Mitigating Delays and Unfairness in Appointment Systems

Qi, Jin

doi:10.1287/mnsc.2015.2353

Cited by 84 publications

(35 citation statements)

References 40 publications

(49 reference statements)

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“…which can be modeled directly using an algebraic modeling software package. In fact, this technique can be applied straightforwardly to obtain exact solutions in adaptive distributionally robust optimization problems found in recent applications such as Meng et al (2015) and Qi (2015). We will use the case study of medical appointment scheduling to show how we could easily apply our results to study various types of ambiguity sets.…”

Section: Remarksmentioning

confidence: 99%

Adaptive Distributionally Robust Optimization

2019

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We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive distrbutaionally robust optimization framework caters for dynamic decision making, where decisions adapt to the uncertain outcomes as they unfold in stages. For tractability considerations, we focus on a class of second-order conic (SOC) representable ambiguity set, though our results can easily be extended to more general conic representations. We show that the adaptive distributionally robust linear optimization problem can be formulated as a classical robust optimization problem. To obtain a tractable formulation, we approximate the adaptive distributionally robust optimization problem using linear decision rule (LDR) techniques. More interestingly, by incorporating the primary and auxiliary random variables of the lifted ambiguity set in the LDR approximation, we can significantly improve the solutions, and for a class of adaptive distributionally robust optimization problems, exact solutions can also be obtained. Using the new LDR approximation, we can transform the distributionally adaptive robust optimization problem to a classical robust optimization problem with an SOC representable uncertainty set. Finally, to demonstrate the potential for solving management decision problems, we develop an algebraic modeling package and illustrate how it can be used to facilitate modeling and obtain high quality solutions for medical appointment scheduling and inventory management problems.

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Section: Remarksmentioning

confidence: 99%

Adaptive Distributionally Robust Optimization

2019

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“…One challenge in addressing these problems in practice is that the appointment duration is often random and its distribution is hard to estimate due to lack of the data. In the light of the distributional uncertainty, robust optimization has recently emerged as a popular framework for solving this class of problems (Kong et al 2013, Mak et al 2015, Qi 2017. In this section, we apply our RSB approach to study an appointment-scheduling problem with real data and compare it with existing approaches.…”

Section: An Appointment-scheduling Problemmentioning

confidence: 99%

Distributionally Robust Selection of the Best

Fan

Zhang

2020

Management Science

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Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large. In this paper, we consider the problem of selecting the best from a finite set of simulated alternatives, in the presence of such input uncertainty. We model such uncertainty by an ambiguity set consisting of a finite number of plausible input distributions, and aim to select the alternative with the best worst-case mean performance over the ambiguity set. We refer to this problem as robust selection of the best (RSB). To solve the RSB problem, we develop a two-stage selection procedure and a sequential selection procedure; we then prove that both procedures can achieve at least a user-specified probability of correct selection under mild conditions. Extensive numerical experiments are conducted to investigate the computational efficiency of the two procedures. Finally, we apply the RSB approach to study a queueing system's staffing problem using synthetic data and an appointment-scheduling problem using real data from a large hospital in China. We find that the RSB approach can generate decisions significantly better than other widely used approaches.

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“…Distributionally robust appointment scheduling problems under various forms of ambiguity sets have been proposed and studied in the literature (see, for instance, Kong et al 2013, Mak et al 2014, Bertsimas et al 2016, Qi 2016. In our computational study, we adopt the covariance dominance ambiguity set and investigate the efficiency of our proposed optimization procedure via Algorithm 1.…”

Section: Case Of Covariance Dominance Ambiguity Setmentioning

confidence: 99%

“…To obtain a tractable optimization model, we adopt the approach of Qi (2016) and consider the following formulation that splits the total waiting time in the system into short delays among every participants.…”

Section: Case Of Covariance Dominance Ambiguity Setmentioning

confidence: 99%

Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

Chen

Sim

2019

Operations Research

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We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinitely constrained ambiguity set can be used to incorporate covariance and entropic dominance in its description. In particular, we demonstrate that our proposed entropic dominance approach can improve the characterization of stochastic independence over existing approach based on covariance information. Although the corresponding distributionally robust optimization problem may not necessarily lead to tractable reformulations, we approach the problem by solving a sequence of tractable distributionally robust optimization problems, each over a relaxed and finitely constrained ambiguity set. When incorporating covariance information in the ambiguity set, we show that the subproblems are in the form of a second order conic program, which is a more computationally attractive format than a positive semidefinite program. We show favorable results in our computational study that this approach converges reasonably well.

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Mitigating Delays and Unfairness in Appointment Systems

Cited by 84 publications

References 40 publications

Adaptive Distributionally Robust Optimization

Adaptive Distributionally Robust Optimization

Distributionally Robust Selection of the Best

Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

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