Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR

Mahmutoğulları, Ali İrfan; Çavuş, Özlem; Aktürk, M. Seli̇m

doi:10.1016/j.ejor.2017.10.038

Cited by 16 publications

(9 citation statements)

References 25 publications

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“…In this section, we present a lower bound for our problem by using scenario grouping. The scenario grouping idea is previously considered by Sandıkçı and Özaltın (2017) and Mahmutogulları et al (2018) in mixed-integer multi-stage stochastic problems. The proposed lower bound is used in the algorithm presented in the next section.…”

Section: Lower Bounds Via Scenario Groupingmentioning

confidence: 99%

“…At stage t, the random cost is the total service cost at stage t. The DEP of risk-averse multi-stage SSLP can be modeled by using parameters and decision variables for each node of the scenario tree. Moreover, linearization of mean-CVaR risk measure is possible by defining additional auxiliary variables and constraints (see, for example, Mahmutogulları et al 2018).…”

Section: Stochastic Server Location Problemmentioning

confidence: 99%

“…Note that for two-stage problems, all partitioning strategies are equivalent since the locations of nodes in the second stage of the scenario tree are interchangeable. For a deeper discussion on the construction of partitions and their impact on the quality of bounds, we refer to Bakır et al (2016) and Mahmutogulları et al (2018) where various extensions on scenario grouping are considered. However, as seen in the results of our computational experiments, using a simple scenario grouping strategy is adequate for the proposed algorithm.…”

Section: Stochastic Server Location Problemmentioning

confidence: 99%

“…Another stream of research focuses on group subproblem approach to obtain bounds for risk-neutral (Sandıkçı et al 2013;Maggioni et al 2014Sandıkçı and Özaltın 2017) and risk-averse (see Maggioni and Pflug 2016;Mahmutogulları et al 2018) mixed-integer multi-stage stochastic programming problems. The method is based on solving the problem for subsets of scenarios instead of the original set of scenarios in order to obtain bounds on the optimal value of the problem.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

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An exact solution approach for risk-averse mixed-integer multi-stage stochastic programming problems

2019

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Risk-averse mixed-integer multi-stage stochastic programming problems are challenging, large scale and non-convex optimization problems. In this study, we propose an exact solution algorithm for a type of these problems with an objective of dynamic mean-CVaR risk measure and binary first stage decision variables. The proposed algorithm is based on an evaluate-andcut procedure and uses lower bounds obtained from a scenario tree decomposition method called as group subproblem approach. We also show that, under the assumption that the first stage integer variables are bounded, our algorithm solves problems with mixed-integer variables in all stages. Computational experiments on risk-averse multi-stage stochastic server location and generation expansion problems reveal that the proposed algorithm is able to solve problem instances with more than one million binary variables within a reasonable time under a modest computational setting.

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Section: Lower Bounds Via Scenario Groupingmentioning

confidence: 99%

Section: Stochastic Server Location Problemmentioning

confidence: 99%

Section: Stochastic Server Location Problemmentioning

confidence: 99%

Section: Introduction and Literature Reviewmentioning

confidence: 99%

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An exact solution approach for risk-averse mixed-integer multi-stage stochastic programming problems

2019

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“…However, the fact that UPM often lead to suboptimal solutions to the second-stage problem problem in which variability is falsely reduced is well-known in the academic literature (Takriti and Ahmed 2004;Barbaro and Bagajewicz 2004). Mahmutogullari et al (2018) presented a scenario tree decomposition approach to handle general risk-averse mixed-integer multi-stage stochastic problems based on the Conditional Value-at-Risk (CVaR) measure. Their approach is tested on a lot-sizing problem under stochastic costs.…”

Section: Introductionmentioning

confidence: 99%

A practical assessment of risk-averse approaches in production lot-sizing problems

Alem

Oliveira

Carrión

2019

International Journal of Production Research

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This paper presents an empirical assessment of four state-of-the-art risk-averse approaches to deal with the capacitated lot-sizing problem under stochastic demand. We analyze two mean-risk models based on the semideviation and on the conditional value-at-risk risk measures, and alternate first and secondorder stochastic dominance approaches. The extensive computational experiments based on different instances characteristics and on a case-study suggest that CVaR exhibits a good tradeoff between risk and performance, followed by the semideviation and first-order stochastic dominance approach. For all approaches, enforcing risk-aversion helps to reduce the cost standard deviation substantially, which is usually accomplished via increasing production rates. Overall, we can say that very risk-averse decisionmakers would be willing to pay an increased price to have a much less risky solution given by CVaR. In less risk-averse settings, though, semideviation and first-order stochastic dominance can be appealing alternatives to provide significantly more stable production planning costs with a marginal increase of the expected costs.

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An Embarrassingly Parallel Method for Large-Scale Stochastic Programs

Sandikçi

Özaltın

2019

Springer Optimization and Its Applications

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Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR

Cited by 16 publications

References 25 publications

An exact solution approach for risk-averse mixed-integer multi-stage stochastic programming problems

An exact solution approach for risk-averse mixed-integer multi-stage stochastic programming problems

A practical assessment of risk-averse approaches in production lot-sizing problems

An Embarrassingly Parallel Method for Large-Scale Stochastic Programs

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