How to compute VRP by considering MTZ subtour constraints?

Hi,

I am doing thesis on VRP and so far I am using bintprog (excluding MTZ subtour constraint). Everything that I have computed is based on binary only. MTZ constraints are as follow:

u1k=0                   for all k
qi<=uik<=C              for all i-idepot and for all k
uik-ujk+xijk.C<=C-qj    for all i-idepot

MTZ constraints are integer constraints unlike the other constraints which are binary. Has anyone done this before? What optimization tool that I can use to solve this problem? Cheers.

[Walter Roberson]

Is there a difference between a "binary" constraint compared to an "integer" that is constrained to 0 or 1 ?

[Brillian]

The binary part of the constraint (not included in the question) is the xijk variables (only takes 0s or 1s). Variable uik on the other hand can be integer that ranges from qi to C. Where qi is the demand of customers and C is the capacity of the trucks.

Answer 1

[Walter Roberson]

Have a look at this example: http://www.mathworks.com/help/optim/ug/binary-integer-programming-example.html as it shows representation of integer values in terms of binary.

[LJ]

people really need to stop posting links as solution.