How to add Binary Variable with condition in LPWhen to use indicator constraints versus big-M approaches in solving (mixed-)integer programsFinding minimum time for vehicle to reach to its destinationReference request: how to model nonlinear regression?How to decide to write an objective function?How to handle real-world (soft) constraints in an optimization problem?Variable bounds in column generationHow to formulate this scheduling problem efficiently?What is this type of scheduling problem called?Labour Model - Resource Allocation based off Product ForecastsLinearize or approximate a square root constraintFinding minimum time for vehicle to reach to its destinationlinearization of objective function
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How to add Binary Variable with condition in LP
When to use indicator constraints versus big-M approaches in solving (mixed-)integer programsFinding minimum time for vehicle to reach to its destinationReference request: how to model nonlinear regression?How to decide to write an objective function?How to handle real-world (soft) constraints in an optimization problem?Variable bounds in column generationHow to formulate this scheduling problem efficiently?What is this type of scheduling problem called?Labour Model - Resource Allocation based off Product ForecastsLinearize or approximate a square root constraintFinding minimum time for vehicle to reach to its destinationlinearization of objective function
$begingroup$
$src_h,s$, $dst_h,s$, $ch_h,s$ are constants.
$a_h,s$, $x_i,j,s$ are binary variables.
$wt_h,s$ are continuous variables.
$mini.$
$$
sum_h in H sum_s in S (src_h,s + ch_h,s + dst_h,s + wt_h,s) times a_h,s
$$
$s.t.$
$$
forall i in H hspace0.3cm forall j in H hspace0.3cm forall s in S hspace0.3cm
$$
$$
wt_j,s geq ((src_i,s + ch_i,s+wt_i,s) - src_j,s) times x_i,j,s
$$
Now $x_i,j,s = 1$ only when vehicle $i$ charges before vehicle $j$. (Finding minimum time for vehicle to reach to its destination) for reference.
Vehicle $i$ charges before $j$ only when $src_i,s < src_j,s$ so how could I force $x_i,j,s = 1$ when this condition meets.
linear-programming optimization
asked 9 hours ago
anoop yadavanoop yadav
1104 bronze badges
$endgroup$
add a comment |
$begingroup$
$src_h,s$, $dst_h,s$, $ch_h,s$ are constants.
$a_h,s$, $x_i,j,s$ are binary variables.
$wt_h,s$ are continuous variables.
$mini.$
$$
sum_h in H sum_s in S (src_h,s + ch_h,s + dst_h,s + wt_h,s) times a_h,s
$$
$s.t.$
$$
forall i in H hspace0.3cm forall j in H hspace0.3cm forall s in S hspace0.3cm
$$
$$
wt_j,s geq ((src_i,s + ch_i,s+wt_i,s) - src_j,s) times x_i,j,s
$$
Now $x_i,j,s = 1$ only when vehicle $i$ charges before vehicle $j$. (Finding minimum time for vehicle to reach to its destination) for reference.
Vehicle $i$ charges before $j$ only when $src_i,s < src_j,s$ so how could I force $x_i,j,s = 1$ when this condition meets.
linear-programming optimization
asked 9 hours ago
anoop yadavanoop yadav
1104 bronze badges
$endgroup$
2
$begingroup$
If $src$ are constants, then you know in advance whether $i$ charges before $j$, and you can just force $x_ijs = 1$ in this case (via a constraint or via treating it like a constant) — or am I missing something?
$endgroup$
– LarrySnyder610
8 hours ago
add a comment |
$begingroup$
$src_h,s$, $dst_h,s$, $ch_h,s$ are constants.
$a_h,s$, $x_i,j,s$ are binary variables.
$wt_h,s$ are continuous variables.
$mini.$
$$
sum_h in H sum_s in S (src_h,s + ch_h,s + dst_h,s + wt_h,s) times a_h,s
$$
$s.t.$
$$
forall i in H hspace0.3cm forall j in H hspace0.3cm forall s in S hspace0.3cm
$$
$$
wt_j,s geq ((src_i,s + ch_i,s+wt_i,s) - src_j,s) times x_i,j,s
$$
Now $x_i,j,s = 1$ only when vehicle $i$ charges before vehicle $j$. (Finding minimum time for vehicle to reach to its destination) for reference.
Vehicle $i$ charges before $j$ only when $src_i,s < src_j,s$ so how could I force $x_i,j,s = 1$ when this condition meets.
linear-programming optimization
asked 9 hours ago
anoop yadavanoop yadav
1104 bronze badges
$endgroup$
$src_h,s$, $dst_h,s$, $ch_h,s$ are constants.
$a_h,s$, $x_i,j,s$ are binary variables.
$wt_h,s$ are continuous variables.
$mini.$
$$
sum_h in H sum_s in S (src_h,s + ch_h,s + dst_h,s + wt_h,s) times a_h,s
$$
$s.t.$
$$
forall i in H hspace0.3cm forall j in H hspace0.3cm forall s in S hspace0.3cm
$$
$$
wt_j,s geq ((src_i,s + ch_i,s+wt_i,s) - src_j,s) times x_i,j,s
$$
Now $x_i,j,s = 1$ only when vehicle $i$ charges before vehicle $j$. (Finding minimum time for vehicle to reach to its destination) for reference.
Vehicle $i$ charges before $j$ only when $src_i,s < src_j,s$ so how could I force $x_i,j,s = 1$ when this condition meets.
linear-programming optimization
linear-programming optimization
asked 9 hours ago
anoop yadavanoop yadav
1104 bronze badges
asked 9 hours ago
anoop yadavanoop yadav
1104 bronze badges
asked 9 hours ago
anoop yadavanoop yadav
1104 bronze badges
asked 9 hours ago
anoop yadavanoop yadav
1104 bronze badges
asked 9 hours ago
anoop yadavanoop yadav
1104 bronze badges
1104 bronze badges
2
$begingroup$
If $src$ are constants, then you know in advance whether $i$ charges before $j$, and you can just force $x_ijs = 1$ in this case (via a constraint or via treating it like a constant) — or am I missing something?
