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Objective function formulation for MILP problem.
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I am trying to make the problem formulation using the MILP.
The objective of the problem is to schedule the appliance based on the time slot and operation mode (kind of energy it uses) with respect to minimize the CO2 emission of the house.
The house includes a set of appliances some of them use electricity for its operation, some use Natural gas and some use Hot water and electricity both for its operation. For instance, a washing machine uses electricity to heat the hot water or it can use hot water directly from the hot water storage tank.
Each appliance denoted by i, each appliance has subtasks denoted by j. 24 hours a day is divided into 96 slots, each slot represents 15 minutes.
I have introduced 3 binary decision variable to create an objective function.
$x_k,i,j^electricity$ indicates whether subtask j of appliance i at time slot k processed by electricity or not. 1 = processed, 0 = not processed.
$y_k,i,j^gas$ indicates whether subtask j of appliance i at time slot k processed by gas or not. 1 = processed, 0 = not processed.
$z_k,i,j^hotwater$ indicates whether subtask j of appliance i at time slot k processed by hot water or not. 1 = processed, 0 = not processed.
objective function:
$$sum_k=1^96sum_i=1^Nsum_j=1^n_i E_k,i,j^electricity.P_k,i,j.x_k,i,j^electricity + E_k,i,j^gas [G_k,i,j.y_k,i,j^gas + H_k,i,j.z_k,i,j^hotwater] $$
where,
E_k,i,j^electricity co2 emission produced by electricity.
P_k,i,j.x_k,i,j amount of electricity used by appliances.
E_k,i,j^gas co2 emission produced by natural gas.
G_k,i,j amount of natural gas used.
H_k,i,j amount of hot water used.
Here i am producing hot water from CHP, so if we use hot water in the appliances it indirectly using the gas.
I want to know whether this objective function correct or not. I am still planning to write constraints.
It would be great if some one guide me.
optimization linear-programming mixed-integer-programming
asked Aug 1 at 13:38
praveenkumar beedanal
11
add a comment |Â
up vote
-1
down vote
favorite
I am trying to make the problem formulation using the MILP.
The objective of the problem is to schedule the appliance based on the time slot and operation mode (kind of energy it uses) with respect to minimize the CO2 emission of the house.
The house includes a set of appliances some of them use electricity for its operation, some use Natural gas and some use Hot water and electricity both for its operation. For instance, a washing machine uses electricity to heat the hot water or it can use hot water directly from the hot water storage tank.
Each appliance denoted by i, each appliance has subtasks denoted by j. 24 hours a day is divided into 96 slots, each slot represents 15 minutes.
I have introduced 3 binary decision variable to create an objective function.
$x_k,i,j^electricity$ indicates whether subtask j of appliance i at time slot k processed by electricity or not. 1 = processed, 0 = not processed.
$y_k,i,j^gas$ indicates whether subtask j of appliance i at time slot k processed by gas or not. 1 = processed, 0 = not processed.
$z_k,i,j^hotwater$ indicates whether subtask j of appliance i at time slot k processed by hot water or not. 1 = processed, 0 = not processed.
objective function:
$$sum_k=1^96sum_i=1^Nsum_j=1^n_i E_k,i,j^electricity.P_k,i,j.x_k,i,j^electricity + E_k,i,j^gas [G_k,i,j.y_k,i,j^gas + H_k,i,j.z_k,i,j^hotwater] $$
where,
E_k,i,j^electricity co2 emission produced by electricity.
P_k,i,j.x_k,i,j amount of electricity used by appliances.
E_k,i,j^gas co2 emission produced by natural gas.
G_k,i,j amount of natural gas used.
H_k,i,j amount of hot water used.
Here i am producing hot water from CHP, so if we use hot water in the appliances it indirectly using the gas.
I want to know whether this objective function correct or not. I am still planning to write constraints.
It would be great if some one guide me.
optimization linear-programming mixed-integer-programming
asked Aug 1 at 13:38
praveenkumar beedanal
11
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I am trying to make the problem formulation using the MILP.
