Production scheduling seeks optimal combination of short manufacturing time, stable inventory, balanced human and machine utilization rate, and short average customer waiting time. Since the problem in general has been proven as NP-hard, we focus on suboptimal scheduling solutions for parallel flow shop machines where jobs are queued in a bottleneck stage. A Genetic Algorithm with Sub-indexed Partitioning genes (GASP) is proposed to allow more flexible job assignments to machines. Our fitness function considers tardiness, earliness, and utilization rate related variable costs to reflect real requirements. A premature convergence bounce is added to traditional genetic algorithms to increase permutation diversity. Finally, a production scheduling system for an electronic plant based on GASP is implemented and illustrated through real production data. The proposed GASP has demonstrated the following advantages: (1) the solutions from GASP are better and with smaller deviations than those from heuristic rules and genetic algorithms with identical partitioning genes; (2) the added premature convergence bounce helps obtain better solutions with smaller deviations; and (3) the consideration of variable costs in the fitness function helps achieve better performance indicators.