P-Graph Synthesis of Open-Structure Biomass Networks

P‑Graph Synthesis of Open-Structure Biomass NetworksHon Loong Lam,† Jirí Jaromír Klemes,*,‡ Petar Sabev Varbanov,‡ and Zdravko Kravanja§

†Department of Chemical and Environmental Engineering, University of Nottingham Malaysia Campus, Jalan Broga,43500 Semenyih, Selangor, Malaysia‡Centre for Process Integration and Intensification - CPI2, Research Institute of Chemical and Process Engineering - MUKKI,Faculty of Information Technology, University of Pannonia, Egyetem u. 10, H-8200, Veszprem, Hungary§Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova ul. 17, SI-2000, Maribor, Slovenia

ABSTRACT: This paper presents an extended implementation of a P-graph for an open-structure biomass network synthesis.Biomass and biofuel production networks syntheses are generally complex tasks of a considerable scale and comprehensiveinteractions. The applications of information technology and computer software tools, in this case P-graph, are essential forproviding fast and as accurate as possible solutions with a user-friendly interface. This work demonstrates the relationships ofmathematical models with P-graph representations. A case study is included that demonstrates the implementation of a frame-work regarding a P-graph for an extension to biomass network synthesis. An assessment and evaluation of P-graph and Mathe-matical Programming as a method for biomass supply chain synthesis concludes this paper.

1. INTRODUCTION

The P-graph framework was first introduced by Friedler et al.1

and further developed for systematic optimal design of industrialprocesses2,3 as generating candidate molecules with desired prop-erties,4 developing a separation network system by Kovacs et. al.5

and later further developed by Heckl et al.,6 synthesizing alter-native sequences for azeotropic distillation system,7 generatingan integrated synthesis of heat exchanger network,8 indentifyingthe pathways for chemical9 and biochemical reaction,10 derivingthe rate law of a catalytic reaction,11 synthesizing the sustain-able process for renewable resources,12 cost-effective reductionof carbon emissions involving fuel cell combined cycles,13 gen-erating regional renewable energy supply chain,14 developing acell-based dynamic heat exchanger models,15 and also solving thesupply chain problem such as minimizing the cost and environ-mental impact of transportation,16 with considering the uncertain-ties along the supply chain.17 These papers show how the syn-thesis of optimal solution can successfully be performed in asystematic way.The holistic biomass supply network synthesis is generally a

complex task of considerable scale and comprehensive interac-tions. This is mainly due to (i) large land areas used to collect andprocess the incoming solar radiation before the energy can beharvested, (ii) the distributed nature of the biomass resources,and (iii) the usually low-energy density of the biomass. It shouldbe noted that due to this complexity, the term used is “supply-network” rather than “supply-chain”.The methods for optimizing supply chains have traditionally

relied on Mathematical Programming (MP). MP has also beenused for renewable energy supply chain studies, such as model-ing, optimization, and synthesis. There are several challengesconcerning biomass utilization that have to be solved:18 (i) Thebioenergy networks should asmuch as possible utilize rawmaterials.(ii) The choices of feedstock and products are mutually related andsignificantly affect the overall economic viability and emissions aswell as each other. (iii) The modeling framework should provideevaluations of alternative options for locating and sequencing the

various processing and transportation operations within thesupply networks.There are some works have been carried out to tackle the bio-

mass supply chain issues. Lam et al.19,20 presented an applicationof the Pinch analysis analogy regarding biomass network syn-thesis, zone clustering, and regional resources management. Lamet al.21 also discussed the complexities of large-scale biomassnetworks and proposed the model-size reduction techniquesaccordingly for solving complex biomass network problems.Freppaz et al.22 demonstrated a decision support system, whichaimed at optimizing forest biomass exploitation for energy supplyat a regional level. Dunnett et al.23 presented a systems’ model-ing framework for the simultaneous design and operationsscheduling of a biomass to heat supply chain. Rentizelas et al.24

