Scheduling to Minimize the Makespan on Identical Parallel Machines: An LP-Based Algorithm

Polyhedral Combinatorics approaches have turned out to be successful computational tools in many hard Combinatorial Optimization problems. We present an approximation algorithm based on linear programming formulations with binary decision variables which are a kind of assignment variables for the classical deterministic scheduling problem of minimizing the makespan on identical machines. The problem is known to be NP-hard in the strong sense. The structure of the corresponding polytope is analyzed, and the strong cutting planes are identi ed. Computational results show that, in all tested cases, the problem can be solved exactly.