Materials and Emission Streams#
This is a continuation of the Multiscale MILP example
We will be adding the following considerations:
material for the establishment of operations
global warming potential induced as a sum of our decisions and choices
See Multiscale MILP#
# !pip install energiapy # uncomment and run to install Energia, if not in environment
from energia import *
m = Model('design_scheduling_material')
m.q = Periods()
m.y = 4 * m.q
m.usd = Currency()
m.declare(Resource, ['power', 'wind', 'solar'])
m.solar.consume(m.q) <= 100
m.wind.consume <= 400
m.power.release.prep(180) >= [0.6, 0.7, 0.8, 0.3]
m.wf = Process()
m.wf(m.power) == -1 * m.wind
m.wf.capacity.x <= 100
m.wf.capacity.x >= 10
m.wf.operate.prep(norm=True) <= [0.9, 0.8, 0.5, 0.7]
m.usd.spend(m.wf.capacity) == 990637 + 3354
m.usd.spend(m.wf.operate) == 49
m.pv = Process()
m.pv(m.power) == -1 * m.solar
m.pv.capacity.x <= 100
m.pv.capacity.x >= 10
m.pv.operate.prep(norm=True) <= [0.6, 0.8, 0.9, 0.7]
m.usd.spend(m.pv.capacity) == 567000 + 872046
m.usd.spend(m.pv.operate) == 90000
m.lii = Storage()
m.lii(m.power) == 0.9
m.lii.capacity.x <= 100
m.lii.capacity.x >= 10
m.usd.spend(m.lii.capacity) == 1302182 + 41432
m.usd.spend(m.lii.inventory) == 2000
β Initiated solar balance in (l0, q) β± 0.0003 s
π Bound [β€] solar consume in (l0, q) β± 0.0013 s
β Initiated wind balance in (l0, y) β± 0.0001 s
π Bound [β€] wind consume in (l0, y) β± 0.0008 s
β Initiated power balance in (l0, q) β± 0.0001 s
π Bound [β₯] power release in (l0, q) β± 0.0007 s
π Bound [β€] wf capacity in (l0, y) β± 0.0002 s
π Bound [β₯] wf capacity in (l0, y) β± 0.0001 s
π Bound [β€] wf operate in (l0, q) β± 0.0003 s
π Bound [=] usd spend in (l0, y) β± 0.0003 s
π§ Mapped time for operate (wf, l0, q) βΊ (wf, l0, y) β± 0.0003 s
π Bound [=] usd spend in (l0, y) β± 0.0002 s
π Bound [β€] pv capacity in (l0, y) β± 0.0002 s
π Bound [β₯] pv capacity in (l0, y) β± 0.0002 s
π Bound [β€] pv operate in (l0, q) β± 0.0003 s
π Bound [=] usd spend in (l0, y) β± 0.0002 s
π§ Mapped time for operate (pv, l0, q) βΊ (pv, l0, y) β± 0.0002 s
π Bound [=] usd spend in (l0, y) β± 0.0002 s
π Bound [β€] lii.stored invcapacity in (l0, y) β± 0.0003 s
π Bound [β₯] lii.stored invcapacity in (l0, y) β± 0.0001 s
π Bound [=] usd spend in (l0, y) β± 0.0002 s
π Bound [=] usd spend in (l0, y) β± 0.0002 s
Indicator Stream#
Indicators scale the impact of some decision or flow and project it only a common dimension allowing the calculation of overall impact as a single metric value
In this case, we consider global warming potential (GWP).
m.gwp = Environ()
Now say that we want to consider the impact of setting up operations (specific to the act of construction)
These can be provided as calculations
m.gwp.emit(m.wf.capacity) == 1000
m.gwp.emit(m.pv.capacity) == 2000
m.gwp.emit(m.lii.capacity) == 3000
m.emit.show()
π Bound [=] gwp emit in (l0, y) β± 0.0003 s
π Bound [=] gwp emit in (l0, y) β± 0.0003 s
π Bound [=] gwp emit in (l0, y) β± 0.0003 s
\[\displaystyle [22]\text{ }{\mathbf{{\mathbf{emit}}}}_{{gwp},{l0},{y},{\mathbf{{cap}}},{wf}} - 1000 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{wf},{l0},{y}} = 0\]
\[\displaystyle [23]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{cap}}},{pv}} - 2000 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} = 0\]
\[\displaystyle [24]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{icap}}},{lii.stored}} - 3000 \cdot {\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} = 0\]
Note that impact streams are mapped across scales but not balanced, unless a negative (relatively) impact is also assessed! In the case of emission, this would be abatement.
Material Stream#
Note that all the objects found in energia.components.commodity.misc are still resources (Land, Material, etc.)
This will allow for the modeling of an expansive type of processes.
Examples:
land clearance to transform agricultural land into industrial, or land remediation
resource intense material recycling
some resource flowing being treated as emission flows
The possibilities are vast⦠The advanced modeler may prefer to use Resource() for everything [see Resource Task Network (RTN) Framework]
In the following example, we consider a limit to cement consumption, as also an expense and gwp impact associated with it
m.cement = Material()
m.cement.consume <= 1000000
m.usd.spend(m.cement.consume) == 17
m.gwp.emit(m.cement.consume) == 0.9
β Initiated cement balance in (l0, y) β± 0.0001 s
π Bound [β€] cement consume in (l0, y) β± 0.0011 s
π Bound [=] usd spend in (l0, y) β± 0.0003 s
π Bound [=] gwp emit in (l0, y) β± 0.0003 s
Next, we provide details of the use of cement across all operations
m.cement.use(m.wf.capacity) == 400
m.cement.use(m.pv.capacity) == 560
m.cement.use(m.lii.capacity) == 300
β Updated cement balance with use(cement, l0, y, capacity, wf) β± 0.0001 s
π Bound [=] cement use in (l0, y) β± 0.0012 s
β Updated cement balance with use(cement, l0, y, capacity, pv) β± 0.0001 s
π Bound [=] cement use in (l0, y) β± 0.0008 s
β Updated cement balance with use(cement, l0, y, invcapacity, lii.stored) β± 0.0003 s
π Bound [=] cement use in (l0, y) β± 0.0010 s
Material use is summed up across all operations, and adheres to an upper bound in terms of consumption.
