The Quadratic Assignment Problem formulated as an integer program: Minimize $$\sum_{i=1}^n\sum_{j=1}^nc_{ij} x_{ij} + \sum_{i=1}^n\sum_{j=1}^n\sum_{k=1}^n\sum_{l=1}^n c_{ijkl}x_{ij}x_{kl}$$ subject to $$\sum_{i=1}^n x_{ij} = 1 \quad \forall j=1,\ldots,n,$$ $$\sum_{j=1}^n x_{ij} = 1 \quad \forall i=1,\ldots,n,$$ $$x_{ij}\in{0,1}\quad \forall i,j=1,\ldots,n.$$ A simple and natural linearization: Minimize $$\sum_{i=1}^n\sum_{j=1}^nc_{ij} x_{ij} + \sum_{i=1}^n\sum_{j=1}^n\sum_{k=1}^n\sum_{l=1}^n c_{ijkl}y_{ijkl}$$ subject to $$\sum_{i=1}^n x_{ij} = 1 \quad \forall j=1,\ldots,n,$$ $$\sum_{j=1}^n x_{ij} = 1 \quad \forall i=1,\ldots,n,$$ $$y_{ijkl} \le x_{ij} \quad \forall i,j,k,l=1,\ldots,n,$$ $$ x_{ij} + x_{kl} \le 1+y_{ijkl} \quad \forall i,j,k,l=1,\ldots,n,$$ $$ y_{ijkl} = y_{klij} \quad \forall i,j,k,l=1,\ldots,n,$$ $$x_{ij},y_{ijkl}\in{0,1}\quad \forall i,j,k,l=1,\ldots,n.$$ My question is: Has this linearization already been studied in the literature? I did not see it in any papers (this one for example). asked 02 Dec '15, 04:23 f10w 
It looks related to http://pubsonline.informs.org/doi/abs/10.1287/opre.43.5.781?journalCode=opre answered 03 Dec '15, 03:20 Erling_MOSEK Thanks but I don't see the considered linearization being mentioned in that paper.
(09 Dec '15, 14:20)
f10w

@Rob Pratt: Your comment answers my question. Please put it as an answer so that I can accept it. Thanks.