# Linearization of product of multiple binary decision varibales

 0 Hi, I want to linearize an objective function like Z=W.X.Y.Z, where W, X, Y, and Z are binary decision variables. Any suggestion would be appreciated. Thanks, asked 15 May '18, 17:52 ESN 11●2 accept rate: 0%

 0 Let's use $$Q$$ for the product. (You have two $$Z$$s in the question.) You need five constraints: $$Q\le W$$ $$Q\le X$$ $$Q\le Y$$ $$Q\le Z$$ $$Q \ge W + X + Y + Z - 3$$ answered 15 May '18, 18:04 Paul Rubin ♦♦ 14.6k●4●12 accept rate: 19%
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