focused on the logistics issue of biomass utilization, especiallystorage and multibiomass supply chain optimization. An Inte-grated Biomass Supply and Logistics (IBSAL) Model was pro-posed and presented by Shahab et al.25 IBSAL consists of a seriesof equations that calculate the collectable fractions of biomass,while tracking biomass moisture during harvesting and storage,machinery performance, compositional changes, and dry matterlosses. Iakovou et al.26 provided an overview of the genericsystem’s components and then the unique characteristics ofwaste biomass-to-energy supply chain management that differ-entiate them from traditional supply chains. Recently, the researchon the biomass supply chains also focuses on the sustainabledevelopment such as the total footprints-based multicriteriaoptimization of regional biomass energy supply chains presentedby Cucek et al.27 and supply chain management of agricultural

Special Issue: L. T. Fan Festschrift

Received: May 7, 2012Revised: August 21, 2012Accepted: August 29, 2012Published: August 29, 2012

Article

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© 2012 American Chemical Society 172 dx.doi.org/10.1021/ie301184e | Ind. Eng. Chem. Res. 2013, 52, 172−180

pubs.acs.org/IECR

waste for biomass utilization and CO2 emission reduction byThanarak.28

Biomass frameworks can be categorized as (i) open-structurednetworks and (ii) fix-structured networks. The open-structuredbiomass network gives rise to a generic model covering all pos-sible connections within the system. These connections can beformed between all points or nodes from different layers, suchas the harvesting, collection and prepreparation, core process-ing, and distribution of products, as shown in Figure 1. The fix-structured biomass network is modeled based on well predefinedsuperstructural nodes (production plants and technologies) andtheir connections, for example the biomass network shown inFigure 2. The open-structured network is typically used for thesynthesis of new biomass supply networks, while the fix-struc-tured network is for the reconstruction of existing ones. In bothcases, a solution network-structure will be selected from thosefeasible connections and technologies that are defined as alter-natives within their superstructures. On the one hand in theopen-structured network problems, there are many alternativesfor selecting plants, technologies, and connections. As a resultthe synthesis task usually poses a highly combinatorial problem.On the other hand, the fix-structured network does not containmany alternatives, and, consequently, it features much simplercombinations.The applications of information technology and computer

software tools, such as the PNS Editor29 which is a softwarepackage designed to solve problems in process network synthesisby P-graphmethodology.1 Those tools are essential for providingfast and as far as possible accurate solutions with a user-friendlyinterface.This paper first presents a brief overview of the P-graph frame-

work. It is followed by a section that presents the P-graph

representation that describes the concept of the supply network.A case study is demonstrated in order to illustrate the advantagesof applying a P-graph to the synthesis of a biomass supplynetwork.

2. P-GRAPH FRAMEWORKThe P-graph is a directed bipartite graph, having two types ofvertices − one for operating units and the other for those objectsrepresenting material or energy-flows’ quantities. The verticesare connected by directed arcs.1 Operating units and processstreams aremodeled by separate sets (O andM respectively), andthe arcs are expressed as ordered pairs. E.g. if an operation o1∈Oconsumes material m1 ∈ M, then the arc representing this re-lationship is (m1, o1).There are several combinatorial instruments associated

with it. The first is the set of axioms ensuring representationunambiguity1 and the consistencies of the resulting super-structures and solution networks. The other instruments arethe three main algorithms as follows: (i) superstructure con-struction−MSG,30 (ii) superstructure traversal and the genera-tion of combinatorially feasible network structures − SSG,31

and (iii) superstructure optimization branch-and-bound algo-rithm ABB.32

The procedure for the supply network synthesis with P-graphapproach follows the algorithm illustrated in Figure 3.

3. BIOMASS SUPPLY NETWORK MODEL WITHP-GRAPH REPRESENTATION

An open-structure four-layer supply chain network has beendeveloped Cucek et al.18 It includes the harvesting, collection andpreprocessing, core processing, and distribution of products (seeFigure 4). This considered system’s boundaries involve a region,

Figure 1. Open-structured regional biomass network (after Lam et al.21).

