A Scalable Bounding Method for Multistage Stochastic Programs

Sandikçi, Burhaneddi̇n; Özaltın, Osman Y.

doi:10.1137/16m1075594

Cited by 16 publications

(16 citation statements)

References 30 publications

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“…However, since complete recourse assumption is a requirement for the branch and bound procedure, this method is also not applicable for our problem. Besides these techniques, scenario groupwise decomposition approach which is recently proposed by [29]…”

Section: Chapter 5 Solution Methodsmentioning

confidence: 99%

“…Let z * (S) be the optimal value of our problem with scenario set S and z(Ŝ) be a lower bound on z * (S) obtained using scenario partitionŜ. The following inequality is satisfied by allŜ selections as proved in Proposition 4.4 in [29]:…”

Section: A Lower Boundmentioning

confidence: 99%

“…In this section, we provide a lower bound on the optimal value of our problem using the scenario groupwise decomposition approach of [29]. In this method, a lower bound is obtained by solving the problem separately for subsets of the scenarios called as groups.…”

Section: A Lower Boundmentioning

confidence: 99%

“…In this case, for each i ∈ IŜ,Ŝ i is called a group. Note that groups do not have to be disjoint to obtain valid bounds, as mentioned in [29]. However, for ease of representation, we consider disjoint groups.…”

Section: A Lower Boundmentioning

confidence: 99%

“…for all s ∈Ŝ i and i ∈ IŜ, which is the ratio of the probability of the scenario to the probability of its group. Once the conditional probabilities are calculated, the weighted summation of the optimal values of the group subproblems provides a lower bound for our minimization problem as proved in [29]. Let z * (S) be the optimal value of our problem with scenario set S and z(Ŝ) be a lower bound on z * (S) obtained using scenario partitionŜ.…”

Section: A Lower Boundmentioning

confidence: 99%

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Multi-stage stochastic programming for demand response optimization

Şahin

Çavuş

Yaman

2020

Computers & Operations Research

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The increase in the energy consumption puts pressure on natural resources and environment and results in a rise in the price of energy. This motivates residents to schedule their energy consumption through demand response mechanism. We propose a multi-stage stochastic programming model to schedule different kinds of electrical appliances under uncertain weather conditions and availability of renewable energy. We incorporate appliances with internal batteries to better utilize the renewable energy sources. Our aim is to minimize the electricity cost and the residents' dissatisfaction. We use a scenario groupwise decomposition approach to compute lower and upper bounds for instances with a large number of scenarios. The results of our computational experiments show that the approach is very effective in finding high quality solutions in small computation times. We provide insights about how optimization and renewable energy combined with batteries for storage result in peak demand reduction, savings in electricity cost and more pleasant schedules for residents with different levels of price sensitivity.

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Section: Chapter 5 Solution Methodsmentioning

confidence: 99%

Section: A Lower Boundmentioning

confidence: 99%

Section: A Lower Boundmentioning

confidence: 99%

Section: A Lower Boundmentioning

confidence: 99%

Section: A Lower Boundmentioning

confidence: 99%

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