Recent Advances in Mixed-Integer Linear Programming (MILP)

Mixed-integer linear programming (MILP) has become a cornerstone of operations research, thanks to the enhanced efficiency of modern solvers. These solvers can now find globally optimal solutions in seconds for problems previously intractable a decade ago. This versatility has led to successful applications across transportation, logistics, supply chain management, revenue management, finance, telecommunications, and manufacturing. Despite this success, many challenges remain, and MILP is a vibrant area of ongoing research. This article surveys the most significant advancements in MILP solution methods, focusing on computational aspects and recent practical performance improvements, emphasizing studies with computational experiments. The survey is structured around branch-and-cut methods, Dantzig-Wolfe decomposition, and Benders decomposition, concluding with a discussion of ongoing challenges and future directions.