A Computational approach to Convex Hull of Zero-one MIP problems with special structure

Abstract

This paper presented a new approach for implementing reformulation-linearization technique (RLT) using matrix operations. It began with employing base-2 expansions of binary variables to express extended form of the main problem and generate matrices transform. The generated matrices provided a powerful tool for implementing different level of RLT. Particularly, the new representation was efficient for deriving results of the problem with special structures. Moreover, it was employed for deriving the convex hull representation of problems with generalized upper bound (GUB) constraint and packing constraints. Finally, as an application of the proposed method, a class of competitive facility location, (1∣p)-centroid, in which two competing companies successively opened their facilities, was studied. The problem was formulated as a bi-level programming problem (BLPP) and then converted into an equivalent one-level mixed-integer linear program so that it could be solved by any MIP solver. Experimental result was reported for instances with different sizes.