In a BIP problem with 2 mutually exclusive alternatives, x1 and x2, the following constraint needs to be added to the formulation if one alternative must be chosen:
A) x1 + x2 ≤ 1.
B) x1 + x2 = 1.
C) x1 - x2 ≤ 1.
D) x1- x2 = 1.
E) None of the choices is correct.

Question

Quizplus · Accepted Answer

The constraint x1 + x2 = 1 ensures that only one of the alternatives can be chosen, as the sum of their binary variables must be equal to 1. Constraint A is not sufficient, as x1 and x2 could both be 0. Constraints C and D do not necessarily ensure that one alternative must be chosen, as x1-x2 could equal 0 or -1.

In a BIP Problem with 2 Mutually Exclusive Alternatives, X1