What is wrong with these constraints ?.
Clash Royale CLAN TAG#URR8PPP
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I have written two constraints for Mixed integer linear problem. I am working on the scheduling problem i.e., Scheduling of hybrid appliances.
For example, the washing machine is appliance indicated by i, which has set of the task like washing, rinsing and spinning etc., indicated by j. Here we divided the 24 hours into 96-time slots each time slot has 15 min indicated by k.
The constraint 1. Says that the tasks of the task of the appliance have to exclusive. It means they should not overlap with each other.
$X_k,u,i,j + Y_k,u,i,j + Z_k,u,i,j$ $leq$ $X_k,u,i,j-1 + Y_k,u,i,j-1 + Z_k,u,i,j-1$ --------------- 1
$j in 2,. . .n_i$
The constraint 2 says that the task of the appliances has to sequential and operate continuously without any interruption.
$sum_k=t^t+H_i -1 sum_j=1^n_i X_k,u,i,j + Y_k,u,i,j + Z_k,u,i,j geq 1$ --------------- 2
$forall i in N$,
$j in 1,. . .n_i$,
$k = 1,2,. . .96$,
$u in 1,2,3. .. 50$,
$X_k,u,i,j, Y_k,u,i,j, Z_k,u,i,j in 0,1$
$X_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by electricity or not; 1 = task processed; 0 = not processed
$Y_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by natural gas or not; 1 = task processed; 0 = not processed
$Z_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by hot water or not; 1 = task processed; 0 = not processed
i index of the appliance.
j index of the task of the appliance.
k index of the time slot(1time slot = 15 min).
u index of each home.
$H_i$ is the operation time of the appliance i.
Do both constraints satisfies my condition?.
It would be great if somebody validate this.
algorithms linear-programming operations-research constraint-programming mixed-integer-programming
asked Aug 26 at 13:37
PraveenRB
103
add a comment |Â
up vote
-2
down vote
favorite
I have written two constraints for Mixed integer linear problem. I am working on the scheduling problem i.e., Scheduling of hybrid appliances.
For example, the washing machine is appliance indicated by i, which has set of the task like washing, rinsing and spinning etc., indicated by j. Here we divided the 24 hours into 96-time slots each time slot has 15 min indicated by k.
The constraint 1. Says that the tasks of the task of the appliance have to exclusive. It means they should not overlap with each other.
$X_k,u,i,j + Y_k,u,i,j + Z_k,u,i,j$ $leq$ $X_k,u,i,j-1 + Y_k,u,i,j-1 + Z_k,u,i,j-1$ --------------- 1
$j in 2,. . .n_i$
The constraint 2 says that the task of the appliances has to sequential and operate continuously without any interruption.
$sum_k=t^t+H_i -1 sum_j=1^n_i X_k,u,i,j + Y_k,u,i,j + Z_k,u,i,j geq 1$ --------------- 2
$forall i in N$,
$j in 1,. . .n_i$,
$k = 1,2,. . .96$,
$u in 1,2,3. .. 50$,
$X_k,u,i,j, Y_k,u,i,j, Z_k,u,i,j in 0,1$
$X_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by electricity or not; 1 = task processed; 0 = not processed
$Y_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by natural gas or not; 1 = task processed; 0 = not processed
$Z_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by hot water or not; 1 = task processed; 0 = not processed
i index of the appliance.
j index of the task of the appliance.
k index of the time slot(1time slot = 15 min).
u index of each home.
$H_i$ is the operation time of the appliance i.
Do both constraints satisfies my condition?.
It would be great if somebody validate this.
algorithms linear-programming operations-research constraint-programming mixed-integer-programming
asked Aug 26 at 13:37
PraveenRB
103
I have a question about your indices. For instance, at $X_t,i,j$ you mention the slot $k$ but $k$ doesn´t appear at the index. On the other hand the index $t$ is not mentioned in the definition. For me it is confusing.
– callculus
Aug 26 at 13:43
@callculus Sorry, I have edited the question.
– PraveenRB
Aug 26 at 13:46
add a comment |Â
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
I have written two constraints for Mixed integer linear problem. I am working on the scheduling problem i.e., Scheduling of hybrid appliances.
For example, the washing machine is appliance indicated by i, which has set of the task like washing, rinsing and spinning etc., indicated by j. Here we divided the 24 hours into 96-time slots each time slot has 15 min indicated by k.
The constraint 1. Says that the tasks of the task of the appliance have to exclusive. It means they should not overlap with each other.
$X_k,u,i,j + Y_k,u,i,j + Z_k,u,i,j$ $leq$ $X_k,u,i,j-1 + Y_k,u,i,j-1 + Z_k,u,i,j-1$ --------------- 1
$j in 2,. . .n_i$
The constraint 2 says that the task of the appliances has to sequential and operate continuously without any interruption.