m.cement.show()
\[\displaystyle [31]\text{ }{\mathbf{{\mathbf{{\mathbf{use}}}}}}_{{cement},{l0},{y},{\mathbf{{icap}}},{lii.stored}} - 300 \cdot {\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} = 0\]
\[\displaystyle [27]\text{ }{\mathbf{{\mathbf{{\mathbf{spend}}}}}}_{{usd},{l0},{y},{\mathbf{{cons}}},{cement}} - 17 \cdot {\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} = 0\]
\[\displaystyle [29]\text{ }{\mathbf{{\mathbf{use}}}}_{{cement},{l0},{y},{\mathbf{{cap}}},{wf}} - 400 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{wf},{l0},{y}} = 0\]
\[\displaystyle [28]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{cons}}},{cement}} - 0.9 \cdot {\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} = 0\]
\[\displaystyle [25]\text{ }{\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} - {\mathbf{{\mathbf{use}}}}_{{cement},{l0},{y},{\mathbf{{cap}}},{wf}} - {\mathbf{{\mathbf{{\mathbf{use}}}}}}_{{cement},{l0},{y},{\mathbf{{cap}}},{pv}} - {\mathbf{{\mathbf{{\mathbf{use}}}}}}_{{cement},{l0},{y},{\mathbf{{icap}}},{lii.stored}} = 0\]
\[\displaystyle [30]\text{ }{\mathbf{{\mathbf{{\mathbf{use}}}}}}_{{cement},{l0},{y},{\mathbf{{cap}}},{pv}} - 560 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} = 0\]
\[\displaystyle [26]\text{ }{\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} - 1000000 \leq 0\]
GWP impact is now the sum of impact from material use as well as constuction
m.emit.show()
\[\displaystyle [22]\text{ }{\mathbf{{\mathbf{emit}}}}_{{gwp},{l0},{y},{\mathbf{{cap}}},{wf}} - 1000 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{wf},{l0},{y}} = 0\]
\[\displaystyle [23]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{cap}}},{pv}} - 2000 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} = 0\]
\[\displaystyle [28]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{cons}}},{cement}} - 0.9 \cdot {\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} = 0\]
\[\displaystyle [24]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{icap}}},{lii.stored}} - 3000 \cdot {\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} = 0\]
Locate Operations#
m.network.locate(m.wf, m.pv, m.lii)
π‘ Assumed wf capacity unbounded in (l0, y) β± 0.0001 s
π‘ Assumed wf operate bounded by capacity in (l0, q) β± 0.0001 s
β Updated power balance with produce(power, l0, q, operate, wf) β± 0.0001 s
π Bound [=] power produce in (l0, q) β± 0.0010 s
β Updated wind balance with expend(wind, l0, y, operate, wf) β± 0.0001 s
π Bound [=] wind expend in (l0, y) β± 0.0008 s
π Operating streams introduced for wf in l0 β± 0.0031 s
π Construction streams introduced for wf in l0 β± 0.0000 s
π Located wf in l0 β± 0.0045 s
π‘ Assumed pv capacity unbounded in (l0, y) β± 0.0001 s
π‘ Assumed pv operate bounded by capacity in (l0, q) β± 0.0001 s
β Updated power balance with produce(power, l0, q, operate, pv) β± 0.0001 s
π Bound [=] power produce in (l0, q) β± 0.0010 s
β Updated solar balance with expend(solar, l0, q, operate, pv) β± 0.0001 s
π Bound [=] solar expend in (l0, q) β± 0.0008 s
π Operating streams introduced for pv in l0 β± 0.0025 s
π Construction streams introduced for pv in l0 β± 0.0000 s
π Located pv in l0 β± 0.0038 s
π‘ Assumed lii capacity unbounded in (l0, y) β± 0.0001 s
π§ Mapped time for inventory (lii.stored, l0, q) βΊ (lii.stored, l0, y) β± 0.0001 s
β Initiated lii.stored balance in (l0, q) β± 0.0003 s
π Bound [β€] lii.stored inventory in (l0, q) β± 0.0030 s
π‘ Assumed lii inventory bounded by capacity in (l0, q) β± 0.0034 s
π‘ Assumed lii.charge capacity unbounded in (l0, y) β± 0.0002 s
π Bound [β€] lii.charge operate in (l0, y) β± 0.0003 s
π‘ Assumed lii.charge operate bounded by capacity in (l0, y) β± 0.0005 s
π§ Mapped time for operate (lii.charge, l0, q) βΊ (lii.charge, l0, y) β± 0.0001 s
β Updated lii.stored balance with produce(lii.stored, l0, q, operate, lii.charge) β± 0.0001 s
π Bound [=] lii.stored produce in (l0, q) β± 0.0008 s
β Updated power balance with expend(power, l0, q, operate, lii.charge) β± 0.0001 s
π Bound [=] power expend in (l0, q) β± 0.0008 s
π Operating streams introduced for lii.charge in l0 β± 0.0028 s
π Construction streams introduced for lii.charge in l0 β± 0.0000 s
π Located lii.charge in l0 β± 0.0044 s
π‘ Assumed lii.discharge capacity unbounded in (l0, y) β± 0.0002 s
π Bound [β€] lii.discharge operate in (l0, y) β± 0.0003 s
π‘ Assumed lii.discharge operate bounded by capacity in (l0, y) β± 0.0005 s
π§ Mapped time for operate (lii.discharge, l0, q) βΊ (lii.discharge, l0, y) β± 0.0001 s
β Updated power balance with produce(power, l0, q, operate, lii.discharge) β± 0.0001 s
π Bound [=] power produce in (l0, q) β± 0.0008 s
β Updated lii.stored balance with expend(lii.stored, l0, q, operate, lii.discharge) β± 0.0002 s
π Bound [=] lii.stored expend in (l0, q) β± 0.0012 s
π Operating streams introduced for lii.discharge in l0 β± 0.0036 s
π Construction streams introduced for lii.discharge in l0 β± 0.0000 s
π Located lii.discharge in l0 β± 0.0053 s
π Construction streams introduced for lii in l0 β± 0.0000 s
π Located lii in l0 β± 0.0145 s
Optimization#
Minimize GWP#
Let us minimize GWP this time. Note that m.usd.spend.opt() can still be used!
