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The appointment scheduling problem (ASP) studies how to manage patient arrivals to a healthcare system to improve system performance. An important challenge occurs when some patients may not show up for an appointment. Although the ASP is well studied in the literature, the vast majority of the existing work does not consider the well-observed phenomenon that patient no-show is influenced by the appointment time, the usual decision variable in the ASP. This paper studies the ASP with random service time (exogenous uncertainty) with known distribution and patient decision-dependent no-show behavior (endogenous uncertainty). This problem belongs to the class of stochastic optimization with decision-dependent uncertainties. Such problems are notoriously difficult as they are typically nonconvex. We propose a stochastic projected gradient path (SPGP) method to solve the problem, which requires the development of a gradient estimator of the objective function—a nontrivial task, as the literature on gradient-based optimization algorithms for problems with decision-dependent uncertainty is very scarce and unsuitable for our model. Our method can solve the ASP problem under arbitrarily smooth show-up probability functions. We present solutions under different patterns of no-show behavior and demonstrate that breaking the assumption of constant show-up probability substantially changes the scheduling solutions. We conduct numerical experiments in a variety of settings to compare our results with those obtained with a distributionally robust optimization method developed in the literature. The cost reduction obtained with our method, which we call the value of distribution information, can be interpreted as how much the system performance can be improved by knowing the distribution of the service times, compared to not knowing it. We observe that the value of distribution information is up to 31% of the baseline cost, and that such value is higher when the system is crowded or/and the waiting time cost is relatively high. Summary of Contribution: This paper studies an appointment scheduling problem under time-dependent patient no-show behavior, a situation commonly observed in practice. The problem belongs to the class of stochastic optimization problems with decision-dependent uncertainties in the operations research literature. Such problems are notoriously difficult to solve as a result of the lack of convexity, and the present case requires different techniques because of the presence of continuous distributions for the service times. A stochastic projected gradient path method, which includes the development of specialized techniques to estimate the gradient of the objective function, is proposed to solve the problem. For problems with a similar structure, the algorithm can be applied once the gradient estimator of the objective function is obtained. Extensive numerical studies are presented to demonstrate the quality of the solutions, the importance of modeling time-dependent no-shows in appointment scheduling, and the value of using distribution information about the service times. [ABSTRACT FROM AUTHOR]

Dupacová's early work in minimax solutions of stochastic programs [[6], [24]] predated by half a century a recent surge of work in distributionally robust optimization. Two others major lines of Dupacová's research contributions concern scenario generation and scenario reduction [[15]], with precursor work including [[5], [21]], and her work on asymptotics [[10], [23]]. Jitka Dupacová was the first woman vice dean at the Faculty of Mathematics and Physics at Charles University in 1979. Stochastic programming has seen recent advances with far-reaching impact involving risk measures, distributionally robust optimization, and applications in areas ranging from energy and natural resources to economics and finance to statistics and machine learning. [Extracted from the article]

Dynamic stochastic optimization models provide a powerful tool to represent sequential decision-making processes. Typically, these models use statistical predictive methods to capture the structure of the underlying stochastic process without taking into consideration estimation errors and model misspecification. In this context, we propose a data-driven prescriptive analytics framework aiming to integrate the machine learning and dynamic optimization machinery in a consistent and efficient way to build a bridge from data to decisions. The proposed framework tackles a relevant class of dynamic decision problems comprising many important practical applications. The basic building blocks of our proposed framework are: (1) a Hidden Markov Model as a predictive (machine learning) method to represent uncertainty; and (2) a distributionally robust dynamic optimization model as a prescriptive method that takes into account estimation errors associated with the predictive model and allows for control of the risk associated with decisions. Moreover, we present an evaluation framework to assess out-of-sample performance in rolling horizon schemes. A complete case study on dynamic asset allocation illustrates the proposed framework showing superior out-of-sample performance against selected benchmarks. The numerical results show the practical importance and applicability of the proposed framework since it extracts valuable information from data to obtain robustified decisions with an empirical certificate of out-of-sample performance evaluation. [ABSTRACT FROM AUTHOR]

This article presents and studies models for multi-criteria budget allocation problems under uncertainty. The proposed models incorporate uncertainties in decision maker's weights using a robust weighted sum approach. The risk averseness of the decision maker in satisfying random risk-related constraints is ensured by using stochastic dominance. A sample average approximation approach together with a cutting surface method is used to solve this model. An analysis for the computation of statistical lower and upper bounds is also given. The proposed models are used to study the budget allocation to ten urban areas in the United States under the Urban Areas Security Initiative. Here the decision maker considers property losses, fatalities, air departures, and average daily bridge traffic as separate criteria. The properties of the proposed modeling and solution methodology are discussed using a RAND Corporation–proposed allocation policy and the current government budget allocation as two benchmarks. The budget results are discussed under several parameter scenarios. [ABSTRACT FROM AUTHOR]

• Strategic Investment in energy planning is sensitive to probability distributions. • Distributionally robust optimization yields good solutions that mitigate sensitivity. • Machine learning tools are used to select the important variables for the models. This paper investigates how the choice of stochastic approaches and distribution assumptions impacts strategic investment decisions in energy planning problems. We formulate a two-stage stochastic programming model assuming different distributions for the input parameters and show that there is significant discrepancy among the associated stochastic solutions and other robust solutions published in the literature. To remedy this sensitivity issue, we propose a combined machine learning and distributionally robust optimization (DRO) approach which produces more robust and stable strategic investment decisions with respect to uncertainty assumptions. DRO is applied to deal with ambiguous probability distributions and Machine Learning is used to restrict the DRO model to a subset of important uncertain parameters ensuring computational tractability. Finally, we perform an out-of-sample simulation process to evaluate solutions performances. The Swiss energy system is used as a case study all along the paper to validate the approach. [ABSTRACT FROM AUTHOR]