Abstract
This article presents a method for the synthesis of regional renewable energy supply chains, based on Mixed-Integer Linear Programming (MILP). This method addresses the challenges presented by biomass resources. The main challenges are the distributive and varied availabilities regarding both location and time. This work also aims to maximise the economically viable utilisation of resources, accounting for the competition between energy and food production. A four-layer supply chain superstructure has been developed, which includes the harvesting, preparation, core processing and distribution of products. This considered system’s boundaries involve a region, which is then divided into zones for optimising conversion operations and transportation flows. An MILP model has been formulated with profit maximisation as the optimisation criterion. The environmental impact is evaluated by the carbon footprint. The sensitivity of the optimal solutions is analysed for different regions’ sizes, transportation costs, pre-processing alternatives and the co-production of food and energy.
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Abbreviations
- UP:
-
Upper bound
- LO:
-
Lower bound
- L1:
-
Harvesting and supply layer
- L2:
-
Collection and pre-processing layer
- L3:
-
Main processing layer
- L4:
-
Use layer
- c:
-
Competing
- conv:
-
Conversion
- tr:
-
Transport
- road:
-
Road conditions
- yb:
-
Yearly basis
- op:
-
Operating costs
- inv:
-
Investment costs
- fix:
-
Fixed part of the annualized investment
- var:
-
Cost coefficient of the annualized investment
- price:
-
Price of the products
- I :
-
Set of supply zones
- M :
-
Set of collection and intermediate process centres
- N :
-
Set of process plants
- T :
-
Set of technology options
- P :
-
Set of products
- J :
-
Set of demand locations
- E :
-
Set of environmental impacts
- J o :
-
Set of demand locations at local level (subset of J)
- J e :
-
Set of demand locations for export (subset of J)
- PI :
-
Set of intermediate products (subset of P)
- PD :
-
Set of directly used products (subset of P)
- PP :
-
Set of produced products from plants (subset of P)
- PIP = PI × PP:
-
Set of pairs of intermediate product and produced product (if a produced product is produced from a given intermediate product)
- PT = PI × T:
-
Set of pairs of intermediate product and applicable process technology for it
- PIC :
-
Set of intermediate products competing for food and energy production (subset of PI)
- i :
-
Index for supply zones
- m :
-
Index for collection and intermediate process centres
- n :
-
Index for process plants
- t :
-
Index for technology options
- p :
-
Index for products
- j :
-
Index for demand locations
- j o :
-
Index for demand locations at local level
- j e :
-
Index for demand locations for export
- pi :
-
Index for intermediate products
- pd :
-
Index for directly used products
- pp :
-
Index for produced products from plants
- pic :
-
Index for intermediate products competing for food and energy production
- e :
-
Index for environmental impacts
- f yb :
-
Cost coefficient for yearly basis
- q m,L2 :
-
Total mass-flow at collection centre m, t/y
- \( q_{pi}^{m,{\text{L}}1,\text{L}2} \) :
-
Product’s mass-flow at collection centre m, t/y
- \( {{Dem}}_{{j^{\text{o}} ,p}} \) :
-
Regional demand at location j o for product p, t/y or MWh/y or MJ/y
- HY pi :
-
Yield for product pi, t/(km2 y)
- A i :
-
Total available area, km2
- \( f_{pi}^{{{\text{conv}},{\text {L2}}}} \) :
-
Conversion factor of intermediate product pi by pre-processing
- \( q_{t}^{m,\text{L}3} \) :
-
Inlet mass-flow to the selected technology, t/y
- \( f_{pi,pp,t}^{{{\text{conv}},{\text {L3}}}} \) :
-
Conversion factor of intermediate product pi by processing
- \( c_{p}^{{{\text{tr}},{\text{L}}a,{\text{L}}b}} \) :
-
