A class of polynomially solvable 0–1 programming problems and an application

It is well known that general 0–1 programming problems are NP-Complete and their optimal solutions cannot be found with polynomial-time algorithms unless P=NP. In this paper, we identify a specific class of 0–1 programming problems that is polynomially solvable, and propose two polynomial-time algorithms to find its optimal solutions. This class of 0–1 programming problems commits to a wide range of real-world industrial applications. We provide an instance of representative in the field of supply chain management.