Solving 0–1 semidefinite programs for distributionally robust allocation of surgery blocks

Zhang, Yiling; Shen, Siqian; Erdogan, S. Ayca

doi:10.1007/s11590-018-1255-9

Cited by 34 publications

(17 citation statements)

References 15 publications

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“…The proof follows Theorem 2.2 in Wagner (2008) [13] and Theorem 2 in Zhang et al (2018) [17]; we omit the details here.…”

Section: Mixed Integer Second-order Conic Program (Mi-socp)mentioning

confidence: 77%

“…Zheng et al (2016) [16] used multiple scenarios to approximate the uncertainty, i.e., adopting the sample average approximation method. Zhang et al (2018) [17] applied a 0-1 SOCP approximation method to solve the appointment scheduling under stochastic service duration with unknown distributions to minimize the expected total waiting time.…”

Section: Distribution-free Approachmentioning

confidence: 99%

“…Similarly with Zhang et al (2018) [17], the out-of-sample test was implemented, and the main idea behind of it as following: (i) For SAA and ESAA, the customer demand is first determined under limited samples and scenarios; (ii) for MA and MI-SOCP, the demand is decided with a given mean vector and covariance matrix. Then, 10,000 scenarios were randomly generated which satisfied the given conditions of customer demand.…”

Section: Out-of-sample Testmentioning

confidence: 99%

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Distribution-Free Stochastic Closed-Loop Supply Chain Design Problem with Financial Management

Yang

Shi

2019

Sustainability

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Financial flow is an important part of supply chain management (SCM) and increasingly playing a crucial role as the amount of global trade increases. Reasonable and scientific financial operation is necessary in closed-loop supply chain management, especially when customer demand is uncertain. However, financial flow, which may lead to an increase in effectiveness, has rarely been considered in the literature. In this paper, we present a closed-loop supply chain design with financial management problem, which is tackled as a stochastic programming model with ambiguity demand set. The main contributions of this work include: (i) A joint chance constrained programming model is proposed to maximize the total profit, and (ii) financial flow and uncertain demand are both taken into consideration. According to the characteristic of the problem, we chose four approaches, namely sample average approximation (SAA), enhanced sample average approximation (ESAA), Markov approximation (MA), and mixed integer second-order conic program (MI-SOCP). Computational experiments were conducted to compare the adopted methods, and 10,000 scenarios were generated to examine the reliability of the methods. Numerical results revealed that the Markov approximation approach can achieve more reliable solutions.

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“…The proof follows Theorem 2.2 in Wagner (2008) [13] and Theorem 2 in Zhang et al (2018) [17]; we omit the details here.…”

Section: Mixed Integer Second-order Conic Program (Mi-socp)mentioning

confidence: 77%

Section: Distribution-free Approachmentioning

confidence: 99%

Section: Out-of-sample Testmentioning

confidence: 99%

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Distribution-Free Stochastic Closed-Loop Supply Chain Design Problem with Financial Management

Yang

Shi

2019

Sustainability

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“…Two types of confidence sets for the possible probability distributions are proposed. For more distribution-free formulation applications, please see Lee and Hsu [20], Kwon and Cheong [21], etc., for the stochastic inventory problem, and Zhang et al [23] for stochastic allocating surgeries problem in operating rooms, and Zheng et al [24] for stochastic disassembly line balancing problem. To the best of our knowledge, there is no research for the stochastic ambulance location problem with only partial information on the uncertain demand.…”

Section: Distribution-free Approachesmentioning

confidence: 99%

“…The ambiguity set describes how likely the uncertain parameters are to be close to the mean in terms of the correlation [12]. Besides, under the momentbased ambiguity set, various stochastic programs with partial distributional information have been successfully modeled and solved [22,23,25]. According to the approximation method in Zhang et al [23], chance constraint (1) can be approximated by…”

Section: Approximated Mip Formulation: Mip-df2mentioning

confidence: 99%

Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

Wang

Liu

Chu

et al. 2018

Journal of Advanced Transportation

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Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level.

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A branch-and-cut algorithm for solving mixed-integer semidefinite optimization problems

Kobayashi

Takano

2019

Comput Optim Appl

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Solving 0–1 semidefinite programs for distributionally robust allocation of surgery blocks

Cited by 34 publications

References 15 publications

Distribution-Free Stochastic Closed-Loop Supply Chain Design Problem with Financial Management

Distribution-Free Stochastic Closed-Loop Supply Chain Design Problem with Financial Management

Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

A branch-and-cut algorithm for solving mixed-integer semidefinite optimization problems

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