Solving Mixed Integer Bilinear Problems Using MILP Formulations

Akshay Gupte, Shabbir Ahmed, Myun Seok Cheon, Santanu Dey
2013 SIAM Journal on Optimization  
In this paper, we examine a mixed integer linear programming (MILP) reformulation for mixed integer bilinear problems where each bilinear term involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first replacing a general integer variable with its binary expansion and then using McCormick envelopes to linearize the resulting product of continuous and binary variables. We present the convex hull of the underlying mixed
more » ... eger linear set. The effectiveness of this reformulation and associated facet-defining inequalities are computationally evaluated on five classes of instances.
doi:10.1137/110836183 fatcat:72ipukixhzbpzfz4lbnwfwr66u