m.gwp.emit.opt()
π§ Mapped samples for emit (gwp, l0, y, capacity, wf) βΊ (gwp, l0, y) β± 0.0001 s
π§ Mapped samples for emit (gwp, l0, y, capacity, pv) βΊ (gwp, l0, y) β± 0.0002 s
π§ Mapped samples for emit (gwp, l0, y, invcapacity, lii.stored) βΊ (gwp, l0, y) β± 0.0003 s
π§ Mapped samples for emit (gwp, l0, y, consume, cement) βΊ (gwp, l0, y) β± 0.0002 s
π Generated Program(design_scheduling_material).mps β± 0.0034 s
Set parameter Username
Academic license - for non-commercial use only - expires 2026-08-01
Read MPS format model from file Program(design_scheduling_material).mps
Reading time = 0.00 seconds
PROGRAM(DESIGN_SCHEDULING_MATERIAL): 93 rows, 87 columns, 215 nonzeros
π Generated gurobipy model. See .formulation β± 0.0153 s
Gurobi Optimizer version 12.0.3 build v12.0.3rc0 (win64 - Windows 11.0 (26100.2))
CPU model: 13th Gen Intel(R) Core(TM) i7-13700, instruction set [SSE2|AVX|AVX2]
Thread count: 16 physical cores, 24 logical processors, using up to 24 threads
Optimize a model with 93 rows, 87 columns and 215 nonzeros
Model fingerprint: 0x347f9574
Variable types: 84 continuous, 3 integer (3 binary)
Coefficient statistics:
Matrix range [6e-01, 1e+06]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [7e+01, 1e+06]
Presolve removed 88 rows and 81 columns
Presolve time: 0.00s
Presolved: 5 rows, 6 columns, 18 nonzeros
Variable types: 6 continuous, 0 integer (0 binary)
Root relaxation: objective 4.752148e+05, 2 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 475214.81481 475214.815 0.00% - 0s
Explored 1 nodes (2 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 24 (of 24 available processors)
Solution count 1: 475215
Optimal solution found (tolerance 1.00e-04)
Best objective 4.752148148148e+05, best bound 4.752148148148e+05, gap 0.0000%
π Generated Solution object for Program(design_scheduling_material). See .solution β± 0.0007 s
β
Program(design_scheduling_material) optimized using gurobi. Display using .output() β± 0.0263 s
Minimize Cost#
The same problem can also be minimized in terms of cost
m.usd.spend.opt()
π§ Mapped samples for spend (usd, l0, y, capacity, wf) βΊ (usd, l0, y) β± 0.0001 s
π§ Mapped samples for spend (usd, l0, y, operate, wf) βΊ (usd, l0, y) β± 0.0003 s
π§ Mapped samples for spend (usd, l0, y, capacity, pv) βΊ (usd, l0, y) β± 0.0002 s
π§ Mapped samples for spend (usd, l0, y, operate, pv) βΊ (usd, l0, y) β± 0.0001 s
π§ Mapped samples for spend (usd, l0, y, invcapacity, lii.stored) βΊ (usd, l0, y) β± 0.0001 s
π§ Mapped samples for spend (usd, l0, y, inventory, lii.stored) βΊ (usd, l0, y) β± 0.0002 s
π§ Mapped samples for spend (usd, l0, y, consume, cement) βΊ (usd, l0, y) β± 0.0002 s
π Generated Program(design_scheduling_material).mps β± 0.0031 s
Warning: row name O0 in column section at line 321 not defined.
