A Robust Optimization Model for Managing Elective Admission in a Public Hospital

Meng, Fanwen; Qi, Jin; Zhang, Meilin; Ang, James S.; Chu, Singfat; Sim, Melvyn

doi:10.1287/opre.2015.1423

Cited by 49 publications

(20 citation statements)

References 27 publications

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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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“…Our findings imply that a large number of stochastic and distributionally robust optimization problems in classical combinatorial optimization [12,13] as well as applications in healthcare [36,37], energy [25,50], finance [27] and supply chain management [11,23] may benefit from randomization.…”

Section: Example 3 (Project Selection Cont'd)mentioning

confidence: 92%

“…Theorem 13 suggests that ambiguity averse decision makers solving problem (3) instead of (4) may unwittingly expose themselves to avoidable risks and thus act irrationally. Furthermore, it indicates that various recent distributionally robust optimization problems involving discrete choices such as appointment scheduling [37], knapsack [12], hospital admission [36], shortest path [13], unit commitment [25], facility location [11], and vehicle routing problems [23] etc. might benefit from randomization.…”

Section: Randomization Under Distributional Ambiguitymentioning

confidence: 99%

“Dice”-sion–Making Under Uncertainty: When Can a Random Decision Reduce Risk?

2019

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Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic decisions are strictly outperformed by random decisions which depend on a randomization device producing uniformly distributed samples that are independent of all uncertain factors affecting the decision problem. We find that in the absence of distributional ambiguity, deterministic decisions are optimal if both the risk measure and the feasible region are convex, or alternatively if the risk measure is mixture-quasiconcave. We show that several classes of risk measures, such as mean (semi-)deviation and mean (semi-)moment measures, fail to be mixture-quasiconcave and can therefore give rise to problems in which the decision maker benefits from randomization. Under distributional ambiguity, on the other hand, we show that for any ambiguity averse risk measure there always exists a decision problem (with a nonconvex-e.g., mixed-integer-feasible region) in which a randomized decision strictly dominates all deterministic decisions.

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“…This approach yields a satisfactory result in an uncertain environment. Moreover, robust scheduling approaches are also adopted in other problems, such as maritime transportation problem [21,22], routing problem [23], and scheduling problem in public health service department [24]. Most recently, a min-max regret makespan minimization in an identical parallel machine scheduling environment with interval data is studied [5]; in particular, they considered the processing time of jobs lies in respective intervals.…”

Section: Literature Reviewmentioning

confidence: 99%

Robust Parallel Machine Scheduling Problem with Uncertainties and Sequence-Dependent Setup Time

Qin

2016

Scientific Programming

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A parallel machine scheduling problem in plastic production is studied in this paper. In this problem, the processing time and arrival time are uncertain but lie in their respective intervals. In addition, each job must be processed together with a mold while jobs which belong to one family can share the same mold. Therefore, time changing mold is required for two consecutive jobs that belong to different families, which is known as sequence-dependent setup time. This paper aims to identify a robust schedule by min–max regret criterion. It is proved that the scenario incurring maximal regret for each feasible solution lies in finite extreme scenarios. A mixed integer linear programming formulation and an exact algorithm are proposed to solve the problem. Moreover, a modified artificial bee colony algorithm is developed to solve large-scale problems. The performance of the presented algorithm is evaluated through extensive computational experiments and the results show that the proposed algorithm surpasses the exact method in terms of objective value and computational time.

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A Robust Optimization Model for Managing Elective Admission in a Public Hospital

Cited by 49 publications

References 27 publications

Adaptive Distributionally Robust Optimization

Adaptive Distributionally Robust Optimization

“Dice”-sion–Making Under Uncertainty: When Can a Random Decision Reduce Risk?

Robust Parallel Machine Scheduling Problem with Uncertainties and Sequence-Dependent Setup Time

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