Dr. Khatere Ghorbani-Moghadam, Dr. Reza Ghanbari, Mr. Javad Mohammadnia,
Volume 11, Issue 2 (9-2025)
Abstract
Linear programming problems with complementary linear constraints (LPCC) are widely studied in operations research and are known to be NP-hard. This paper explores a specific case of LPCC where the product of two variables must be zero, i.e., xp xm=0. This scenario frequently arises in optimization problems, particularly those involving absolute values that cannot be expressed as linear or integer programming problems. To tackle this, we will present a branch-and-bound algorithm, and we will implement the algorithm on numerical examples and compare its performance with existing methods.
