MIT15_053S13_iprefguide

# Xi xj 1 if item i is not selected then item j is not

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Unformatted text preview: If item i is selected, then item j is not selected. xi + xj : 1 If item i is not selected, then item j is not selected. -x i + x j : 0 At most one of items i, j, and k are selected. xi + xj + xk : 1 At most two of items i, j, and k are selected. xi + xj + xk : 2 Exactly one of items i, j, and k are selected. xi + xj + xk = 1 At least one of items i, j and k are selected. xi + xj + xk � 1 Table 2. Simple constraints involving two or three binary variables. Restricting a variable to take on one of several values. Suppose that we wanted to restrict x to be one of the elements {4, 8, 13}. This is accomplished as follows. x = 4 w1 + 8 w2 + 13 w 3 w 1 + w 2 + w 3 = 1 wi E {0, 1} for i = 1 to 4. If we wanted to restrict x to be one of the elements {0, 4, 8, 13}, it suffices to use the above formulation with the equality constraint changed to "w1 + w2 + w3 : 1." Section 4. Other logical constraints, and the big M method. Binary variables that are 1 when a constraint is satisfied. We next consider binary variables that are defined to be 1 if...
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