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There are three projects.  Binary variablesX1, X2, and X3are defined as follows: Xi=     1 if project i is...

There are three projects.  Binary variablesX1, X2, and X3are defined as follows:

Xi=     1 if project i is selected, and

Xi=     0 if project i is not selected,           for i = 1, 2, 3.

5. Write a constraint to represent: “Project 2 and project 3 must go together.  That is, it is not allowed to select one while deselect the other”.

6. Write a constraint to represent: “The three projects can not be all selected.  There must be at least one that is not selected”.

7. Write a constraint to represent: “If project 2 is selected, then project 1 must be selected; but if project 2 is not selected, then there is no restriction on project 1”.

8. (Bonus question) Write a constraint to represent: “If project 1 is not selected, then project 2 must not be selected; but if project 1 is selected, then there is no restriction on project 2”.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

5) A contraint to represent that projects 2 and 3 both need to be selected if any one of them is selected by :

(X2 - X3) = 0 i.e X2= X3

6) This also can be represented by a lot of constraints, we'll see two such contraints:

X1*X2*X3= 0 , hence with constraint we have rules out the possibility of X1=X2=X3=1 (i.e the case where all the projects are selected)

OR

X1+X2+X3 <3

7) X2 * (1 - X1) = 0 , Hence with this constraint we have successfully ruled out the case X2=1 but X1 = 0 (i.e project 2 was selected but project 1 wasn't)

8) (1 - X1) * X2 = 0 , Hence when X1 is 0 then X2 has to be equal to zero but if X1 =1 then X2 can take any value.

Thank You. Do leave a thumbs up if this helped. You can comment for further queries

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