tonne ) and the same cost forbiomass as the biomass-burning power plant ( £ /tonne ) we arrive at a total material costof £ . M .We were unable to find any accurate data for overheads and production costs of co-firingplants. Instead we use the values derived for the coal-firing power plant and multiply themby three, to scale from 900 MW to 3960 MW assuming a large economy of scale. A.9 Composter
There appears to be very little data on the economics of various types of composter; lowgrade, high grade and in-vessel. Instead it seems that any economic analysis is on a case bycase basis. As such we do not treat all three of these ‘industry types’ independently but rathersimply as composters. This means that the only difference in the composters in the modelwill be in their structural role in the metabolic interactions network. We base our analysis ofcomposters on [26] which looks at a Canadian composter in 1993. We do not believe that thisshould pose any issues to the accuracy of the figures derived as approximations due to thefact that composting is a well established technique, and whilst some efficiencies may havebeen made we do not believe that this would drastically effect the economics of a composter.In what follows we use the standard notation C$ to refer to Canadian dollars, also C$1 in1993 is now worth £ . . /L ( £ . £ , £
41. [26, Table 2] gives that 2050 tonnes of waste is used each year, whilst [26, p. 1]gives that bulking agents cost is between C$12 and C$13 per tonne of waste. We use a value ofC$12.5 ( £ .
97 inflation adjusted. This gives a total material price of - £ , £ , A.10 Waste Incinerator
We base the analyse for waste incinerators on Newlincs [27] which burns 56,000 tonnes of wastea year to produce 3MW of electricity and 3MW of heat. The incinerator operates for 8000(full time equivalent) hours per annum, meaning that it produces 24GWh of electricity and ofheat. We use the same sale price for the electricity as the anaerobic digester, £ . /M W h .The same document that this figure came from also gives a value for the amount heat is soldfor [18, Appendix A-5]; e . /M W h ( £ .
04 inflation adjusted). Thus the total revenuefrom the sale of electricity and heat is £ . M . However there is another source of revenuethat the incinerator receives, namely subsidies. PFI credits [28] provide an additional revenueof £
40 for every tonne of waste burnt, in total an additional £ . M . We use this combinedvalue for our analysis. However PFI credits have recently (early 2013) been cancelled meaningthat this subsidy is no longer being paid, this has caused legal action to be bought [29] bythose affected. Without this additional subsidy our economic analysis of waste incineratorsshows them making a loss year on year and not being economically viable.The material cost for waste incinerators is negative as they process waste from other20ndustries. We use the same figure for the cost of waste as we have used throughout ouranalysis, first mentioned in that of anaerobic digester, of £ /tonne . Giving a total cost ofmaterials of − £ . M . We use [30] to calculate the overheads and production costs. [30,Table 10.11] gives that the total costs are e . /tonne ( £ . /tonne inflation adjusted),and [30, Table 10.45] gives that the ratio between operational costs and overheads is 3.4:1.We use operational costs as production costs meaning that production costs are £ . M andoverheads are £ . M . A.11 Landfill
There are two different types of landfill sites in our model of the Humber region, those whichdeal with non-hazardous waste and those which deal with hazardous waste. There appears tobe very little data available for costs associated with hazardous landfill, and in particular theoverheads and ‘production’ costs. As such we shall use a very rough estimate and say thatthey are twice as much as for non-hazardous landfill per tonne. Both types of landfills are atthe end point of the material chain meaning that they do not actually sell any product. Theyonly revenue generation is from the service they supply in taking waste from other industries- in our current classification this is the negative material cost. As such the amount generatedfrom sales for each of the landfill types is £ £ /tonne ) gives a material cost of £ − . M . For hazardous wastewe assume that a landfill processes 55,000 tonnes a year (this is the total hazardous wasteprocessed in landfill in Yorkshire an the Humber) [32]. We use this figure as there are onlya few landfills which are licensed to take hazardous landfill in the Humber region and theyare not separate entities from those which process non-hazardous landfill. We use a figure of £ /tonnes [33] for the negative cost of the waste. This means that the total material costfor a hazardous landfill is £ . M .To calculate the overheads and production costs we use figures from [31, Table 8]. Forthe overheads we use the construction costs (remaining phases ($5 . /tonne ) + contingency($0 . /tonne )), the site development costs ($0 . /tonne ), and the net interest on revenuebonds ($3 . /tonne ). This gives overheads of $10 . /tonne ( £ . /tonne inflation ad-justed). For the production costs we use the operating costs; $15 . /tonne ( £ . /tonne inflation adjusted). Multiplying these figures by the annual processing volume for the non-hazardous landfill and twice the annual processing volume for the hazardous landfill gives thevalues used in Table 4. A.12 Waste Aggregator
In analysing waste aggregators we found that there was very little data available. The data wasparticularly sparse for the smaller waste aggregators, this made it impossible to rigorouslyinitialise the large regional and small local waste aggregators. Instead we were forced tosimply scale the values derived for a national waste aggregator. The scaling we used can notbe rigorously justified either but rather came as result of private correspondence [17] in whichit was suggested that a national waste aggregator has a turnover of approximately £ £ M and £ M , andsmall local waste aggregators have a turnover of less than £ M . We therefore use a scalingfor large regional waste aggregators of 10% of national waste aggregators, and for small localwaste aggregators of 0 .