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie301184e | Ind. Eng. Chem. Res. 2013, 52, 172−180173

which is then divided into zones for optimizing conver-sion operations and transportation flows. This model has beenformulated with profit maximization as the optimizationcriterion.

Some of the important mass-balance equations are summa-rized in the following equations; the environmental impact, costfunctions, and the objective functions are fully presented in thepaper of Cucek et al.18

The mass balance model follows the four-layer nature of thenetwork’s superstructure Figure 4, starting from the harvestingand supply (L1) layer, collection and preprocessing (L2), mainprocessing (L3), up to the use of the (L4) layer.Biomass pi produced at zone i, is transported from L1 to

collection centers m at L2:

∑= ∀ ∈ ∀ ∈∈

q q pi PI i I,i pim

m Mi m pim

,,L1

, ,,L1,L2

(1)

This equation is then represented in the P-graph approach inFigure 5.Constraint in eq 2 is used to determine the selection or

rejection of the collection and intermediate process center m.

Figure 2. Fix-structured biomass network (after Lam et al.14).

Figure 3. P-graph biomass supply network synthesis procedure (afterLam et al.14).

Figure 4. The open-structure of the networks for renewable energyproduction and consumption (after Cucek et al.18).



These centers have to operate within the minimal and maximalproducts’ mass flows:

∑ ∑· ≤ ≤ · ∀ ∈∈ ∈

q y q q y m Mmm

i I pi PIi m pim m

m,L2,LO L2

, ,,L1,L2 ,L2,UP L2

(2)

The pretreated intermediate product pi can be transported fromthe collection and intermediate process center m at L2 to theprocess plant n at L3 or directly to customer j at L4, if the productpi is also a direct product pd(pi). Figure 6 shows the P-graphrepresentation of these relationships.

∑ ∑ ∑ ∑· = +

∀ ∈ ∀ ∈

∈ ∈ ∈ ∈ ⊆q f q q

m M pi PI,

i Ii m pim

pin N

m n pim

j J pd PD PIm j pdm

, ,,L1,L2 conv,L2

, ,,L2,L3

, ,,L2,L4

(3)

At plan n, the intermediate product pi is sent to the alternativetechnologies t:

∑ ∑= ∀ ∈ ∀ ∈∈ ∈

q q n N pi PI,m M

m n pim

pi t PTn pi tm

, ,,L2,L3

( , ), ,

,T,L2,L3

(4)

where the intermediate product is converted into the end-product pp using the corresponding conversion factor f pi,pp,t

conv,L3.Process conversion is handled as the amount of product flow-ratecompared to the inlet flow-rate to the processing plant withtechnology t, f n,pi,pp,t

m,T,L2,L3 (t/y) and is shown in eq 5 and Figure 7.

· =

∀ ∈ ∈ ∈ ∈

∈

q f q

n N pi PI pp PP t T

pi pp PIP

( , , , ,

( , ) )

n pi tm

pi pp t n pi pp tm

, ,,T,L2,L3

, ,conv,L3

, , ,,T,L2,L3

(5)

The produced products pp are finally collected from differenttechnologies and plants and sent to customers:

∑ ∑ ∑= ∀ ∈ ∈∈ ∈ ∈

q q n N pp PP,pi t PT pi pp PIP

n pi pp tm

j Jn j ppm

( , ) ( , ), , ,

,T,L2,L3, ,

,L3,L4

(6)

The P-graph representation of the L3-L4 relationship is shown inFigure 8.

