The problem addressed in this paper is to minimize the deviations of workloads assigned to worker and to maximize the total utilizations(degree of skill) between workers and machines simultaneously. Each worker can handle the set of machines with the different degree of skill and each machine has the workloads needed to be processed. Also, each worker has to be assigned to at least one machine with the minimum workload deviation. This problem can be formulated as a preemptive goal programming with generalized assignment constraints. The proposed algorithm consists of two phases. First, a capacitated circulation network is constructed to assign the workers to machines with the maximum total utilizations while considering workloads balance. Then, a refinement process is applied to the split machines to satisfy the feasibility condition. The real industrial application in a plastic extrusion manufacturer is included along with several computational experiments.