Minimizing Makespan on Identical Parallel Machines

A heuristic algorithm is developed for the classical scheduling problem in which independent jobs are nonpreemptively scheduled on identical parallel machines with the objective of minimizing the makespan with load balancing. The algorithm uses iteratively the LPT procedure to be successful computational tools in many hard Combinatorial Optimization problems. We present an approximation algorithm based on balance the Hopfild with binary decision variables which are a kind of assignment variables for the classical deterministic scheduling problem of minimizing the makespan on identical machines. These problems are characterized by their complexity, known as NP-hard in most cases. Computational results indicate that the proposed algorithm is very competitive with respect to well-known constructive algorithms for a large number of benchmark.