$endgroup$
– LarrySnyder610
8 hours ago
add a comment |
2
$begingroup$
If $src$ are constants, then you know in advance whether $i$ charges before $j$, and you can just force $x_ijs = 1$ in this case (via a constraint or via treating it like a constant) — or am I missing something?
$endgroup$
– LarrySnyder610
8 hours ago
2
2
$begingroup$
If $src$ are constants, then you know in advance whether $i$ charges before $j$, and you can just force $x_ijs = 1$ in this case (via a constraint or via treating it like a constant) — or am I missing something?
$endgroup$
– LarrySnyder610
8 hours ago
$begingroup$
If $src$ are constants, then you know in advance whether $i$ charges before $j$, and you can just force $x_ijs = 1$ in this case (via a constraint or via treating it like a constant) — or am I missing something?
$endgroup$
– LarrySnyder610
8 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Add two indicator constraints:
- when $x_i,j,s = 1$, the condition must be true ($i$ charges before $j$)
- when $x_i,j,s = 0$, the condition must be false ($i$ charges after $j$)
Most commercial solvers have simple APIs that allow you to add indicator constraints directly, without reformulation. For example, here's the documentation for Gurobi's addGenConstrIndicator function.
answered 9 hours ago
SimonSimon
4721 silver badge13 bronze badges
$endgroup$
4
$begingroup$
Here is an earlier OR.SE post on using indicator constraints, with answers focusing on a couple of different packages: or.stackexchange.com/questions/231/…
$endgroup$
– dxb
8 hours ago
add a comment |
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1 Answer
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oldest
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1 Answer
1
active
oldest
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active
oldest
votes
active
oldest
votes
$begingroup$
Add two indicator constraints:
- when $x_i,j,s = 1$, the condition must be true ($i$ charges before $j$)
- when $x_i,j,s = 0$, the condition must be false ($i$ charges after $j$)
Most commercial solvers have simple APIs that allow you to add indicator constraints directly, without reformulation. For example, here's the documentation for Gurobi's addGenConstrIndicator function.
answered 9 hours ago
SimonSimon
4721 silver badge13 bronze badges
$endgroup$
4
$begingroup$
Here is an earlier OR.SE post on using indicator constraints, with answers focusing on a couple of different packages: or.stackexchange.com/questions/231/…
$endgroup$
– dxb
8 hours ago
add a comment |
$begingroup$
Add two indicator constraints:
- when $x_i,j,s = 1$, the condition must be true ($i$ charges before $j$)
- when $x_i,j,s = 0$, the condition must be false ($i$ charges after $j$)
Most commercial solvers have simple APIs that allow you to add indicator constraints directly, without reformulation. For example, here's the documentation for Gurobi's addGenConstrIndicator function.
answered 9 hours ago
SimonSimon
4721 silver badge13 bronze badges
$endgroup$
4
$begingroup$
Here is an earlier OR.SE post on using indicator constraints, with answers focusing on a couple of different packages: or.stackexchange.com/questions/231/…
$endgroup$
– dxb
8 hours ago
add a comment |
$begingroup$
Add two indicator constraints:
- when $x_i,j,s = 1$, the condition must be true ($i$ charges before $j$)
- when $x_i,j,s = 0$, the condition must be false ($i$ charges after $j$)
Most commercial solvers have simple APIs that allow you to add indicator constraints directly, without reformulation. For example, here's the documentation for Gurobi's addGenConstrIndicator function.
answered 9 hours ago
SimonSimon
4721 silver badge13 bronze badges
$endgroup$
Add two indicator constraints:
- when $x_i,j,s = 1$, the condition must be true ($i$ charges before $j$)
- when $x_i,j,s = 0$, the condition must be false ($i$ charges after $j$)
Most commercial solvers have simple APIs that allow you to add indicator constraints directly, without reformulation. For example, here's the documentation for Gurobi's addGenConstrIndicator function.
answered 9 hours ago
SimonSimon
4721 silver badge13 bronze badges
answered 9 hours ago
SimonSimon
4721 silver badge13 bronze badges
answered 9 hours ago
SimonSimon
4721 silver badge13 bronze badges
answered 9 hours ago
SimonSimon
4721 silver badge13 bronze badges
4721 silver badge13 bronze badges
4
$begingroup$
Here is an earlier OR.SE post on using indicator constraints, with answers focusing on a couple of different packages: or.stackexchange.com/questions/231/…
$endgroup$
– dxb
8 hours ago
add a comment |
4
$begingroup$
Here is an earlier OR.SE post on using indicator constraints, with answers focusing on a couple of different packages: or.stackexchange.com/questions/231/…
$endgroup$
– dxb
8 hours ago
4
4
$begingroup$
Here is an earlier OR.SE post on using indicator constraints, with answers focusing on a couple of different packages: or.stackexchange.com/questions/231/…
$endgroup$
– dxb
8 hours ago
$begingroup$
Here is an earlier OR.SE post on using indicator constraints, with answers focusing on a couple of different packages: or.stackexchange.com/questions/231/…
$endgroup$
– dxb
8 hours ago
add a comment |
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$begingroup$
If $src$ are constants, then you know in advance whether $i$ charges before $j$, and you can just force $x_ijs = 1$ in this case (via a constraint or via treating it like a constant) — or am I missing something?
$endgroup$
– LarrySnyder610
8 hours ago