Transportation cost coefficient of product from layer a to the layer b, €/(t km)
- c fix,inv,L2 :
-
Fixed investment costs by pre-processing, €/y
- \( c_{t}^{{{\text{fix}},{\text{inv}},{\text {L3}}}}\) :
-
Fixed part of investment costs by processing, €/y
- \( c_{t}^{{{\text{var}},{\text{inv}},{\text {L3}}}} \) :
-
Variable part of investment cost by processing, €/t
- \( ei_{p,e}^{{{\text{tr}},{\text{L}}a,{\text{L}}b}} \) :
-
Transport environmental impact factor from layer a to the layer b, \( t_{{{\text{CO}}_{2} }} \)/(t km)
- \( ei_{pi,e}^{{\text {L2}}} \) :
-
Environmental impact factor caused by pre-processing, \( t_{{{\text{CO}}_{2} }} \)/t
- \( ei_{pi,t,e}^{\text{L}3} \) :
-
Environmental impact factor by the processing, \( t_{{{\text{CO}}_{2} }} \)/t
- \( D_{x,y}^{{{\text{L}}a,{\text{L}}b}} \) :
-
Distance between object x in layer a and object y in layer b, km
- \( f_{x,y}^{{{\text{road}},{\text{L}}a,{\text{L}}b}} \) :
-
Road condition factor between object x in layer a and object y in layer b
- \( c_{p}^{\text{price}} \) :
-
Price of the product, €/t or €/MWh or €/MJ
- N i :
-
The size of set I
- N m :
-
The size of set M
- N n :
-
The size of set N
- N j :
-
The size of set J
- \( q_{i,pi}^{m,\text{L}1} \) :
-
Production rate of intermediate product pi at supply zone i, t/y
- \( A_{{i,{pic}}}^{\text{c}} \) :
-
Competing area for food and energy at zone i for product pi, km2
- \( q_{x,y,p}^{{m,{\text{L}}a,{\text{L}}b}} \) :
-
Mass-flow of product p from object x in layer a to object y in layer b, t/y
- \( q_{n,pi,t}^{m,T,\text{L}2,\text{L}3} \) :
-
Mass-flow of intermediate product pi to the selected technology t at the process plant n, t/y
- \( q_{n,pi,pp,t}^{m,T,\text{L}2,\text{L}3} \) :
-
Mass-flow of produced products pp from intermediate product pi with the selected technology t at the process plant n, t/y
- ENVB e :
-
Total environmental burden type e, t/y
- c tr :
-
Transportation costs, €/y
- c op :
-
Operating costs, €/y
- \( c_{pi}^{{{\text{op}},\text{L}2}} \) :
-
Operating costs by the pre-processing for product pi, €/t
- \( c_{pi,t}^{{{\text{op}},\text{L}3}} \) :
-
Operating costs by the processing for product pi and technology t, €/t
- c inv :
-
Annual investment costs, €/y
- c pi :
-
Raw material costs for product pi, €/t
- P B :
-
Profit before taxes, €/y
- \( y_{m}^{\text{L}2} \) :
-
Binary variable for existence of collection and intermediate process centre m
- \( y_{n,t}^{\text{L}3} \) :
-
Binary variable for existence of technology t at process plant n
- MILP:
-
Mixed-integer linear programming
- RES:
-
Renewable energy sources
- MIP:
-
Mixed-integer programming
- MSW:
-
Municipal solid waste
- DDGS:
-
Distillers dried grains with solubles
- CFP:
-
Carbon footprint
- GAMS:
-
General algebraic modelling system
- MOO:
-
Multi-objective optimisation
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Acknowledgement
This work has been carried out as part of a Collaborative PhD study at the University of Maribor and the University of Pannonia, supported by the Bilateral SI-HU Project TET SI-11/2008 ‘Process systems engineering and sustainable development’. Also the financial supports from the EC project Marie Curie Chair (EXC) MEXC-CT-2003-042618 ‘Integrated Waste to Energy Management to Prevent Global Warming—INEMAGLOW’ and from the Slovenian Research Agency (Program No. P2-0032, Project No. L2-0358 and PhD research fellowship contract No. 1000-08-310074) are gratefully acknowledged.
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Čuček, L., Lam, H.L., Klemeš, J.J. et al. Synthesis of regional networks for the supply of energy and bioproducts. Clean Techn Environ Policy 12, 635–645 (2010). https://doi.org/10.1007/s10098-010-0312-6
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DOI: https://doi.org/10.1007/s10098-010-0312-6