Consider four binary decision variables: x1, x2, X3, X4 E {0,1}. Suppose that the sum of these decision variables must be equal to an odd number. For instance, setting x, = 1, x, = 1, x3 = 1, and x4 = 0 satisfies the condition while setting x, = 1, x, = 1, x3 = 0, and x4 = 0 does not satisfy the condition. Derive a system of constraints, and potentially additional decision variables, that would eliminate all possible cases that do not satisfy the aforementioned condition.

Question

It's Integer programming question. 

Consider four binary decision variables: x1, x2, X3, X4 E {0,1}. Suppose that the sum of these decision
variables must be equal to an odd number. For instance, setting x, = 1, x, = 1, x3 = 1, and x4 = 0 satisfies
the condition while setting x, = 1, x, = 1, x3 = 0, and x4 = 0 does not satisfy the condition. Derive a
system of constraints, and potentially additional decision variables, that would eliminate all possible cases
that do not satisfy the aforementioned condition.
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Transcribed Image Text

Consider four binary decision variables: x1, x2, X3, X4 E {0,1}. Suppose that the sum of these decision variables must be equal to an odd number. For instance, setting x, = 1, x, = 1, x3 = 1, and x4 = 0 satisfies the condition while setting x, = 1, x, = 1, x3 = 0, and x4 = 0 does not satisfy the condition. Derive a system of constraints, and potentially additional decision variables, that would eliminate all possible cases that do not satisfy the aforementioned condition.

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