$sum_k=t^t+H_i -1 sum_j=1^n_i X_k,u,i,j + Y_k,u,i,j + Z_k,u,i,j geq 1$ --------------- 2
$forall i in N$,
$j in 1,. . .n_i$,
$k = 1,2,. . .96$,
$u in 1,2,3. .. 50$,
$X_k,u,i,j, Y_k,u,i,j, Z_k,u,i,j in 0,1$
$X_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by electricity or not; 1 = task processed; 0 = not processed
$Y_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by natural gas or not; 1 = task processed; 0 = not processed
$Z_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by hot water or not; 1 = task processed; 0 = not processed
i index of the appliance.
j index of the task of the appliance.
k index of the time slot(1time slot = 15 min).
u index of each home.
$H_i$ is the operation time of the appliance i.
Do both constraints satisfies my condition?.
It would be great if somebody validate this.
algorithms linear-programming operations-research constraint-programming mixed-integer-programming
asked Aug 26 at 13:37
PraveenRB
103
I have written two constraints for Mixed integer linear problem. I am working on the scheduling problem i.e., Scheduling of hybrid appliances.
For example, the washing machine is appliance indicated by i, which has set of the task like washing, rinsing and spinning etc., indicated by j. Here we divided the 24 hours into 96-time slots each time slot has 15 min indicated by k.
The constraint 1. Says that the tasks of the task of the appliance have to exclusive. It means they should not overlap with each other.
$X_k,u,i,j + Y_k,u,i,j + Z_k,u,i,j$ $leq$ $X_k,u,i,j-1 + Y_k,u,i,j-1 + Z_k,u,i,j-1$ --------------- 1
$j in 2,. . .n_i$
The constraint 2 says that the task of the appliances has to sequential and operate continuously without any interruption.
$sum_k=t^t+H_i -1 sum_j=1^n_i X_k,u,i,j + Y_k,u,i,j + Z_k,u,i,j geq 1$ --------------- 2
$forall i in N$,
$j in 1,. . .n_i$,
$k = 1,2,. . .96$,
$u in 1,2,3. .. 50$,
$X_k,u,i,j, Y_k,u,i,j, Z_k,u,i,j in 0,1$
$X_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by electricity or not; 1 = task processed; 0 = not processed
$Y_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by natural gas or not; 1 = task processed; 0 = not processed
$Z_k,u,i,j$ indicates whether task j of appliance i at time slot k processed by hot water or not; 1 = task processed; 0 = not processed
i index of the appliance.
j index of the task of the appliance.
k index of the time slot(1time slot = 15 min).
u index of each home.
$H_i$ is the operation time of the appliance i.
Do both constraints satisfies my condition?.
It would be great if somebody validate this.
algorithms linear-programming operations-research constraint-programming mixed-integer-programming
asked Aug 26 at 13:37
PraveenRB
103
edited Aug 29 at 7:42
asked Aug 26 at 13:37
PraveenRB
103
asked Aug 26 at 13:37
PraveenRB
103
asked Aug 26 at 13:37
PraveenRB
103
103
I have a question about your indices. For instance, at $X_t,i,j$ you mention the slot $k$ but $k$ doesn´t appear at the index. On the other hand the index $t$ is not mentioned in the definition. For me it is confusing.
– callculus
Aug 26 at 13:43
@callculus Sorry, I have edited the question.
– PraveenRB
Aug 26 at 13:46
add a comment |Â
I have a question about your indices. For instance, at $X_t,i,j$ you mention the slot $k$ but $k$ doesn´t appear at the index. On the other hand the index $t$ is not mentioned in the definition. For me it is confusing.
– callculus
Aug 26 at 13:43
@callculus Sorry, I have edited the question.
– PraveenRB
Aug 26 at 13:46
I have a question about your indices. For instance, at $X_t,i,j$ you mention the slot $k$ but $k$ doesn´t appear at the index. On the other hand the index $t$ is not mentioned in the definition. For me it is confusing.
– callculus
Aug 26 at 13:43
I have a question about your indices. For instance, at $X_t,i,j$ you mention the slot $k$ but $k$ doesn´t appear at the index. On the other hand the index $t$ is not mentioned in the definition. For me it is confusing.
– callculus
Aug 26 at 13:43
@callculus Sorry, I have edited the question.
– PraveenRB
Aug 26 at 13:46
@callculus Sorry, I have edited the question.
– PraveenRB
Aug 26 at 13:46
add a comment |Â
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I have a question about your indices. For instance, at $X_t,i,j$ you mention the slot $k$ but $k$ doesn´t appear at the index. On the other hand the index $t$ is not mentioned in the definition. For me it is confusing.
– callculus
Aug 26 at 13:43
@callculus Sorry, I have edited the question.
– PraveenRB
Aug 26 at 13:46