Multi-agent task allocation is a well-studied field with many proven algorithms. In real-world applications, many tasks have complicated coupled relationships that affect the feasibility of some algorithms. In this paper, we leverage on the properties of potential games and introduce a scheduling algorithm to provide feasible solutions in allocation scenarios with complicated spatial and temporal dependence. Additionally, we propose the use of random sampling in a Distributed Stochastic Algorithm to enhance speed of convergence. We demonstrate the feasibility of such an approach in a simulated disaster relief operation and show that feasibly good results can be obtained when the confirmation and sample size requirements are properly selected.