Abstract: The uncertainty nature of a grid makes the traditional job scheduling algorithms to work improperly in an open, heterogeneous grid resembling in the real world environment. As most of the job scheduling tasks cannot be fit commonly into a single description model considering data assumption available in grid nodes, the job scheduling becomes the challenging task. In present research, new mathematical computation method called Multi-Stage Stochastic Integer Programming (MSIP) is proposed for overcoming process uncertainty during job and data aware scheduling of a grid computing. In case of computational load as generated by grid applications, the uncertainty problem can be solved by MSIP approach. A number of jobs can be defined with job execution time and resources after completion of MSIP. This is done for expressing the uncertain expected time to compute of jobs and analyze operation properties based on the resources for computing data and job aware scheduling in grid computing environment. The proposed harmony search called Hybrid Ant Colony (HAC) offers efficient grid utilization for both resource providers and consumers by solve problems related to data and job aware scheduling. Using this method, both resource providers and consumers are allowed to take autonomous scheduling decisions. Moreover, sufficient data incentives can be derived based on Community workflow Scheduler (CSF) of their interest. In other hand, experimental results ensured the ability of the proposed MSIP algorithms in representing uncertainty in a grid computing environment.