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linear-programmingmixed-integer-programmingor-tools
BartKrul
BartKrul

Reputation: 647

Implementing an OR constraint in Google OR-tools?

I'm trying to solve a variant of the transportation problem with a constraint which makes me able to specify the amount of supplies a truck should take to from a certain source towards a certain destination.

For example:

Source S1 has a supply of 40.
Source S2 has a supply of 40.
Source S3 has a supply of 20.
Destination D1 has a a demand of 40.

I want to be able to make it so that demand of D1 is fulfilled by TWO suppliers who each deliver 20.

In constraint form I think this would be: 

S1D1 = 0 OR 20
S2D1 = 0 OR 20
S3D1 = 0 or 20

S1D1 + S2D1 + S3D1 = 40

But I have no idea how to implement the OR constraint in Google OR-tools. I think I have to look at a mixed integer integer solver, but I can't find any examples or documentation that would solve my problem.

Upvotes: 1

Views: 1090

Answers (1)

BartKrul
BartKrul

Reputation: 647

Erwin you are right.

I used a mixed integer solver and used the following constraints.

Constraints:

A variable is an integer and between 0 and 1 (so it's 1 or 0).

20 S1D1 + 20 S2D1 + 20 S3D1 = 40

this was a simplified example, in my problem I actually have more destinations. To make sure a source doesn't provide more than it has the following constraint was used (use 2 destinations as example, Destination 2 has a demand of 40 provided by once source):

20 S1D1 + 40 S1D2 <= 40 (repeat this for all sources)

Thanks for your help.

Upvotes: 2

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