Read MPS format model from file Program(design_scheduling_material).mps
Reading time = 0.00 seconds
PROGRAM(DESIGN_SCHEDULING_MATERIAL): 94 rows, 88 columns, 223 nonzeros
π Generated gurobipy model. See .formulation β± 0.0123 s
Gurobi Optimizer version 12.0.3 build v12.0.3rc0 (win64 - Windows 11.0 (26100.2))
CPU model: 13th Gen Intel(R) Core(TM) i7-13700, instruction set [SSE2|AVX|AVX2]
Thread count: 16 physical cores, 24 logical processors, using up to 24 threads
Optimize a model with 94 rows, 88 columns and 223 nonzeros
Model fingerprint: 0x59224a16
Variable types: 85 continuous, 3 integer (3 binary)
Coefficient statistics:
Matrix range [6e-01, 1e+06]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [7e+01, 1e+06]
Presolve removed 82 rows and 76 columns
Presolve time: 0.00s
Presolved: 12 rows, 12 columns, 34 nonzeros
Variable types: 12 continuous, 0 integer (0 binary)
Root relaxation: objective 3.024203e+08, 6 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 3.024203e+08 3.0242e+08 0.00% - 0s
Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 24 (of 24 available processors)
Solution count 1: 3.0242e+08
Optimal solution found (tolerance 1.00e-04)
Best objective 3.024202544136e+08, best bound 3.024202544136e+08, gap 0.0000%
π Generated Solution object for Program(design_scheduling_material). See .solution β± 0.0005 s
β
Program(design_scheduling_material) optimized using gurobi. Display using .output() β± 0.0230 s
m.show()
Mathematical Program for Program(design_scheduling_material)
Index Sets
\[\displaystyle {currencies} = \{ {{usd}} \}\]
\[\displaystyle {resources} = \{ {{power}, {wind}, {solar}, {lii.stored}} \}\]
\[\displaystyle {locations} = \{ {{l0}} \}\]
\[\displaystyle {y} = \{ {{{{y}_{0}}}} \}\]
\[\displaystyle {q} = \{ {{{{q}_{0}}}, {{{q}_{1}}}, {{{q}_{2}}}, {{{q}_{3}}}} \}\]
\[\displaystyle {processes} = \{ {{wf}, {pv}, {lii.charge}, {lii.discharge}} \}\]
\[\displaystyle {storages} = \{ {{lii}} \}\]
\[\displaystyle {materials} = \{ {{cement}} \}\]
Objective
\[\displaystyle min \hspace{0.2cm} {\mathbf{emit}}_{{gwp},{l0},{{{y}_{0}}}}\]
\[\displaystyle min \hspace{0.2cm} {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}}}\]
s.t.
Balance Constraint Sets
\[\displaystyle [0]\text{ }{\mathbf{{\mathbf{{cons}}}}}_{{solar},{l0},{y},{q}} - {\mathbf{{\mathbf{{\mathbf{{expd}}}}}}}_{{solar},{l0},{y},{q},{\mathbf{{opr}}},{pv}} = 0\]
\[\displaystyle [2]\text{ }{\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{wind},{l0},{y}} - {\mathbf{{\mathbf{{expd}}}}}_{{wind},{l0},{y},{\mathbf{{opr}}},{wf}} = 0\]
\[\displaystyle [4]\text{ }-{\mathbf{{\mathbf{{rlse}}}}}_{{power},{l0},{y},{q}} + {\mathbf{{\mathbf{prod}}}}_{{power},{l0},{y},{q},{\mathbf{{opr}}},{wf}} + {\mathbf{{\mathbf{{\mathbf{prod}}}}}}_{{power},{l0},{y},{q},{\mathbf{{opr}}},{pv}} - {\mathbf{{\mathbf{{\mathbf{{expd}}}}}}}_{{power},{l0},{y},{q},{\mathbf{{opr}}},{lii.charge}} + {\mathbf{{\mathbf{{\mathbf{prod}}}}}}_{{power},{l0},{y},{q},{\mathbf{{opr}}},{lii.discharge}} = 0\]
\[\displaystyle [25]\text{ }{\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} - {\mathbf{{\mathbf{use}}}}_{{cement},{l0},{y},{\mathbf{{cap}}},{wf}} - {\mathbf{{\mathbf{{\mathbf{use}}}}}}_{{cement},{l0},{y},{\mathbf{{cap}}},{pv}} - {\mathbf{{\mathbf{{\mathbf{use}}}}}}_{{cement},{l0},{y},{\mathbf{{icap}}},{lii.stored}} = 0\]
\[\displaystyle [37]\text{ }-{\mathbf{{\mathbf{{\mathbf{{\mathbf{{inv}}}}}}}}}_{{lii.stored},{l0},{y},{q}} + {\mathbf{{\mathbf{{\mathbf{{\mathbf{{inv}}}}}}}}}_{{lii.stored},{l0},{y},{{q}-1}} + {\mathbf{{\mathbf{{\mathbf{prod}}}}}}_{{lii.stored},{l0},{y},{q},{\mathbf{{opr}}},{lii.charge}} - {\mathbf{{\mathbf{{\mathbf{{expd}}}}}}}_{{lii.stored},{l0},{y},{q},{\mathbf{{opr}}},{lii.discharge}} = 0\]
Binds Constraint Sets
\[\displaystyle [1]\text{ }{\mathbf{{\mathbf{{cons}}}}}_{{solar},{l0},{y},{q}} - 100 \leq 0\]
\[\displaystyle [3]\text{ }{\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{wind},{l0},{y}} - 400 \leq 0\]
\[\displaystyle [5]\text{ }-{\mathbf{{\mathbf{{rlse}}}}}_{{power},{l0},{y},{q}} + {\mathrm{Ο}}_{{}} \leq 0\]
\[\displaystyle [6]\text{ }{\mathbf{{\mathbf{{cap}}}}}_{{wf},{l0},{y}} - 100 \cdot {\mathbf{{\mathbf{{\breve{{cap}}}}}}}_{{wf},{l0},{y}} \leq 0\]
\[\displaystyle [7]\text{ }10 \cdot {\mathbf{{\mathbf{{\breve{{cap}}}}}}}_{{wf},{l0},{y}} - {\mathbf{{\mathbf{{cap}}}}}_{{wf},{l0},{y}} \leq 0\]
