Browsing by Subject "CVaR"

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    ItemOpen Access
    Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR
    (Elsevier B.V., 2018) Mahmutoğulları, Ali İrfan; Çavuş, Özlem; Aktürk, M. Selim
    Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non-convex due to integrality restrictions, and the objective function is nonlinear in general. We propose a scenario tree decomposition approach, namely group subproblem approach, to obtain bounds for such problems with an objective of dynamic mean conditional value-at-risk (mean-CVaR). Our approach does not require any special problem structure such as convexity and linearity, therefore it can be applied to a wide range of problems. We obtain lower bounds by using different convolution of mean-CVaR risk measures and different scenario partition strategies. The upper bounds are obtained through the use of optimal solutions of group subproblems. Using these lower and upper bounds, we propose a solution algorithm for risk-averse mixed-integer multi-stage stochastic problems with mean-CVaR risk measures. We test the performance of the proposed algorithm on a multi-stage stochastic lot sizing problem and compare different choices of lower bounds and partition strategies. Comparison of the proposed algorithm to a commercial solver revealed that, on the average, the proposed algorithm yields 1.13% stronger bounds. The commercial solver requires additional running time more than a factor of five, on the average, to reach the same optimality gap obtained by the proposed algorithm.
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    ItemOpen Access
    Carbon restricted newsvendor problem under CVAR objective and resource constraints
    (2014) Korkmaz, Özüm
    Newsboy problem has been studied in the literature extensively. The classical newsvendor, representing the risk neutral decision maker, determines the optimal order/production quantity by maximizing the expected profit or minimizing the expected total cost of a single period with stochastic demand. This approach is not suitable if one also aims to reduce the chances of facing unexpected losses due to demand uncertainty. In this thesis, two problems are investigated with a single product newsvendor under CVaR maximization objective. The first problem addresses the newsvendor model with two different carbon emission reduction policies, namely, mandatory emission allowance and carbon emission trading mechanism. In the second problem, as an extension of the first one, a newsvendor with multiple resource constraints is considered for the cases where the resources have quotas with trade options. Analytical expressions for optimal order/production quantities are determined together with the optimal trading policy and numerical examples are provided.