Abstract The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from subproblems: conflict graph dual proof analysis. While detects sets contradicting variable bounds implication graph, derives linear the LP’s unboundedne...

One of important problems in supply chains management is supplier selection. In a company, there are massive data from various departments so that extracting knowledge from the company’s data is too complicated. Many researchers have solved this problem by some methods like fuzzy set theory, goal programming, multi objective programming, the liner programming, mixed integer programming, analyti...