\[\displaystyle [8]\text{ }{\mathbf{{\mathbf{{opr}}}}}_{{wf},{l0},{y},{q}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{cap}}}}}_{{wf},{l0},{y}} \leq 0\]
\[\displaystyle [12]\text{ }{\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} - 100 \cdot {\mathbf{{\mathbf{{\mathbf{{\breve{{cap}}}}}}}}}_{{pv},{l0},{y}} \leq 0\]
\[\displaystyle [13]\text{ }10 \cdot {\mathbf{{\mathbf{{\mathbf{{\breve{{cap}}}}}}}}}_{{pv},{l0},{y}} - {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} \leq 0\]
\[\displaystyle [14]\text{ }{\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{pv},{l0},{y},{q}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} \leq 0\]
\[\displaystyle [18]\text{ }{\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} - 100 \cdot {\mathbf{{\mathbf{{\breve{{icap}}}}}}}_{{lii.stored},{l0},{y}} \leq 0\]
\[\displaystyle [19]\text{ }10 \cdot {\mathbf{{\mathbf{{\breve{{icap}}}}}}}_{{lii.stored},{l0},{y}} - {\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} \leq 0\]
\[\displaystyle [26]\text{ }{\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} - 1000000 \leq 0\]
\[\displaystyle [38]\text{ }{\mathbf{{\mathbf{{\mathbf{{inv}}}}}}}_{{lii.stored},{l0},{y},{q}} - {\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} \leq 0\]
\[\displaystyle [39]\text{ }{\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.charge},{l0},{y}} - {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{lii.charge},{l0},{y}} \leq 0\]
\[\displaystyle [43]\text{ }{\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.discharge},{l0},{y}} - {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{lii.discharge},{l0},{y}} \leq 0\]
Calculations Constraint Sets
\[\displaystyle [9]\text{ }{\mathbf{{\mathbf{spend}}}}_{{usd},{l0},{y},{\mathbf{{cap}}},{wf}} - 993991 \cdot {\mathbf{{\mathbf{{cap}}}}}_{{wf},{l0},{y}} = 0\]
\[\displaystyle [11]\text{ }{\mathbf{{\mathbf{{\mathbf{spend}}}}}}_{{usd},{l0},{y},{\mathbf{{opr}}},{wf}} - 49 \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{wf},{l0},{y}} = 0\]
\[\displaystyle [15]\text{ }{\mathbf{{\mathbf{{\mathbf{spend}}}}}}_{{usd},{l0},{y},{\mathbf{{cap}}},{pv}} - 1439046 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} = 0\]
\[\displaystyle [17]\text{ }{\mathbf{{\mathbf{{\mathbf{spend}}}}}}_{{usd},{l0},{y},{\mathbf{{opr}}},{pv}} - 90000 \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{pv},{l0},{y}} = 0\]
\[\displaystyle [20]\text{ }{\mathbf{{\mathbf{{\mathbf{spend}}}}}}_{{usd},{l0},{y},{\mathbf{{icap}}},{lii.stored}} - 1343614 \cdot {\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} = 0\]
\[\displaystyle [21]\text{ }{\mathbf{{\mathbf{{\mathbf{spend}}}}}}_{{usd},{l0},{y},{\mathbf{{inv}}},{lii.stored}} - 2000 \cdot {\mathbf{{\mathbf{{inv}}}}}_{{lii.stored},{l0},{y}} = 0\]
\[\displaystyle [22]\text{ }{\mathbf{{\mathbf{emit}}}}_{{gwp},{l0},{y},{\mathbf{{cap}}},{wf}} - 1000 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{wf},{l0},{y}} = 0\]
\[\displaystyle [23]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{cap}}},{pv}} - 2000 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} = 0\]
\[\displaystyle [24]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{icap}}},{lii.stored}} - 3000 \cdot {\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} = 0\]
\[\displaystyle [27]\text{ }{\mathbf{{\mathbf{{\mathbf{spend}}}}}}_{{usd},{l0},{y},{\mathbf{{cons}}},{cement}} - 17 \cdot {\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} = 0\]
\[\displaystyle [28]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y},{\mathbf{{cons}}},{cement}} - 0.9 \cdot {\mathbf{{\mathbf{{\mathbf{{cons}}}}}}}_{{cement},{l0},{y}} = 0\]
\[\displaystyle [29]\text{ }{\mathbf{{\mathbf{use}}}}_{{cement},{l0},{y},{\mathbf{{cap}}},{wf}} - 400 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{wf},{l0},{y}} = 0\]
\[\displaystyle [30]\text{ }{\mathbf{{\mathbf{{\mathbf{use}}}}}}_{{cement},{l0},{y},{\mathbf{{cap}}},{pv}} - 560 \cdot {\mathbf{{\mathbf{{\mathbf{{cap}}}}}}}_{{pv},{l0},{y}} = 0\]
\[\displaystyle [31]\text{ }{\mathbf{{\mathbf{{\mathbf{use}}}}}}_{{cement},{l0},{y},{\mathbf{{icap}}},{lii.stored}} - 300 \cdot {\mathbf{{\mathbf{{icap}}}}}_{{lii.stored},{l0},{y}} = 0\]