Local demand for products p is the sum of the producedproducts from plants pp and the directly used products pd:

∑ ∑ ∑ ∑≥ +

∀ ∈ ∀ ∈

∈ ∈ ⊆ ∈ ∈ ⊆Dem q q

j J p P,

j pn N pp PP P

n j ppm

m M pd PD Pm j pdm

o

, , ,,L3,L4

, ,,L2,L4

o o o

(7)

Objective Function. The objective function maximizes theprofit before tax (PB):

∑ ∑ ∑

∑ ∑ ∑

∑ ∑ ∑

∑ ∑ ∑

∑ ∑

= ·

+ ·

+ · ·

+ · ·

− · − − −

∈ ∈ ∈

∈ ∈ ∈

∈ ∈ ∈

∈ ∈ ∈

∈ ∈

P q c

q c

q c

q c

q c c c c

0.9

0.9

n N j J pp PPn j ppm L L

pp

m M j J pd PDm j pdm

pd

n N j J pp PPn j ppm

pp

m M j J pd PDm j pdm

pd

i I pi PIi pim

pi

B , ,, 3, 4 price

, ,,L2,L4 price

, ,,L3,L4 price

, ,,L2,L4 price

,,L1 tr op inv

oo

oo

ee

ee

(8)

The income represents the revenue from selling the productsand from the tax imposed on the waste. The expenses repre-sent the raw materials’ cost with price cpi, the transportationcost (ctr), the operating cost (cop), and annualized networkinvestments (cinv).

Figure 5. P-graph representations of the relationships between L1-L2.

Figure 6. P-graph representations of the relationships between L2-L3and L2-L4.

Figure 7. P-graph representation of the technology selection-scheme inthe Plant n.

Figure 8. P-graph representation of the relationships between L3-L4.



4. DEMONSTRATION CASE STUDYThe data for this study were developed based on Central Europeanconditions,. The structure of the bioenergy supply chain network isillustrated in Figure 9. The objective of superstructure optimization isto find an economically optimal strategy for coproducing bioethanol,heat, electricity, furniture boards, and corn for food. According to theabove definition of ‘sets’, the demonstrated region was divided intoten zones (the rectangular box in Figure 9), each covering an area of100 km2. The availability of resources is specified in Table 1 for each

zone. Several biomass were considered as the potential rawmaterials:corn grain (CG), corn stover (CS), wood chips (WC), municipalsolid waste (MSW), manure (MN), and timber (TB).Various possible geographical features have been considered in

the case study, for example, a hill and a lake, as illustrated in Figure 9.These features change the road conditions and the distances forbiomass transportation within the considered case. In this casestudy, six collection centers (m), three plants (n), two locationsof local customer demands (j1,2), and one export market (j3) arepresent. The transport conditions and distances between eachlayer are specified in Figure 9.Several technological options for raw material processing were

considered during the synthesis. These are the dry-grind processfor corn-based ethanol plants, anaerobic digestion of biomasswaste, incineration of MSW, corn stover and wood-waste, andthe sawing of timber for manufacturing boards.4.1. Identification of Materials and Units in the P-

Graph Method. This step produces the specifications for theinputs to and outputs from the system, along with those for the

intermediate materials. The latter can be regarded as the steppingstones on the paths from the system inputs to the products. As anexample, materials/streams, identified for the considered system,are listed in Table 2. The demands for the products and theirprices are shown in Table 3. In addition to the relevant material/

Figure 9. Regional plan for the demonstrated case study (after Cucek et al.18).

Table 1. Regional Supply Data for the Case Study

zoneavailable area forplanting (km2)

forestry area(km2)

biomasswaste (t/d)

MSW(kg/(capita·d))

1 20 - 4 -2 20 - 4 -3 65 15 2.75 -4 30 60 1.25 -5 40 10 2.75 16 25 - 2.75 17 65 - 3 -8 45 15 2 -9 - 100 - -10 10 30 2.5 -

