Solving mixed integer bilinear problems using MILP Formulations

Akshay Gupte, Shabbir Ahmed, Myun Seok Cheon, Santanu Dey

Research output: Contribution to journalArticlepeer-review


In this paper, we examine a mixed integer linear programming reformulation for mixed integer bilinear problems where each bilinearterm 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 integer linear set. The effectiveness of this reformulation and associated facet-defining inequalities are computationally evaluated on five classes of instances.

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Original languageEnglish
Pages (from-to)721-744
Number of pages24
JournalSiam journal on optimization
Issue number2
Publication statusPublished - 18 Apr 2013


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