SUSTAINABLE USE OF ENVIRONMENTAL RESOURCES: OPTIMIZATION OF LOGISTICS OPERATIONS - Energy Research Developments: Tidal Energy, Energy Efficiency and Solar Energy - page 263

where:

• C T represents the biomass transportation cost (per unit time);

• C R is the biomass collection cost (per unit time).

Transportation costs may be expressed as

N

∑ =

C = C d MV u (2.2)

T TR i i i

i 1

where:

C TR [€ Km -1 Kg -1 ] is the unit transportation cost;
d i [ Km ] is the distance of the i-th parcel from the plant;
MV i [ Kg m -3 ] is biomass density of the i-th parcel.
Collection costs may be expressed as

= N

=

C Cr MV u

(2.3)

R i i i

i 1

where Cr i [ € Kg -1 ] is the unit collection cost for parcel i .

Such costs are strongly influenced from the characteristics of the territory: every parcel
has its collection costs, depending on the viability conditions, the presence of infrastructures,
the terrain accessibility and slope. In order to take into account such aspects, unit collection
costs have been grouped and defined considering four levels about biomass collection: from
an easy level to a non-practicable level.
Thus, the overall cost function that has to be minimized is

N N

∑ ∑

C = C d MV u + Cr MV u

(2.4)

TR i i i i i i

i = 1 i = 1

The minimization of the cost function (2.4) has to be carried out under constraints
relevant to biomass collection and to the biomass flow entering the plant.
Limits on biomass collection : the possibility of biomass collection on a territory must
respect the forest regulations inside the Forest Plans which contains all the guidelines about
the methods of forest management, treatment, and use. From the analysis of such documents
and data, it is possible to consider a medium “cut turnover system” for coppice and high
forest equal to 20 and 100 years, respectively, corresponding to a percentage of annual cutting
of 5% and 1%.
In every parcel, known the biomass quantity

x , in m 3 , the quantity that may be collected

is