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Unformatted text preview: t to xi + x j ≤ 1 n
j =1 xj x j ∈{0,1} whenever aij = 1 (i.e., i ∈ S j ) Problem P1 for each j ∈{1,..., n}. Section 2. Modular arithmetic.
In this very brief section, we show how to constrain a variable x to be odd or even, and we show how
to constraint x to be a mod(b). (That is, there is an integer q such that a + qb = x.) In each case, we
need to add a new variable w, where w � 0 and integer.
Constraint. IP Constraint x is odd. x  2w = 1. x is even. x  2w = 0. x = a (mod b) x  bw = a. Table 1. Modular arithmetic formulations. Section 3. Simple logical constraints.
Here we address different logical constraints that can be transformed into integer programming
constraints.
In the first set, we describe the logical constraints in terms of selection of items from a subset. Logical Constraint. IP Constraint If item i is selected, then item j is also selected. xi  xj : 0 Either item i is selected or item j is selected, but not both. xi + xj = 1 Item i is selected or item j is selected or both. xi + xj � 1...
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This note was uploaded on 03/18/2014 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.
 Spring '07
 JamesOrli
 Management

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