SUSTAINABLE USE OF ENVIRONMENTAL RESOURCES: OPTIMIZATION OF LOGISTICS OPERATIONS - Energy Research Developments: Tidal Energy, Energy Efficiency and Solar Energy - page 264

u ≤ α ⋅ x i=1,…,N (2.5)

i i i

u

i ≥

0 i=1,…,N (2.6)

where α is the maximum percentage of biomass quantity that is fixed by law. These
coefficients assume a value equal to 0.05 for coppice and 0.01 for high forest, according to
the local regulations.
Constraints on biomass flow : the biomass quantity entering the considered plant should
be equal to the plant capacity. This yields the following constraint

PCI

N

CAP

=

MV u = (2.7)

i i

3600 ⋅ 8000 η

i 1

e

where:
PCI is the low heating value assumed constant for not-treated biomasses, assuming a
medium humidity of 30-35%;
η is the plant electric energy efficiency;
8000 are the functioning hours in a year;
3600 is a conversion factor (hours in seconds).

The overall problem (cost function and constraints) so formalized is a linear
programming problem and can be solved by commonly used optimization tools.

2.2. Tactical Planning: Formalization of the Decision Problem

Referring to a given plant, as in the previous subsection, and considering the biomass
growth dynamics, the objective is now to plan collection in the first five years of the plant.
This means that the decision variables, namely u t i , are now functions of the parcels and of
time discrete values. Moreover, state variables

t 3 − 1

⋅ hm ] have to be introduced, in order
to represent the available biomass in parcel i at time t . Apart this, the two optimization
problems do not present substantial differences in their formulation.
The cost function in this case is expressed as:

x [

T − 1 N T − 1 N

∑∑ ∑∑

t
i

t
i

C = C d MV u + Cr MV u

(2.8)

TR i i i i

t == 0 i 1 t == 0 i 1

where T is the length of the optimization horizon. Similarly, the constraints must be written
for any time interval, that is