This paper considers a coordinated scheduling problem between multi-suppliers and an manufacture. When the supplier has insufficient inventory to meet the manufacture's order, the supplier may use the expedited production and the expedited transportation. In this case, we consider a scheduling problem to minimize the total cost of suppliers and manufacture. We suggest an population management genetic algorithm with local search and crossover (GALPC). By the computational experiments comparing with general genetic algorithm, the objective value of GALPC is reduced by 8% and the calculation time of GALPC is reduced by 70%.