Raw Materials Supply

  • José Miguel Laínez
  • Mar Pérez-Fortes
  • Aarón D. Bojarski
  • Luis Puigjaner
Part of the Green Energy and Technology book series (GREEN)


The pressure on reducing environmental footprint is facilitating the emergence of energy supply chains that have biomass as main feedstock. For the development of efficient energy supply chains from biomass it is required to properly integrate the various elements that comprise such systems (e.g., biomass supply, pre-treatment facilities and technologies for biomass to energy and/or fuels conversion). Additionally, it is recognised that a concerted effort is required, embracing the different supply chain entities, in order to correctly estimate environmental burdens and to propose effective environmental strategies. This chapter proposes the use of a mathematical modelling approach as an analytical tool that can support decision-making towards accomplishing the design and planning of efficient multiple source—multiple product bio-energy supply chains. The mathematical formulation of this problem becomes a multi-objective MILP (moMILP). Criteria selected for the objective function are the net present value (NPV) and the overall environmental impact, which is computed using the Impact 2002+ indicator. The main advantages of this approach are highlighted through a case study of a biomass-based supply chain that comprises different components geographically distributed over Spain. For comparison purposes, such a supply chain is contrasted to one embracing coal usage.


Supply Chain Life Cycle Assessment Life Cycle Inventory Life Cycle Impact Assessment Supply Chain Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.





f, f′

Facility locations




Equipment technology


Materials (states)

t, t

Planning periods


Mid-point environmental impact categories


End-point environmental impact categories



Set of mid-point environmental interventions that are combined into end-point damage factors g


Set of suppliers e that provide raw materials

\( \hat{E}_{\text{prod}} \)

Set of suppliers e that provide production services

\( \bar{E}_{\text{tr}} \)

Set of suppliers e that provide transportation services


Set of locations f where supplier e is placed


Set of materials s that are final products


Set of tasks i that can be performed in technology j

\( \bar{J}_{e} \)

Technology j that is available at supplier e

\( \tilde{J}_{f} \)

Technology j that can be installed at location f


Technologies that can perform task i


Set of market locations


Set of non-distribution tasks


Set of materials s that are raw materials


Set of supplier locations


Set of tasks producing material s

\( \bar{T}_{s} \)

Set of tasks consuming material s


Set of distribution tasks



Maximum availability of raw material s in period t in location f


Demand of product s at market f in period t


Distance from location f to location f


Fixed cost per unit of technology j capacity at location f in period t

\( I_{ft}^{J} \)

Investment required to establish a processing facility in location f in period t


Normalising factor of damage category g


Price of product s at market f in period t

\( {\text{Price}}_{jft}^{J} \)

Investment required per unit of technology j capacity increased at facility f in period t


Discount rate


Moisture for material s

\( {\text{Water}}_{ij}^{\max } \)

Maximum moisture for task i performed in equipment j

\( \alpha_{sij} \)

Mass fraction of task i for production of material s in equipment j

\( \bar{\alpha }_{sij} \)

Mass fraction of task i for consumption of material s in equipment j

\( \beta_{jf} \)

Minimum utilisation rate of technology j capacity that is allowed at location f

\( \zeta_{ag} \)

g end-point damage characterisation factor for environmental intervention a

\( \theta_{{ijff^{\prime}}} \)

Capacity utilisation rate of technology j by task i whose origin is location f and destination location f

\( \rho_{{eff^{\prime}t}}^{\text{tr}} \)

Unitary transportation costs from location f to location f′ during period t

\( \tau_{ijfet}^{{{\text{ut}}1}} \)

Unitary cost associated with task i performed in equipment j from location f and payable to external supplier e during period t

\( \tau_{sfet}^{{{\text{ut}}2}} \)

Unitary cost associated with handling the inventory of material s in location f and payable to external supplier e during period t

\( \chi_{est} \)

Unitary cost of raw material s offered by external supplier e in period t

\( \psi_{{ijff^{\prime}a}} \)

a environmental category impact CF for task i performed using technology j receiving materials from node f and delivering it at node f

\( \psi_{ija}^{T} \)

a environmental category impact CF for the transportation of a mass unit of material over a length unit

Binary Variables


1 if technology j is installed at location f in period t, 0 otherwise

Continuous Variables


Normalised end-point damage g for location f in period t

\( {\text{DamC}}_{g}^{\text{SC}} \)

Normalised end-point damage g along the whole SC


Economic value of purchases executed in period t to supplier e


Economic value of sales executed in period t


Investment on fixed assets in period t


Fixed cost in period t


Total capacity of technology j during period t at location f


Capacity increment of technology j at location f during period t


Mid-point a environmental impact associated to site f which rises from activities in period t

\( {\text{Impact}}_{f}^{2002} \)

Total environmental impact for site f

\( {\text{Impact}}_{\text{overall}}^{2002} \)

Total environmental impact for the whole SC


Lower heating value for material s in task i


Net present value


Activity magnitude of task i in equipment j in period t whose origin is location f and destination location f


Amount of material s for flexible task i in equipment j in period t whose origin is location f and destination location f


Profit achieved in period t

\( {\text{Purch}}_{et}^{\text{pr}} \)

Amount of money payable to supplier e in period t associated with production activities

\( {\text{Purch}}_{et}^{\text{rm}} \)

Amount of money payable to supplier e in period t associated with consumption of raw materials

\( {\text{Purch}}_{et}^{\text{tr}} \)

Amount of money payable to supplier e in period t associated with consumption of transport services


Amount of product s sold from location f in market f′ in period t


Amount of stock of material s at location f in period t



Lower bound


Upper bound



Biomass utilisation networks




Cost benefit analysis


Carbon capture and storage


Characterisation factors



Eco-indicator 99

Damage environmental metric


Energy Independence and Security Act


Forest wood residues


Greenhouse gas


Green supply chain management

IMPACT 2002+

Mid-point and end-point (damage) environmental metric


Life cycle assessment


Life cycle impact assessment


Life cycle inventory


State task network


Multi-objective mixed integer linear programming


Net present Value


Supply chain management


State task network


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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • José Miguel Laínez
    • 1
  • Mar Pérez-Fortes
    • 1
  • Aarón D. Bojarski
    • 1
  • Luis Puigjaner
    • 1
  1. 1.ETSEIBUniversitat Politècnica de CatalunyaBarcelonaSpain

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