\[\displaystyle [32]\text{ }{\mathbf{{\mathbf{prod}}}}_{{power},{l0},{y},{q},{\mathbf{{opr}}},{wf}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{wf},{l0},{y},{q}} = 0\]
\[\displaystyle [33]\text{ }{\mathbf{{\mathbf{{expd}}}}}_{{wind},{l0},{y},{\mathbf{{opr}}},{wf}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{wf},{l0},{y}} = 0\]
\[\displaystyle [34]\text{ }{\mathbf{{\mathbf{{\mathbf{prod}}}}}}_{{power},{l0},{y},{q},{\mathbf{{opr}}},{pv}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{pv},{l0},{y},{q}} = 0\]
\[\displaystyle [35]\text{ }{\mathbf{{\mathbf{{\mathbf{{expd}}}}}}}_{{solar},{l0},{y},{q},{\mathbf{{opr}}},{pv}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{pv},{l0},{y},{q}} = 0\]
\[\displaystyle [41]\text{ }{\mathbf{{\mathbf{{\mathbf{prod}}}}}}_{{lii.stored},{l0},{y},{q},{\mathbf{{opr}}},{lii.charge}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.charge},{l0},{y},{q}} = 0\]
\[\displaystyle [42]\text{ }{\mathbf{{\mathbf{{\mathbf{{expd}}}}}}}_{{power},{l0},{y},{q},{\mathbf{{opr}}},{lii.charge}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.charge},{l0},{y},{q}} = 0\]
\[\displaystyle [45]\text{ }{\mathbf{{\mathbf{{\mathbf{prod}}}}}}_{{power},{l0},{y},{q},{\mathbf{{opr}}},{lii.discharge}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.discharge},{l0},{y},{q}} = 0\]
\[\displaystyle [46]\text{ }{\mathbf{{\mathbf{{\mathbf{{expd}}}}}}}_{{lii.stored},{l0},{y},{q},{\mathbf{{opr}}},{lii.discharge}} - {\mathrm{Ο}}_{{}} \cdot {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.discharge},{l0},{y},{q}} = 0\]
Mapping Constraint Sets
\[\displaystyle [10]\text{ }{\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{wf},{l0},{y}} - \sum_{i \in {q}} {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{wf}, {l0}, {y}, i} = 0\]
\[\displaystyle [16]\text{ }{\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{pv},{l0},{y}} - \sum_{i \in {q}} {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{pv}, {l0}, {y}, i} = 0\]
\[\displaystyle [36]\text{ }{\mathbf{{\mathbf{{\mathbf{{inv}}}}}}}_{{lii.stored},{l0},{y}} - \sum_{i \in {q}} {\mathbf{{\mathbf{{\mathbf{{inv}}}}}}}_{{lii.stored}, {l0}, {y}, i} = 0\]
\[\displaystyle [40]\text{ }{\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.charge},{l0},{y}} - \sum_{i \in {q}} {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.charge}, {l0}, {y}, i} = 0\]
\[\displaystyle [44]\text{ }{\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.discharge},{l0},{y}} - \sum_{i \in {q}} {\mathbf{{\mathbf{{\mathbf{{opr}}}}}}}_{{lii.discharge}, {l0}, {y}, i} = 0\]
\[\displaystyle [47]\text{ }{\mathbf{{\mathbf{{\mathbf{emit}}}}}}_{{gwp},{l0},{y}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{emit}}}}}}}}_{{gwp},{l0},{y},{\mathbf{{cap}}},{wf}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{emit}}}}}}}}_{{gwp},{l0},{y},{\mathbf{{cap}}},{pv}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{emit}}}}}}}}_{{gwp},{l0},{y},{\mathbf{{icap}}},{lii.stored}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{emit}}}}}}}}_{{gwp},{l0},{y},{\mathbf{{cons}}},{cement}} = 0\]
\[\displaystyle [48]\text{ }{\mathbf{{\mathbf{{\mathbf{spend}}}}}}_{{usd},{l0},{y}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{spend}}}}}}}}_{{usd},{l0},{y},{\mathbf{{cap}}},{wf}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{spend}}}}}}}}_{{usd},{l0},{y},{\mathbf{{opr}}},{wf}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{spend}}}}}}}}_{{usd},{l0},{y},{\mathbf{{cap}}},{pv}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{spend}}}}}}}}_{{usd},{l0},{y},{\mathbf{{opr}}},{pv}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{spend}}}}}}}}_{{usd},{l0},{y},{\mathbf{{icap}}},{lii.stored}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{spend}}}}}}}}_{{usd},{l0},{y},{\mathbf{{inv}}},{lii.stored}} - {\mathbf{{\mathbf{{\mathbf{{\mathbf{spend}}}}}}}}_{{usd},{l0},{y},{\mathbf{{cons}}},{cement}} = 0\]
Function Sets
\[\displaystyle {\mathbf{emit}}_{{gwp},{l0},{{{y}_{0}}}}\]
\[\displaystyle {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}}}\]
m.output()
Solution for Program(design_scheduling_material)
Objective
\[\displaystyle min \hspace{0.2cm} {\mathbf{emit}}_{{gwp},{l0},{{{y}_{0}}}}=475214.8148148147\]
Variables
\[\displaystyle {\mathbf{{cons}}}_{{solar},{l0},{{{y}_{0}}},{{{q}_{0}}}}=66.6666666666667\]
\[\displaystyle {\mathbf{{cons}}}_{{solar},{l0},{{{y}_{0}}},{{{q}_{1}}}}=88.88888888888894\]