Table 2. Materials and Unit for P-Graph

symbolsP-graph

classification description

CG raw material corn grain, produce from plantation areaCS raw material corn stover, produce from plantation areaTB raw material timber, produce from forestry areaWC raw material wood chips, residues from wood industryMSW raw material municipal solid waste, waste from resident areaMN raw material manure, residues from farming activityheat product/output heatElc product/output electricityBioE product/output bioethanolDDGS product/output distillers dried grains with solublesdig product/output digestatesboards product/output board for furnituretl operating unit bioethanol plantt2 operating unit anaerobic digestiont3 operating unit general incinerationt4 operating unit boards makingt5 operating unit MSW incinerationil,2,...,10 operating location 10 zones that supply the biomass to the

networkm1,2,...,6 operating location 6 collection centersnl,2,3 operating location 3 biomass conversion plantsjl,2 operating location 2 local biomass product demandsj3 operating location biomass products export market

Table 3. Demands for the Products and Their Prices

demand price

heat 174,000 MWh/y 61 €/MWhelectricity 87,000 MWh/y 100 €/MWhbioethanol 3,480 t/y 550 €/tcorn-food 5,800 t/y 121 €/tDDGS - 120 €/tdigestate - 24 €/tboards - 250 €/t



stream prices, other performance and economic data for thecalculation are referred to in a previous paper:18 a) characteristicsof the biomass, b) investment and operating cost of the pre-processing and process plants, c) product conversion rate, andd) parameters for environmental impact and transportation.4.2. Identification of the Operating Candidate. This

modeling step produces a set of candidate operating units, capable oftransforming certain materials/streams into other ones so that thedesired products can be produced from the specified raw materialsthrough the defined intermediates.13 The candidate operating unitssuch as the collection centers, process plants, and conversion techno-logies can be regarded as potential bridges between the intermediates.The hyperstructure is generated based on the P-graph

representation as shown in Section 3. The hyperstructure isdeveloped to find sufficient operating unit candidates so thatthere is at least one path connecting every product to at least onerawmaterial. For illustration purposes, a part of the network fromZone−5 (i5) is shown in Figure 10. As defined in Table 1, Zone-5

(i5) is suitable for a plantation which could produce corn grain(CG5) and corn stover (CS5) as the potential raw materials.Moreover, there is also some forestry area in Zone-5 whichprovides the raw materials of timber (TB5) and wood chips(WC5). The residence and farming activity in this zone alsocontributes municipal solid waste (MSW5) and manure (MN5).All these potential materials are then connected to all possiblecollection centers, namely m1, m2, ... m6. The locations of the

collection centers are illustrated in Figure 9. Once the rawmaterials are collected, they are sent to all feasible process plants(n1, n2, n3) for further biomass conversion. The location of theprocess plants is selected based on the optimum solution of themaximum profit which is subject to the transportation costs aswell as the technologies (t) selected in the plant. Figure 10 showsan example that, once the corn stover is collected at m3, it is thensent to process plant n2 for further processing by an incinerator(t3). Finally the product of biomass conversion, electricity andheat are sent to local demand j2.The software tool Process Network Synthesis Editor29 is used

to obtain the optimum solution for minimum production cost.

5. RESULTS AND DISCUSSIONThe synthesis of biomass network has been performed based onthe superstructure type involving 4 layers: supply, collection andpretreatment, processing, use. It has been implemented in aprevious work as a Mixed-Integer Linear Programming (MILP)model33 and has been solved using GAMS (v. 23.6), CPLEXsolver.34 In this the synthesis as been performed using a P-graphmodel. The optimum selection of technologies, plants location,and the annual amount of biomass product has been formulatedwith profit maximization as the optimization criterion as shown inSection 3. Both optimization results from the MILP and the P-graph procedures are very similar regarding the optimum profitvalue around 34 M €/y, with only 4.3% difference, which wasmainly because of the decimal point rounding. The optimumpathways/structures resulting from the P-graph are given in Table4 and Figure 11, which include the following: input biomassquantities, type of energy carriers (input and intermediatematerials), operating units, and final products for customers.Figure 11 shows an overall roadmap solution for the biomass

supply chain problem discussed in the previous section. Forexample the corn stover stock from Zone 6, CS6, is transportedto the collection point m1. Thereafter this corn stover is be sentto the conversion process complex n1 for further processinginto other biomass products, such as distillers dried grains withsolubles (DDGS), bioethanol, electricity, and heat. Thesespecific final products are then distributed to the customers(j1, j2, and j3). For instance, those DDGSn1 produced from com-plex n1 are sent to customer j3 as DDGSj3.Combine the information and results presented in Table 3 and

