Hello,

I am currently working on solving a University Examination Timetabling Problem (UETP) using the Binary Integer Programming (BIP) method in AIMMS. My model includes two soft constraints, where preference values are restricted to integers from 1 to 5 (i.e., 5, 4, 3, 2, 1).

After running the model in AIMMS, I obtained the following results:

• Best LP Bound: 4080.487042

• Best Solution: 4041

• Gap: 0.98%

From my understanding:

• The Best LP Bound represents the theoretical lower bound from the linear relaxation of the integer program.

• The Best Solution is the best feasible (integer) solution found so far.

• When the Gap reaches 0%, the Best Solution should equal the Best LP Bound.

My question is:
Since I am solving a binary integer problem, how is it possible that when the gap reaches 0%, the Best Solution appears as a decimal value (e.g., 4080.487042)? Shouldn’t the solution remain strictly integer (since it’s binary), and therefore the objective value also be an integer?

Any clarification would be greatly appreciated. Thank you!