\[\displaystyle {\mathbf{{cons}}}_{{solar},{l0},{{{y}_{0}}},{{{q}_{2}}}}=100.00000000000006\]
\[\displaystyle {\mathbf{{cons}}}_{{solar},{l0},{{{y}_{0}}},{{{q}_{3}}}}=77.77777777777781\]
\[\displaystyle {\mathbf{{cons}}}_{{wind},{l0},{{{y}_{0}}}}=322.22222222222223\]
\[\displaystyle {\mathbf{{cons}}}_{{cement},{l0},{{{y}_{0}}}}=104148.14814814815\]
\[\displaystyle {\mathbf{{rlse}}}_{{power},{l0},{{{y}_{0}}},{{{q}_{0}}}}=159.78395061728415\]
\[\displaystyle {\mathbf{{rlse}}}_{{power},{l0},{{{y}_{0}}},{{{q}_{1}}}}=157.49999999999997\]
\[\displaystyle {\mathbf{{rlse}}}_{{power},{l0},{{{y}_{0}}},{{{q}_{2}}}}=180.0\]
\[\displaystyle {\mathbf{{rlse}}}_{{power},{l0},{{{y}_{0}}},{{{q}_{3}}}}=155.5555555555556\]
\[\displaystyle {\mathbf{{cap}}}_{{wf},{l0},{{{y}_{0}}}}=100.0\]
\[\displaystyle {\mathbf{{cap}}}_{{pv},{l0},{{{y}_{0}}}}=100.00000000000006\]
\[\displaystyle {\mathbf{{cap}}}_{{lii.charge},{l0},{{{y}_{0}}}}=27.160493827160423\]
\[\displaystyle {\mathbf{{cap}}}_{{lii.discharge},{l0},{{{y}_{0}}}}=24.44444444444438\]
\[\displaystyle {\mathbf{{\breve{{cap}}}}}_{{wf},{l0},{{{y}_{0}}}}=1.0\]
\[\displaystyle {\mathbf{{\breve{{cap}}}}}_{{pv},{l0},{{{y}_{0}}}}=1.0\]
\[\displaystyle {\mathbf{{opr}}}_{{wf},{l0},{{{y}_{0}}},{{{q}_{0}}}}=100.0\]
\[\displaystyle {\mathbf{{opr}}}_{{wf},{l0},{{{y}_{0}}},{{{q}_{1}}}}=88.8888888888889\]
\[\displaystyle {\mathbf{{opr}}}_{{wf},{l0},{{{y}_{0}}},{{{q}_{2}}}}=55.55555555555556\]
\[\displaystyle {\mathbf{{opr}}}_{{wf},{l0},{{{y}_{0}}},{{{q}_{3}}}}=77.77777777777777\]
\[\displaystyle {\mathbf{{opr}}}_{{wf},{l0},{{{y}_{0}}}}=322.22222222222223\]
\[\displaystyle {\mathbf{{opr}}}_{{pv},{l0},{{{y}_{0}}},{{{q}_{0}}}}=66.6666666666667\]
\[\displaystyle {\mathbf{{opr}}}_{{pv},{l0},{{{y}_{0}}},{{{q}_{1}}}}=88.88888888888894\]
\[\displaystyle {\mathbf{{opr}}}_{{pv},{l0},{{{y}_{0}}},{{{q}_{2}}}}=100.00000000000006\]
\[\displaystyle {\mathbf{{opr}}}_{{pv},{l0},{{{y}_{0}}},{{{q}_{3}}}}=77.77777777777781\]
\[\displaystyle {\mathbf{{opr}}}_{{pv},{l0},{{{y}_{0}}}}=333.33333333333354\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.charge},{l0},{{{y}_{0}}}}=27.160493827160423\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.charge},{l0},{{{y}_{0}}},{{{q}_{0}}}}=6.882716049382552\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.charge},{l0},{{{y}_{0}}},{{{q}_{1}}}}=20.27777777777787\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.charge},{l0},{{{y}_{0}}},{{{q}_{2}}}}=0.0\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.charge},{l0},{{{y}_{0}}},{{{q}_{3}}}}=0.0\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.discharge},{l0},{{{y}_{0}}}}=24.44444444444438\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.discharge},{l0},{{{y}_{0}}},{{{q}_{0}}}}=0.0\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.discharge},{l0},{{{y}_{0}}},{{{q}_{1}}}}=0.0\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.discharge},{l0},{{{y}_{0}}},{{{q}_{2}}}}=24.44444444444438\]
\[\displaystyle {\mathbf{{opr}}}_{{lii.discharge},{l0},{{{y}_{0}}},{{{q}_{3}}}}=0.0\]
\[\displaystyle {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}},{\mathbf{{cap}}},{wf}}=99399100.0\]
\[\displaystyle {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}},{\mathbf{{opr}}},{wf}}=15788.888888888889\]
\[\displaystyle {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}},{\mathbf{{cap}}},{pv}}=143904600.0000001\]
\[\displaystyle {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}},{\mathbf{{opr}}},{pv}}=30000000.00000002\]
\[\displaystyle {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}},{\mathbf{{icap}}},{lii.stored}}=36493219.75308632\]
\[\displaystyle {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}},{\mathbf{{inv}}},{lii.stored}}=68086.41975308595\]
\[\displaystyle {\mathbf{spend}}_{{usd},{l0},{{{y}_{0}}},{\mathbf{{cons}}},{cement}}=1770518.5185185184\]
\[\displaystyle {\mathbf{{icap}}}_{{lii.stored},{l0},{{{y}_{0}}}}=27.160493827160423\]
\[\displaystyle {\mathbf{{\breve{{icap}}}}}_{{lii.stored},{l0},{{{y}_{0}}}}=1.0\]
\[\displaystyle {\mathbf{{inv}}}_{{lii.stored},{l0},{{{y}_{0}}}}=34.043209876542974\]
\[\displaystyle {\mathbf{{inv}}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{0}}}}=6.882716049382552\]
\[\displaystyle {\mathbf{{inv}}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{1}}}}=27.160493827160423\]