Figure 11, most of the raw materials are sent to the collectionpoint m1 and continue the process at a biorefinery plant locatedwithin the same zone, n1. This is mainly because of the customerj1 requested huge demand for biomass products in this zone. Itcan be seen that for the biomass production within this relativelysmall-sized area, the central processing is economically morefavorable than the distributed one (Table 4). The results alsoindicate that the reduction in cost of transportation has asignificant effect on overall costing.It should also be noted that the amount of biomass satisfied the

entire demand for electricity and biofuels in both cities j1 and j2.

Figure 10. An example of P-graph representation of the Zone i5 biomasssupply chain network.

Table 4. Location of the Plant and Yearly Amount of Bioenergy

products

technologies plant location heat (MWh/y) electricity (MWh/y) ethanol (t/y) DDGS (t/y) digestate (t/y) boards (t/y)

bioethanol plant (t1) n1 - - 63,300 48,995 - -anaerobic digestion (t2) n3 36,469 25,462 - - 6,571 -general incineration (t3) n1 and n2 27,097 19,053 - - - -boards making (t4) n1 - - - - - 9,182MSW incineration (t5) n1, n2, and n3 329,360 229,779 - - - -



Almost 95% of the ethanol and 70% of the electricity wereexported via the market place indicated as j3.

6. ADVANTAGES OF THE P-GRAPH

The P-graph shows its advantages as a powerful and flexibleoptimization tool for all concluded case studies. For the demon-strated biomass supply chain network synthesis it has been ratherobvious. The P-graph is very efficient for effective examination of‘what-if’ scenarios and conduction of the sensitivity analyses.The other advantages are summarized below:1) Easy to implement. Most users, such as engineers and

policy-makers, tend to favor algebraic and visualization tools suchas the PNS Editor. The users of P-graph do not need specialtraining with a modeling mathematical background, which isnaturally appreciated by practicing engineers. The user just needsto define the relationships between the units and the respectiveinput/output materials. P-graph models can be formulated ingeneric data-independent form; they are developed once onlyand can then be used for different applications by specifying onlythe related data inputs.2) Flexibility during future extensions. Whenever new poten-

tial raw materials or technology are introduced, they can bedefined under the P-graph framework, and the optimum solutionwill be recalculated using the new specifications.3) Easily captures the synthetic and semantic contents of a

process superstructure. It can be efficiently applied to model-sizereduction by eliminating nonfeasible solutions within thenetwork. P-graph is therefore especially powerful when optimiz-ing open superstructures with many infeasible routes between allpossible connections from each zone to each collection-node,from each collection to each process and technological node, andfrom there to each user node.4) Fast solutions when generating all feasible solutions,

especially for fixed-structured networks as demonstrated else-where.

7. CONCLUSIONS

This paper demonstrated the efficiency of applications of theP-graph method for the synthesis of an open-structure biomassproduction supply network. The relationships between the op-timization equations and the related P-graph representationshave been demonstrated on an open-structure biomass network.