1% of national waste aggregators.21e base the values for a national waste aggregator on the annual accounts of Biffa [34]. In2011 Biffa had an annual revenue of £ . M , a production cost of £ . M (cost of sales),a distribution cost of £ . M and an administrative expense of £ . M , [34, p. 16]. On [34,p. 33] is a list of the sources of revenue, this includes the money received for taking wastefrom various sources, which totals £ M . We use this value for the materials cost − £ M ( − £ . M inflation adjusted). For the sales we consider the revenue less the money receivedfor taking waste, that is £ . M ( £ .
55 inflation adjusted). The production cost is £ . M ( £ . M inflation adjusted). For the overheads we use the distribution costsand the administrative expenses, that is £ . M ( £ . M inflation adjusted). A.13 Biodiesel Production: Waste
We base our analysis of biodiesel production on Brocklesby which has a turnover of between$20 M [35] and $30 M [36]. We take the average of these two figures $25 M ( £ . M ). Fromprivate correspondence [37] with a representative from Brocklesby we use a volume of 20,000tonnes as a proxy for the final amount of biodiesel produced. Converting this to litres gives22 . M L (density of biodiesel is 0.88 [38]). Thus the capacity of Brockslesby is between 23and 32 [39] million litres per annum. We take the average value, to give an annual capacityof 27 . M L . In [40, Table 6.9] the material cost is given as the range $0 . /L to $0 . /L (note that unlike the other waste streams we have previously considered for other industrytypes, due to the economic value of waste oils, this is actually a positive price). Averagingthis material cost gives $0 . /L ( £ . /L inflation adjusted), leading to a total materialcost of £ . M .[40, Table 6.9] also gives an estimate for the production costs of $0 . /L ( £ . /L inflation adjusted), multiplying this by the annual capacity gives the figure used in Table 4.For the overhead costs we use the overhead, packaging and storage costs as given in [41, Table4], this gives the value for a plant with 9 M L capacity of between $0 . M and $0 . M .Multiplying these values by three (to adjust for capacity) and averaging gives an overheadcost of $2 . M ( £ . M inflation adjusted). A.14 Biodiesel Production: Virgin Feedstock
We base the analysis of biodiesel production from virgin feedstock on our previous analysisfor biodiesel production from waste, Section A.13. For the revenue figure we use the top valuefound in Section A.13 $30 M ( £ . M ) instead of the average in order for our analysis of thisindustry type to show a profit. We still use the same capacity as in the production from wastecase, 27 . M L . In order to find the material and production cost we again use [40, Table 6.9]which gives a material cost of $0 . /L ( £ . /L inflation adjusted), and a production costof $0 . /L ( £ . /L inflation adjusted). Multiplying these figures by the capacity gives thevalues shown in Table 4. For the overheads we use the same value as that used in Section A.13. A.15 Chemical Production: Biological
The analysis for chemical production is based on Croda. All data is drawn from its 2012annual statement [42]. Croda had revenue of £ , . M and “consume[s] £ . M of in-ventories” [42, p. 86] a year - we use this as the cost of materials. To derive values for theoverheads and production costs we use the figures for ‘cost of sales’ and profits. Croda’s ‘costof sales’ are £ . M and the profits are £ . M [42]. For the overheads we use the revenueless the profit less the cost of sales, that is £ . M . Finally for the production costs we usethe cost of sales figure less the material cost, i.e. £ . M .22 .16 Bioethanol Production: Virgin Feedstock Our analysis of bioethanol production is based on Vireol which has a capacity to produce 200million litres of bioethanol a year [43]. Recent 12 month low and high spot prices for ethanolwere $2 . /gal and $2 . /gal respectively [44], giving an average ethanol price of $2 . /gal ( £ . /L ) (one gallon - American - being 3.785 litres). This gives an approximate revenueof £ . M . To calculate the cost of materials we use [40, Table 5.6] which gives a feedstockcost of $0 . /gal ( £ . /L inflation adjusted). Multiplying this by the capacity gives amaterial cost of £ . M .To find a value for the production costs we extrapolate from [40, Table 5.7] to arrive ata value of $0 . /gal ( £ . /L inflation adjusted). Multiplying this by the capacity givesthe desired value. Also in [40, Table 5.7] we find values for operating labour, SGA andmaintenance of $0 . /gal , $0 . /gal and $0 . /gal respectively. We use these values to finda proxy for the overheads. For biodiesel production the overheads were calculated as 60% ofoperating labour, supervision and maintenance [41, Table 4]. If we use this same ratio forbioethanol production, and use SGA as an approximation for supervision cost we arrive ata figure for overheads of $0 . /gal ( £ . /L inflation adjusted). Multiplying this value bythe capacity of 200 million litres gives £ . M , the value shown in Table 4. A.17 Bioprocessor