\[\displaystyle {\mathbf{{inv}}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{2}}}}=0.0\]
\[\displaystyle {\mathbf{{inv}}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{3}}}}=0.0\]
\[\displaystyle {\mathbf{emit}}_{{gwp},{l0},{{{y}_{0}}},{\mathbf{{cap}}},{wf}}=100000.0\]
\[\displaystyle {\mathbf{emit}}_{{gwp},{l0},{{{y}_{0}}},{\mathbf{{cap}}},{pv}}=200000.00000000012\]
\[\displaystyle {\mathbf{emit}}_{{gwp},{l0},{{{y}_{0}}},{\mathbf{{icap}}},{lii.stored}}=81481.48148148127\]
\[\displaystyle {\mathbf{emit}}_{{gwp},{l0},{{{y}_{0}}},{\mathbf{{cons}}},{cement}}=93733.33333333333\]
\[\displaystyle {\mathbf{emit}}_{{gwp},{l0},{{{y}_{0}}}}=475214.8148148147\]
\[\displaystyle {\mathbf{use}}_{{cement},{l0},{{{y}_{0}}},{\mathbf{{cap}}},{wf}}=40000.0\]
\[\displaystyle {\mathbf{use}}_{{cement},{l0},{{{y}_{0}}},{\mathbf{{cap}}},{pv}}=56000.00000000003\]
\[\displaystyle {\mathbf{use}}_{{cement},{l0},{{{y}_{0}}},{\mathbf{{icap}}},{lii.stored}}=8148.148148148127\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{0}}},{\mathbf{{opr}}},{wf}}=100.0\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{1}}},{\mathbf{{opr}}},{wf}}=88.8888888888889\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{2}}},{\mathbf{{opr}}},{wf}}=55.55555555555556\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{3}}},{\mathbf{{opr}}},{wf}}=77.77777777777777\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{0}}},{\mathbf{{opr}}},{pv}}=66.6666666666667\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{1}}},{\mathbf{{opr}}},{pv}}=88.88888888888894\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{2}}},{\mathbf{{opr}}},{pv}}=100.00000000000006\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{3}}},{\mathbf{{opr}}},{pv}}=77.77777777777781\]
\[\displaystyle {\mathbf{prod}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{0}}},{\mathbf{{opr}}},{lii.charge}}=6.882716049382552\]
\[\displaystyle {\mathbf{prod}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{1}}},{\mathbf{{opr}}},{lii.charge}}=20.27777777777787\]
\[\displaystyle {\mathbf{prod}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{2}}},{\mathbf{{opr}}},{lii.charge}}=0.0\]
\[\displaystyle {\mathbf{prod}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{3}}},{\mathbf{{opr}}},{lii.charge}}=0.0\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{0}}},{\mathbf{{opr}}},{lii.discharge}}=0.0\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{1}}},{\mathbf{{opr}}},{lii.discharge}}=0.0\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{2}}},{\mathbf{{opr}}},{lii.discharge}}=24.44444444444438\]
\[\displaystyle {\mathbf{prod}}_{{power},{l0},{{{y}_{0}}},{{{q}_{3}}},{\mathbf{{opr}}},{lii.discharge}}=0.0\]
\[\displaystyle {\mathbf{{expd}}}_{{wind},{l0},{{{y}_{0}}},{\mathbf{{opr}}},{wf}}=322.22222222222223\]
\[\displaystyle {\mathbf{{expd}}}_{{solar},{l0},{{{y}_{0}}},{{{q}_{0}}},{\mathbf{{opr}}},{pv}}=66.6666666666667\]
\[\displaystyle {\mathbf{{expd}}}_{{solar},{l0},{{{y}_{0}}},{{{q}_{1}}},{\mathbf{{opr}}},{pv}}=88.88888888888894\]
\[\displaystyle {\mathbf{{expd}}}_{{solar},{l0},{{{y}_{0}}},{{{q}_{2}}},{\mathbf{{opr}}},{pv}}=100.00000000000006\]
\[\displaystyle {\mathbf{{expd}}}_{{solar},{l0},{{{y}_{0}}},{{{q}_{3}}},{\mathbf{{opr}}},{pv}}=77.77777777777781\]
\[\displaystyle {\mathbf{{expd}}}_{{power},{l0},{{{y}_{0}}},{{{q}_{0}}},{\mathbf{{opr}}},{lii.charge}}=6.882716049382552\]
\[\displaystyle {\mathbf{{expd}}}_{{power},{l0},{{{y}_{0}}},{{{q}_{1}}},{\mathbf{{opr}}},{lii.charge}}=20.27777777777787\]
\[\displaystyle {\mathbf{{expd}}}_{{power},{l0},{{{y}_{0}}},{{{q}_{2}}},{\mathbf{{opr}}},{lii.charge}}=0.0\]
\[\displaystyle {\mathbf{{expd}}}_{{power},{l0},{{{y}_{0}}},{{{q}_{3}}},{\mathbf{{opr}}},{lii.charge}}=0.0\]
\[\displaystyle {\mathbf{{expd}}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{0}}},{\mathbf{{opr}}},{lii.discharge}}=0.0\]
\[\displaystyle {\mathbf{{expd}}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{1}}},{\mathbf{{opr}}},{lii.discharge}}=0.0\]
\[\displaystyle {\mathbf{{expd}}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{2}}},{\mathbf{{opr}}},{lii.discharge}}=27.160493827160423\]
\[\displaystyle {\mathbf{{expd}}}_{{lii.stored},{l0},{{{y}_{0}}},{{{q}_{3}}},{\mathbf{{opr}}},{lii.discharge}}=0.0\]