We present a general framework for robust satisficing that favors solutions for which a risk-aware objective function would best attain an acceptable target even when the actual probability distribution deviates from the empirical distribution. The satisficing decision maker specifies an acceptable target, or loss of optimality compared with the empirical optimization model, as a trade-off for the model’s ability to withstand greater uncertainty. We axiomatize the decision criterion associated with robust satisficing, termed as the fragility measure, and present its representation theorem. Focusing on Wasserstein distance measure, we present tractable robust satisficing models for risk-based linear optimization, combinatorial optimization, and linear optimization problems with recourse. Serendipitously, the insights to the approximation of the linear optimization problems with recourse also provide a recipe for approximating solutions for hard stochastic optimization problems without relatively complete recourse. We perform numerical studies on a portfolio optimization problem and a network lot-sizing problem. We show that the solutions to the robust satisficing models are more effective in improving the out-of-sample performance evaluated on a variety of metrics, hence alleviating the optimizer’s curse.
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.
Problem definition: We consider the intraday scheduling problem in a group of orthopaedic clinics where the planner schedules appointment times, given a sequence of appointments. We consider patient re-entry—where patients may be required to go for an x-ray examination, returning to the same doctor they have seen—and variability in patient behaviours such as walk-ins, earliness, and no-shows, which leads to inefficiency such as long patient waiting time and physician overtime. Academic/practical relevance: In our data set, 25% of the patients are required to go for x-ray examination. We also found significant variability in patient behaviours. Hence, patient re-entry and variability in behaviours are common, but we found little in the literature that could handle them. Methodology: We formulate the problem as a two-stage optimization problem, where scheduling decisions are made in the first stage. Queue dynamics in the second stage are modeled under a P-Queue paradigm, which minimizes a risk index representing the chance of violating performance targets, such as patient waiting times. The model reduces to a sequence of mixed-integer linear-optimization problems. Results: Our model achieves significant reductions, in comparative studies against a sample average approximation (SAA) model, on patient waiting times, while keeping server overtime constant. Our simulations further characterize the types of uncertainties under which SAA performs poorly. Managerial insights: We present an optimization model that is easy to implement in practice and tractable to compute. Our simulations indicate that not accounting for patient re-entry or variability in patient behaviours will lead to suboptimal policies, especially when they have specific structure that should be considered.
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