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 their 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 negative effects that include healthcare overtime, longer patient waiting times, and even bed shortages. The difficulty of quantifying these costs and the need to safeguard against their overutilization lead us to propose a resource satisficing framework that renders the violation of resource constraints less likely and also diminishes their impact whenever they occur. The risk of resource overutilization is captured by our resource satisficing index (RSI), which is inspired by Aumann and Serrano (2008) riskiness index and is calibrated to coincide with the expected utilization rate when the random resource usage corresponds to some referenced probability distribution commonly associated with the type of resource. RSI, unlike the expected utilization rate, is risk sensitive and could better mitigate the risks of overutilization. Our satisficing approach aims to balance out the overutilization risks by minimizing the largest RSIs among all resources and time periods, which, under our proposed partial adaptive scheduling policy, can be formulated and solved via a converging sequence of mixed-integer optimization problems. A computational study establishes that our approach reduces resource overutilization risks to a greater extent than does the benchmark method using the first fit (FF) heuristics.
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