Workload Balancing in Parallel Machines based on Semi-matching Theory

This paper addresses the problem of scheduling jobs on parallel machines with machine eligibility restrictions so as to balance the workload among machines. A weighted bipartite graph model G=[J U M,E,W] is used to formulate the studied problem. We propose a two-phase algorithm to find the optimal solution. In phase 1,the initial solution construction algorithm is used to build an initial solution, followed by an improvement algorithm to improve the initial solution to optimal one in phase 2. Computational results are presented for a set of randomly generated instances.