The objective of the problem is to schedule the appliance based on the time slot and operation mode (kind of energy it uses) with respect to minimize the CO2 emission of the house.
The house includes a set of appliances some of them use electricity for its operation, some use Natural gas and some use Hot water and electricity both for its operation. For instance, a washing machine uses electricity to heat the hot water or it can use hot water directly from the hot water storage tank.
Each appliance denoted by i, each appliance has subtasks denoted by j. 24 hours a day is divided into 96 slots, each slot represents 15 minutes.
I have introduced 3 binary decision variable to create an objective function.
$x_k,i,j^electricity$ indicates whether subtask j of appliance i at time slot k processed by electricity or not. 1 = processed, 0 = not processed.
$y_k,i,j^gas$ indicates whether subtask j of appliance i at time slot k processed by gas or not. 1 = processed, 0 = not processed.
$z_k,i,j^hotwater$ indicates whether subtask j of appliance i at time slot k processed by hot water or not. 1 = processed, 0 = not processed.
objective function:
$$sum_k=1^96sum_i=1^Nsum_j=1^n_i E_k,i,j^electricity.P_k,i,j.x_k,i,j^electricity + E_k,i,j^gas [G_k,i,j.y_k,i,j^gas + H_k,i,j.z_k,i,j^hotwater] $$
where,
E_k,i,j^electricity co2 emission produced by electricity.
P_k,i,j.x_k,i,j amount of electricity used by appliances.
E_k,i,j^gas co2 emission produced by natural gas.
G_k,i,j amount of natural gas used.
H_k,i,j amount of hot water used.
Here i am producing hot water from CHP, so if we use hot water in the appliances it indirectly using the gas.
I want to know whether this objective function correct or not. I am still planning to write constraints.
It would be great if some one guide me.
optimization linear-programming mixed-integer-programming
asked Aug 1 at 13:38
praveenkumar beedanal
11
I am trying to make the problem formulation using the MILP.
The objective of the problem is to schedule the appliance based on the time slot and operation mode (kind of energy it uses) with respect to minimize the CO2 emission of the house.
The house includes a set of appliances some of them use electricity for its operation, some use Natural gas and some use Hot water and electricity both for its operation. For instance, a washing machine uses electricity to heat the hot water or it can use hot water directly from the hot water storage tank.
Each appliance denoted by i, each appliance has subtasks denoted by j. 24 hours a day is divided into 96 slots, each slot represents 15 minutes.
I have introduced 3 binary decision variable to create an objective function.
$x_k,i,j^electricity$ indicates whether subtask j of appliance i at time slot k processed by electricity or not. 1 = processed, 0 = not processed.
$y_k,i,j^gas$ indicates whether subtask j of appliance i at time slot k processed by gas or not. 1 = processed, 0 = not processed.
$z_k,i,j^hotwater$ indicates whether subtask j of appliance i at time slot k processed by hot water or not. 1 = processed, 0 = not processed.
objective function:
$$sum_k=1^96sum_i=1^Nsum_j=1^n_i E_k,i,j^electricity.P_k,i,j.x_k,i,j^electricity + E_k,i,j^gas [G_k,i,j.y_k,i,j^gas + H_k,i,j.z_k,i,j^hotwater] $$
where,
E_k,i,j^electricity co2 emission produced by electricity.
P_k,i,j.x_k,i,j amount of electricity used by appliances.
E_k,i,j^gas co2 emission produced by natural gas.
G_k,i,j amount of natural gas used.
H_k,i,j amount of hot water used.
Here i am producing hot water from CHP, so if we use hot water in the appliances it indirectly using the gas.
I want to know whether this objective function correct or not. I am still planning to write constraints.
It would be great if some one guide me.
optimization linear-programming mixed-integer-programming
asked Aug 1 at 13:38
praveenkumar beedanal
11
asked Aug 1 at 13:38
praveenkumar beedanal
11
asked Aug 1 at 13:38
praveenkumar beedanal
11
asked Aug 1 at 13:38
praveenkumar beedanal
11
11
add a comment |Â
add a comment |Â
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