We consider a multi-stage generalization of the interval-based stochastic dominance (ISD) principles introduced by Liu et al. [Interval-based stochastic dominance: Theoretical framework and application to portfolio ch...
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We consider a multi-stage generalization of the interval-based stochastic dominance (ISD) principles introduced by Liu et al. [Interval-based stochastic dominance: Theoretical framework and application to portfolio choices. Ann. Oper. Res., 2021, 307, 329-361]. The ISD criterion was motivated specifically in a financial context to allow for contiguous integer SD orders on different portions of a portfolio return distribution against a benchmark distribution. A continuous spanning of SD conditions between first-, second-, and third-order stochastic dominance was introduced in that context, relying on a reference point. Here, by extending the partial order to random data processes, we apply ISD conditions to a multi-period portfolio selection problem and verify the modeling and computational implications of such an extension. Several theoretical and methodological issues arise in this case that motivate this contribution. The problem is formulated in scenario form as a multi-stage stochastic recourse program, and we study two possible generalizations of ISD principles in which we either enforce ISD constraints at each stage, independently from the scenario tree process evolution, or we do so conditionally along the scenario tree. We present a comprehensive set of computational results to show that, depending on the benchmark investment policy and the adopted ISD formulation, stochastic dominance conditions of first- or second-order can be enforced dynamically over a range of possible values of the reference point, and their solution carries a specific rationale. The computational constraints induced by the multistage ISD formulation are also emphasized and discussed in detail.
Renewable power generation combined with energy storage (ES) is expected to bring enormous economical and environmental benefits to the future smart grid. However, the ES management in smart grid is facing significant...
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Renewable power generation combined with energy storage (ES) is expected to bring enormous economical and environmental benefits to the future smart grid. However, the ES management in smart grid is facing significant technical challenges due to the volatile nature of renewable energy sources and the buffering effect of ES units. The challenges are further complicated by the increasing size and complexity of the system, as well as the consideration of random usage patterns of electrical appliances by customers. To address these challenges, this study proposes a parallel decomposition method for large-scale stochastic programming in a distribution system with renewable energy sources and ES units. By leveraging nested decomposition, the problem can be converted into independent sub-problems with a series of time periods. In addition, the reformulated problem is fully parallel for speed up in execution. The performance of the proposed method is evaluated based on the IEEE 4-bus and 33-bus test distribution systems with real photovoltaic generation and electrical appliance usage data. The case study demonstrates that the proposed scheme can substantially reduce the system operation cost, with low computational complexity.
In response to market pressures resulting in increased competition, product proliferation and greater customization, firms in many industries have adopted modern technologies to provide operational flexibility on seve...
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In response to market pressures resulting in increased competition, product proliferation and greater customization, firms in many industries have adopted modern technologies to provide operational flexibility on several dimensions. In this paper, we consider the role of product mix flexibility, defined as the ability to produce a variety of products, in an environment characterized by multiple products, uncertainty in product life cycles and dynamic demands. Using a scenario-based approach for capturing the evolution of demand, we develop a stochasticprogramming model for determining technology choices and capacity plans. Since the resulting model is likely to be large and may not be easy to solve with standard software packages, we develop a solution procedure based on augmented Lagrangian method and restricted simplicial decomposition. The scope of our approach for deriving context specific managerial insights is illustrated by the results of limited computations. Finally, we demonstrate the versatility of our approach by deriving a special case of the general model to address some tactical issues related to new product introduction.
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