Conditional value‐at‐risk beyond finance: a survey

Treatment planning in high dose-rate brachytherapy has traditionally been conducted with manual forward planning, but inverse planning is today increasingly used in clinical practice. There is a large variety of proposed optimization models and algorithms to model and solve the treatment planning problem. Two major parts of inverse treatment planning for which mathematical optimization can be used are the decisions about catheter placement and dwell time distributions. Both these problems as well as integrated approaches are included in this review. The proposed models include linear penalty models, dose-volume models, mean-tail dose models, quadratic penalty models, radiobiological models, and multiobjective models. The aim of this survey is twofold: (i) to give a broad overview over mathematical optimization models used for treatment planning of brachytherapy and (ii) to provide mathematical analyses and comparisons between models. New technologies for brachytherapy treatments and methods for treatment planning are also discussed. Of particular interest for future research is a thorough comparison between optimization models and algorithms on the same dataset, and clinical validation of proposed optimization approaches with respect to patient outcome.

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“…An overview of applications where CVaR have been used can be found in Ref. [75].…”

Section: Mathematical Modelsmentioning

confidence: 99%

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

2021

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“…CVaR η measures the average profit falling below the η‐quantile level VaR η (Chen et al., 2017b; Li et al., 2018; Zhou et al., 2018b). That is, CVaR η is sensitive to worst outcomes (Filippi et al., 2020). When a manufacturer is risk averse, the manufacturer's decisions and the profit will be influenced by his risk behavior.…”

Section: Extension: the Risk‐averse Scenariomentioning

confidence: 99%

Pricing decisions with different time sequences in a cross‐border dual‐channel supply chain

Xue

2021

Int Trans Operational Res

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This paper investigates pricing decisions with different time sequences in a cross‐border dual‐channel supply chain, in which the manufacturer produces products in country A and sells them to country B via a retail channel and an online channel. Meanwhile, we design three scenarios, the manufacturer‐led earlier scenario, the manufacturer‐led later scenario, and the retailer‐led scenario, to analyze the effects of time sequences when the manufacturer is risk neutral or risk averse. Through modeling and analysis, it is concluded that whether the manufacturer is risk averse or not, the manufacturer prefers the manufacturer‐led earlier scenario and the retailer's preference is the retailer‐led scenario. That is, when considering the time sequences, the players are encouraged to make all decisions in the first stage. Moreover, this paper analyzes the effects of the exchange rate and delivery lead time on the players’ pricing decisions. The theoretical and numerical analyses also show that the effects of an increasing exchange rate on the profits of the manufacturer and retailer are associated with the cost of the online channel. Additionally, while reducing the delivery lead time can attract customers, a moderate delivery lead time is more advantageous for the manufacturer. Finally, we further verify the robustness of the impacts of time sequences when the manufacturer is risk averse. Interestingly, if the cost of the online channel is higher, then the risk‐averse behavior benefits the retailer.

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“…The concept of CVaR has gained much attention since Rockafellar and Uryasev [57] showed that it can be formulated using a linear model. Apart from in radiation therapy, CVaR has been used in a wide range of applications, see [58] for a review. To focus on its use in radiation therapy, we refer to it as mean-tail-dose (MTD).…”

Section: Mean-tail-dose Modelsmentioning

confidence: 99%

Treatment Planning of High Dose-Rate Brachytherapy - Mathematical Modelling and Optimization

Morén

2021

Linköping Studies in Science and Technology. Dissertations

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Cancer is a widespread class of diseases that each year affects millions of people. It is mostly treated with chemotherapy, surgery, radiation therapy, or combinations thereof. High doserate (HDR) brachytherapy (BT) is one modality of radiation therapy, which is used to treat for example prostate cancer and gynecologic cancer. In BT, catheters (i.e., hollow needles) or applicators are used to place a single, small, but highly radioactive source of ionizing radiation close to or within a tumour, at dwell positions. An emerging technique for HDR BT treatment is intensity modulated brachytherapy (IMBT), in which static or dynamic shields are used to further shape the dose distribution, by hindering the radiation in certain directions.The topic of this thesis is the application of mathematical optimization to model and solve the treatment planning problem. The treatment planning includes decisions on catheter placement, that is, how many catheters to use and where to place them, as well as decisions for dwell times. Our focus is on the latter decisions. The primary treatment goals are to give the tumour a sufficiently high radiation dose while limiting the dose to the surrounding healthy organs, to avoid severe side effects. Because these aims are typically in conflict, optimization models of the treatment planning problem are inherently multiobjective. Compared to manual treatment planning, there are several advantages of using mathematical optimization for treatment planning. First, the optimization of treatment plans requires less time, compared to the time-consuming manual planning. Secondly, treatment plan quality can be improved by using optimization models and algorithms. Finally, with the use of sophisticated optimization models and algorithms the requirements of experience and skill level for the planners are lower. The use of optimization for treatment planning of IMBT is especially important because the degrees of freedom are too many for manual planning.The contributions of this thesis include the study of properties of treatment planning models, suggestions for extensions and improvements of proposed models, and the development of new optimization models that take clinically relevant, but uncustomary aspects, into account in the treatment planning. A common theme is the modelling of constraints on dosimetric indices, each of which is a restriction on the portion of a volume that receives at least a specified dose, or on the lowest dose that is received by a portion of a volume. Modelling dosimetric indices explicitly yields mixed-integer programs which are computationally demanding to solve. We have therefore investigated approximations of dosimetric indices, for example using smooth non-linear functions or convex functions. Contributions of this thesis are also a literature review of proposed treatment planning models for HDR BT, including mathematical analyses and comparisons of models, and a study of treatment planning for IMBT, which shows how robust optimization can be used to mitigate the risks fro...

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Conditional value‐at‐risk beyond finance: a survey

Cited by 64 publications

References 156 publications

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

Pricing decisions with different time sequences in a cross‐border dual‐channel supply chain

Treatment Planning of High Dose-Rate Brachytherapy - Mathematical Modelling and Optimization

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