Two-stage Robust Approach Research Articles

Hybrid energy storage configuration method for wind power microgrid based on EMD decomposition and two-stage robust approach

Data centers are usually characterized by high energy loads, which raises increasing sustainability concerns in both academic and daily usage. To mitigate the uncertainty and high volatility of distributed wind energy generation, this paper proposes a hybrid energy storage allocation strategy by means of the Empirical Mode Decomposition (EMD) technique and the two-stage robust method. First, this paper conducts the evolution analyses for the over- and under-evaluated uncertainty of wind power fluctuation under different time scales. Second, we employ the EMD technique to configure a high-frequency flywheel energy storage device, realizing the wind power transformation from large fluctuations to small fluctuations and the convergence of the wind power fluctuation curves in minute- and hour levels. Finally, based on the hour-level wind energy stable power curves, we carry out two-stage robust planning for the equipment capacity of low-frequency cold storage tanks and lithium bromide chillers. The case study on a data center microgrid in northeastern China confirms the effectiveness of our proposed strategy.

A two-stage robust approach for minimizing the weighted number of tardy jobs with objective uncertainty

A two-stage robust approach for minimizing the weighted number of tardy jobs with objective uncertainty

A two-stage robust approach to integrated station location and rebalancing vehicle service design in bike-sharing systems

A bike-sharing system is a shared mobility mechanism that provides an alternative transportation mode for short trips with almost no added travel speed loss. However, this model’s low usage ratio and high depreciation rate pose a risk to the sustainable development of the bike-sharing industry. Our study proposes a new integrated station location and rebalancing vehicle service design model. This model aims to maximize daily revenue under a given total investment for station locations and bike acquisition. To address demand ambiguity due to possible bias and loss of data, we present a two-stage robust optimization model with a demand-related uncertainty set. The first stage of our model determines the station locations, initial bike inventory, and service areas of rebalancing vehicles. In contrast to the literature, which either simplifies the rebalancing process as an inventory transshipment problem or formulates it as a complex dynamic bike rebalancing problem, we assign each rebalancing vehicle to a service area composed of several specified stations. An approximate maximum travel distance for each rebalancing vehicle is also designed and constrained to ensure that the rebalancing operation can be performed within each period. In the second stage, our model optimizes the daily fleet operation and maximizes the total revenue minus the rebalancing cost. To solve our model, we design a customized row generation approach. Our numerical studies demonstrate that our algorithm can efficiently obtain exact solutions in small instances. For a real-size problem, the nearly optimal solutions of our model also reveal a high-quality worst-case performance with a small loss in mean performance, particularly when the value of the budget ratio (that is, the average number of bikes per station) is at a medium level. Moreover, the distribution of service areas depends on the bike supply and demand level at each station. The optimal fleet rebalancing operation does not have to be confined to one geographical area. Furthermore, our robust model can achieve larger mean and worst-case revenues and a higher revenue stability than a stochastic model with a small data set.

Relationships between technical efficiency and subsidies for Czech farms: A two-stage robust approach

Subsidies for agriculture in the European Union have been a matter of debate for a long time. However, even after many years of debate, it remains unclear whether the subsidies have a positive or negative effect on farm efficiency. We propose a robust two-stage framework to study the subsidies-effect to farm technical efficiency while controlling farm heterogeneity. First, technical efficiency scores are computed using a modern robust data envelopment analysis model. Then, a quantile regression model is applied to explain the relationship between technical efficiency and the total subsidies and other commonly used explanatory variables. In the empirical part, we analyze a sample of Czech farms during the period from 2010 to 2015. It is revealed that the subsidies-effect is negative and varies based on the technical efficiency of the farm. Higher efficient farms face a less distorting effect than lower efficient farms.

A two-stage robust approach for the reliable logistics network design problem

This paper examines a three-echelon logistics network in which all supply and transshipment nodes are subject to disruption. We use uncertainty sets to describe the possible scenarios without depending on probabilistic information. We adopt a two-stage robust optimization approach where location decisions are made before and recourse decisions are made after the disruptions are known. We construct three two-stage robust models, which are solved exactly by a column-and-constraint-generation algorithm. Numerical tests demonstrate that the proposed algorithm outperforms the Benders decomposition method in both solution quality and computational time, and that the system’s reliability can be improved with only a slight increase in the normal cost.

Design of a reliable hierarchical location-allocation model under disruptions for health service networks: A two-stage robust approach

This study proposes a novel reliable hierarchical location-allocation model for health service network designs where facilities are subject to the risk of disruptions. To characterize the relationship between various levels of the concerned health network, a two-level multi-flow nested hierarchy with service referral is taken into account. The queuing system is considered in the model which handles uncertainty associated with demand as well as service. To ensure the service quality, a minimum limit reflected in the probability of patients’ waiting time is defined. The proposed model is formulated based on a two-stage robust optimization approach in which decisions are defined in two stages such that a first-stage solution should be robust against the possible realizations of the disruption that can only be revealed in a second stage. A solution procedure based on Benders decomposition type algorithm is implemented to solve the model. To illustrate the applicability of the proposed model, a practical case study is presented. The results show that the proposed model can be applied as a flexible decision support tool for decision makers to adopt appropriate strategies and policies in designing a reliable and robust health service network.

Robust optimal sizing of a hybrid energy stand-alone system

This paper deals with the optimal design of a stand-alone hybrid system composed of wind turbines, solar photovoltaic panels and batteries. To compensate for a possible lack of energy from these sources, an auxiliary fuel generator guarantees to meet the demand in every case but its use induces important costs. We have chosen a two-stage robust approach to take account of the stochastic behavior of the solar and wind energy production and also of the demand. We seek to determine the optimal system, i.e. the one that generates a minimum total cost when the worst case scenario relating to this system occurs. We use a constraint generation algorithm where each sub-problem (the recourse problem) can be reformulated by a mixed-integer linear program and hence solved by a standard solver. We also propose a polynomial time dynamic programming algorithm for the recourse problem and show that, in some cases, this algorithm is much more efficient than mixed-integer linear programming. Finally, we report computational experiments on instances constructed from real data, that show the efficiency of the proposed approach and we study the addition of constraints linking the uncertainty in consecutive time periods.

Job Scheduling With Uncertain Local Generation in Smart Buildings: Two-Stage Robust Approach

In this paper, we consider a job scheduling problem with random local generation, in which some jobs must be scheduled ahead of time while the others can be scheduled in a real-time fashion. To capture the randomness of the locally distributed generation, we develop a two-stage robust optimization model by considering an uncertainty set without probability information. Given that the problem is challenging, a nested column-and-constraint generation algorithm is implemented to find an optimal solution. Some computational study, along with management insights, is presented to show the effectiveness of the proposed model in dealing with the worst case situations.