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6

$begingroup$

Notation

• $textsrc_h,s,textdst_h,s,textch_h,s$ are constants.




• $a_h,s,x_i,j,s$ are binary variables.




• $textwt_h,s$ are continuous variables.

Problem

beginalignmin.&qquadsum_h in Hsum_sin S(textsrc_h,s+textch_h,s+textdst_h,s+textwt_h,s)times a_h,s\texts.t.&qquadforall i,jin H,,forall sin S:textwt_j,sgeq((textsrc_i,s+textch_i,s+textwt_i,s)-textsrc_j,s)times x_i,j,sendalign

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 $textsrc_i,s < textsrc_j,s$ so how could I force $x_i,j,s = 1$ when this condition meets?

linear-programming optimization

share|improve this question

edited Aug 4 at 8:27

TheSimpliFire♦

1,98166 silver badges3838 bronze badges

asked Aug 3 at 21:18

anoop yadavanoop yadav

13255 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  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♦
  Aug 3 at 21:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  yes, you are right.
  $endgroup$
  – anoop yadav
  Aug 4 at 8:50
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In that case I will write it as an answer in case it is useful to future readers.
  $endgroup$
  – LarrySnyder610♦
  Aug 5 at 0:41
  

  
  
  
  

add a comment | 

6

$begingroup$

Notation

• $textsrc_h,s,textdst_h,s,textch_h,s$ are constants.




• $a_h,s,x_i,j,s$ are binary variables.




• $textwt_h,s$ are continuous variables.

Problem

beginalignmin.&qquadsum_h in Hsum_sin S(textsrc_h,s+textch_h,s+textdst_h,s+textwt_h,s)times a_h,s\texts.t.&qquadforall i,jin H,,forall sin S:textwt_j,sgeq((textsrc_i,s+textch_i,s+textwt_i,s)-textsrc_j,s)times x_i,j,sendalign

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 $textsrc_i,s < textsrc_j,s$ so how could I force $x_i,j,s = 1$ when this condition meets?

linear-programming optimization

share|improve this question

edited Aug 4 at 8:27

TheSimpliFire♦

1,98166 silver badges3838 bronze badges

asked Aug 3 at 21:18

anoop yadavanoop yadav

13255 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  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♦
  Aug 3 at 21:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  yes, you are right.
  $endgroup$
  – anoop yadav
  Aug 4 at 8:50
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In that case I will write it as an answer in case it is useful to future readers.
  $endgroup$
  – LarrySnyder610♦
  Aug 5 at 0:41
  

  
  
  
  

add a comment | 

$begingroup$

Notation

• $textsrc_h,s,textdst_h,s,textch_h,s$ are constants.




• $a_h,s,x_i,j,s$ are binary variables.




• $textwt_h,s$ are continuous variables.

Problem

beginalignmin.&qquadsum_h in Hsum_sin S(textsrc_h,s+textch_h,s+textdst_h,s+textwt_h,s)times a_h,s\texts.t.&qquadforall i,jin H,,forall sin S:textwt_j,sgeq((textsrc_i,s+textch_i,s+textwt_i,s)-textsrc_j,s)times x_i,j,sendalign

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 $textsrc_i,s < textsrc_j,s$ so how could I force $x_i,j,s = 1$ when this condition meets?

linear-programming optimization

share|improve this question

edited Aug 4 at 8:27

TheSimpliFire♦

1,98166 silver badges3838 bronze badges

asked Aug 3 at 21:18

anoop yadavanoop yadav

13255 bronze badges

$endgroup$

share|improve this question

edited Aug 4 at 8:27

TheSimpliFire♦

1,98166 silver badges3838 bronze badges

asked Aug 3 at 21:18

anoop yadavanoop yadav

13255 bronze badges

share|improve this question

edited Aug 4 at 8:27

TheSimpliFire♦

1,98166 silver badges3838 bronze badges

asked Aug 3 at 21:18

anoop yadavanoop yadav

13255 bronze badges

edited Aug 4 at 8:27

TheSimpliFire♦

1,98166 silver badges3838 bronze badges

edited Aug 4 at 8:27

TheSimpliFire♦

1,98166 silver badges3838 bronze badges

asked Aug 3 at 21:18

anoop yadavanoop yadav

13255 bronze badges

asked Aug 3 at 21:18

anoop yadavanoop yadav

13255 bronze badges

2 Answers
2

active

oldest

votes

5

$begingroup$

Since the $textsrc$ are constants, you know in advance whether $i$ charges before $j$, and you can just force $x_ijs=1$ in this case (via a constraint or by treating it like a constant).

share|improve this answer

answered Aug 5 at 0:42

LarrySnyder610♦LarrySnyder610

5,5871414 silver badges6464 bronze badges

$endgroup$

add a comment | 

9

$begingroup$

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.

share|improve this answer

answered Aug 3 at 21:29

SimonSimon

65222 silver badges1313 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/…
  $endgroup$
  – Dipayan Banerjee
  Aug 3 at 21:44
  

  
  
  
  

add a comment | 

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5

$begingroup$

Since the $textsrc$ are constants, you know in advance whether $i$ charges before $j$, and you can just force $x_ijs=1$ in this case (via a constraint or by treating it like a constant).

share|improve this answer

answered Aug 5 at 0:42

LarrySnyder610♦LarrySnyder610

5,5871414 silver badges6464 bronze badges

$endgroup$

add a comment | 

5

$begingroup$

Since the $textsrc$ are constants, you know in advance whether $i$ charges before $j$, and you can just force $x_ijs=1$ in this case (via a constraint or by treating it like a constant).

share|improve this answer

answered Aug 5 at 0:42

LarrySnyder610♦LarrySnyder610

5,5871414 silver badges6464 bronze badges

$endgroup$

add a comment | 

$begingroup$

Since the $textsrc$ are constants, you know in advance whether $i$ charges before $j$, and you can just force $x_ijs=1$ in this case (via a constraint or by treating it like a constant).

share|improve this answer

answered Aug 5 at 0:42

LarrySnyder610♦LarrySnyder610

5,5871414 silver badges6464 bronze badges

$endgroup$

share|improve this answer

answered Aug 5 at 0:42

LarrySnyder610♦LarrySnyder610

5,5871414 silver badges6464 bronze badges

answered Aug 5 at 0:42

LarrySnyder610♦LarrySnyder610

5,5871414 silver badges6464 bronze badges

answered Aug 5 at 0:42

LarrySnyder610♦LarrySnyder610

5,5871414 silver badges6464 bronze badges

9

$begingroup$

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.

share|improve this answer

answered Aug 3 at 21:29

SimonSimon

65222 silver badges1313 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/…
  $endgroup$
  – Dipayan Banerjee
  Aug 3 at 21:44
  

  
  
  
  

add a comment | 

9

$begingroup$

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.

share|improve this answer

answered Aug 3 at 21:29

SimonSimon

65222 silver badges1313 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/…
  $endgroup$
  – Dipayan Banerjee
  Aug 3 at 21:44
  

  
  
  
  

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.

share|improve this answer

answered Aug 3 at 21:29

SimonSimon

65222 silver badges1313 bronze badges

$endgroup$

share|improve this answer

answered Aug 3 at 21:29

SimonSimon

65222 silver badges1313 bronze badges

answered Aug 3 at 21:29

SimonSimon

65222 silver badges1313 bronze badges

answered Aug 3 at 21:29

SimonSimon

65222 silver badges1313 bronze badges