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Over the last few years, grid technologies have progressed towards a service-oriented paradigm that enables a new way of service provisioning based on utility computing models. Users consume these services based on their QoS (quality of service) requirements. In such ldquopay-per-userdquo grids, workflow execution cost must be considered during scheduling based on users' QoS constraints. In this paper, we propose a budget constraint based scheduling, which minimizes execution time while meeting a specified budget for delivering results. A new type of genetic algorithm is developed to solve the scheduling optimization problem and we test the scheduling algorithm in a simulated grid testbed.