We study the problem of advance scheduling of ward admission requests in a public hospital, which affects the usage of critical resources such as operating theaters and hospital beds. Given the stochastic arrivals of patients and uncertain usage of resources, it is often infeasible for the planner to devise a risk‐free schedule to meet these requests without violating resource capacity constraints and creating adverse effects that include healthcare overtime, long patient waiting times, and bed shortages. The difficulty of quantifying these costs and the need to safeguard against resource overutilization lead us to propose a resource satisficing framework that renders the violation of resource constraints less likely and also diminishes its impact whenever it occurs. The risk of resource overutilization is captured by our resource satisficing index (RSI), which is calibrated to reflect a risk‐adjusted utilization rate for a better interpretation to the healthcare planner. Unlike the expected utilization rate, RSI is risk‐sensitive and serves to mitigate the risks of overutilization better whenever overutilization can be avoided in expectation. Our satisficing approach aims to balance out the overutilization risks by minimizing the maximal RSI among all resources and periods. Under our proposed partial adaptive scheduling policy, the resource satisficing model can be formulated and solved via a converging sequence of mixed‐integer linear optimization problems. A computational study establishes that our approach reduces resource overutilization risks to a greater extent than the benchmark methods.