Table 3: Comparison of CP and MIP models.

InstanceCPIP
No. of variablesNo. of constraintsCPU time (s)Objective No. of variablesNo. of constraintsCPU time (s)Objective

a-11825390.1501823010.250
a-20.1750.275
a-30.11500.1150

b-133719640.550657119037.450
b-21000+751000+75
b-33.61251000+175

c-14071393716.5754693918844.475
c-25.71251000+125
c-31000+3001000+275

The instance results in bold are proved to be optimal.