The P-graph is easy for a user without a mathematical modelingbackground, as the user just needs to define the inputs andoutputs for certain operating units. The P-graphs are powerfulregarding the reduction of search space, which leads to fastersolutions of extensive problems.The P-graph can be further supplemented by Mathematical

Programming (MP), exhibiting useful and complementaryadvantages. Future development can be based on both furtherdevelopment of the P-graph framework and also on combiningboth the methods described.35 The possible research directionsfor combined P-graph and MP methods are as follows: 1.Multiple objective optimization for biomass supply networksthat involve the economic, environmental, and social impacts,simultaneously. 2. A fast P-graph solution could provide mappingsets for the MP model in order to reduce superstructure and,hence, the model’s size. 3. Probably the most promising is thecombination: The MP method could act as the external modulefor the P-graph, in order to provide external calculation/datasuch as nonlinear equations and experimental results for a furtheroptimization system approach.With the use of the combined P-graph and MP framework,

larger and more complex supply networks’ problems could beefficiently solved by exploiting the powerful complementarycapabilities of both approaches.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe financial support from Grant Agreement No. 262205, theHungarian project Tarsadalmi Megujulas Operating Program(TAMOP-4.2.2/B-10/1-2010-0025), and Slovenian ProgramNo. P2-0032 is gratefully acknowledged.

■ NOMENCLATURE

SuperscriptsUP upper boundLO lower boundL1 harvesting and supply layer

Figure 11. Graphical P-graph solution for optimum biomass supply chain.



mailto:[email protected]

L2 collection and preprocessing layerL3 main processing layerL4 customer layerconv conversiontr transportroad road conditionsyb yearly basisop operating costsinv investment costsfix cost coefficient for the fixed part of the annualized

investmentvar. cost coefficient for the variable part of the annualized

investmentSetsI set of supply zonesM set of collection and intermediate process centersN set of process plantsT set of technological optionsP set of productsJ set of demand locationsSubsetsJo set of local demand locations jo (subset of J)Je set of demand locations je for export (subset of J)PI set of intermediate products pi (subset of P)PD set of directly used products pd (subset of P)PP set of produced products from plants pp (subset of P)Indexesi index for supply zonesm index for collection and intermediate process centersn index for process plantst index for technological optionsp index for productsj index for demand locationsjo index for demand locations at local levelje index for demand locations for exportpi index for intermediate productspd index for directly used productspp index for produced products from plantsScalarsf yb cost coefficient for yearly basisqm,L2 minimal or maximal flow-rate at collection center m, t/yParametersqpim,L1,L2 product’s mass flow-rate at collection center m, t/yDemj

o,p regional demand at location jo for product p, t/y

f piconv,L2 conversion factor of intermediate product pi by

preprocessingqtm,L3 inlet mass flow-rate to the selected technology, t/yf pi,pp,tconv,L3 conversion factor of intermediate product pi by

processingcptr,La,Lb transportation cost coefficient of product from layer a

to layer b, €/ycfix,inv,L2 coefficient for the fixed part of the annualized

investment by preprocessing, €/yctfix,inv,L3 coefficient for the fixed part of the annualized

investment by processing, €/yctvar.,inv,L3 coefficient for the variable part of the annualized

investment by processing, €/yDx,y

La,Lb distance between object x in layer a and object y inlayer b, km

f x,yroad,La,Lb road condition factor between object x in layer a and

object y in layer bcpprice price of the product, €/t or €/MWh or €/MJ

Variables

qipim,L1

production rate of intermediate product pi at supplyzone i, t/y

qx,y,pm,La,Lb mass flow-rate of product p from object x in layer a to

object y in layer b, t/yqn,pi,tm,T,L2,L3 mass flow-rate of intermediate product pi to the

selected technology t at the process plant n, t/yqn,pi,pp,tm,T,L2,L3 mass flow-rate of produced products pp from

intermediate product pi with the selected technologyt at the process plant n, t/y

ctr transportation costs, €/ycop operating costs, €/ycpiop,L2 operating costs by the preprocessing for product pi, €/ycpi,top,L3 operating costs by the processing for product pi and

technology t, €/ycinv annual investment, €/ycpi price for intermediate product pi, €/tPB profit before taxes, €/y

Binary VariablesymL2 binary variable for existence of collection and intermediate

process center m

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