Geoscience Reference
In-Depth Information
cost term is also included in (
16.14
) to account for the operation of non-selectable
facilities.
Equalities (
16.15
) are the flow balance constraints. For each location and product,
the total inflow comprises the amount of product generated at that location, the total
amount of product obtained after processing various items, and the total amount of
product shipped to this location from other locations. The total inflow is equal to the
total outflow which includes the total amount of product recovered at that location
and the total amount of product shipped to other locations. Constraints (
16.16
)
ensure that the recovery target for each product category and recovery option
is met. Recovery targets are usually stipulated by legislations for different types
of recovery options. Inequalities (
16.17
)-(
16.19
) are the capacity constraints.
Constraints (
16.17
) guarantee that the total amount of recovered products at the
selectable facilities does not exceed the total capacity. Similar conditions are set
at non-selectable facilities by inequalities (
16.18
). Constraints (
16.19
) restrict the
expansion of capacity at selectable facilities to be within given limits. Similar to the
forward LND model, constraints (
16.20
)-(
16.21
) impose that products can only be
shipped from operated facilities. Lastly, conditions (
16.22
)-(
16.24
) set the domains
of the decision variables.
.P
2
/ Maximize
X
r2R
X
X
RE
r`p
v
r`p
`2L
p2P
X
r2R
X
X
RC
r`p
v
r`p
X
r2R
X
FC
ri
y
ri
`2L
p2P
i2N
r
X
r2R
X
SC
ri
.1
y
ri
/
X
r2R
X
OC
ri
y
ri
X
r2R
X
OC
rj
i2E
r
i2I
r
j2J
r
X
`2L
X
X
TC
``
0
p
x
``
0
p
X
r2R
X
EC
ri
w
ri
(16.14)
`
0
2Lnf`g
p2P
i2I
r
subject to g
`p
C
X
r2R
X
LJ
rqp
v
r`q
C
X
`
0
2Lnf`g
x
`
0
`p
D
q2P
X
v
r`p
C
X
`
0
2Lnf`g
x
``
0
p
; `
2
L; p
2
P
(16.15)
r2R
X
v
r`p
RT
rp
; r
2
R; p
2
P
(16.16)
`2L
X
v
rip
KR
ri
y
ri
C
w
ri
; r
2
R; i
2
I
r
(16.17)
p2P
X
v
rjp
KR
rj
; r
2
R; j
2
J
r
(16.18)
p2P
0
w
ri
ER
ri
y
ri
; r
2
R; i
2
I
r
(16.19)
