The service flow management is one from the most challenges especially in heterogeneous environments which has several and various processors for computing. Service flow is used to explain services configuration process when service's formation according to the precedence relations of configuration should be considered. Its management should take into account multi-objective constraints. The total execution time should not be completed after the specified time that leading to consider the deadline constraint into account. Also the cost minimization that is a critical issue shouldn't be ignored. Obtaining the optimal management in a sensible time is so hard because there are many candidate with different processing power and price, constraints from the user and the precedence of heterogeneous services. In this paper, the service flow management problem is solved by a genetic algorithm that considers deadline and cost constraints. It focuses on the improvement of execution time to meet the deadline constraint and minimizes the execution cost according to the budget in heterogeneous computing. The results from the applied experiments proves that the proposed algorithm can be able to minimize total cost, and consolidate the execution time with the deadline constraint. It reach to a near-optimal solution in reasonable time. It outperforms the compared algorithms in the metric of Schedule Length Ratio (SLR), cost, risk ratio, speed up and completion time measurements.