arXiv:2507.01225v1 Announce Type: cross Abstract: Organizations around the world schedule jobs (programs) regularly to perform various tasks dictated by their end users. With the major movement towards using a cloud computing infrastructure, our organization follows a hybrid approach with both cloud and on-prem servers. The objective of this work is to perform capacity planning, i.e., estimate resource requirements, and job scheduling for on-prem grid computing environments. A key contribution of our approach is handling uncertainty in both resource usage and duration of the jobs, a critical aspect in the finance industry where stochastic market conditions significantly influence job characteristics. For capacity planning and scheduling, we simultaneously balance two conflicting objectives: (a) minimize resource usage, and (b) provide high quality-of-service to the end users by completing jobs by their requested deadlines. We propose approximate approaches using deterministic estimators and pair sampling-based constraint programming. Our best approach (pair sampling-based) achieves much lower peak resource usage compared to manual scheduling without compromising on the quality-of-service.