Multi-Objective Two-Stage Stochastic Programming for Adaptive Interdisciplinary Pain Management with Piecewise Linear Network Transition Models

Abstract A systematic way for the optimal design of renewable-based hydrogen refuelling stations in the presence of uncertainty in the hydrogen demand is presented. A two-stage stochastic programming approach is used to simultaneously minimize the total annual cost and the CO2 footprint due to the electricity generation sources. The first-stage (design) variables correspond to the sizing of the devices, while the second-stage (operation) variables correspond to the scheduling of the installed system that is affected by uncertainties. The demand of a fleet of fuel cell vehicles is synthesized by means of a Poisson distribution and different scenarios are generated by random sampling. We formulate our problem as a large-scale mixed-integer linear program and we rely on a two-level approximation scheme to keep the problem computationally tractable. A solely deterministic setting which does not take into account uncertainties leads to underestimated device sizes, resulting in a significant fraction of demand remaining unserved with a consequent loss in revenue. The multi-objective optimization produces a convex Pareto front, showing that a reduction in carbon footprint comes with increasing costs and thus diminishing profit.

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Multi-objective capacity optimization of a hybrid energy system in two-stage stochastic programming framework

Energy Reports ◽

10.1016/j.egyr.2021.03.037 ◽

2021 ◽

Vol 7 ◽

pp. 1837-1846

Author(s):

Rong Li ◽

Yong Yang

Keyword(s):

Stochastic Programming ◽

Energy System ◽

Capacity Optimization ◽

Two Stage ◽

Hybrid Energy System ◽

Hybrid Energy ◽

Multi Objective ◽

Programming Framework

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Multi-Objective Two-Stage Stochastic Programming Model for a Proposed Casualty Transportation System in Large-Scale Disasters: A Case Study

Mathematics ◽

10.3390/math9040316 ◽

2021 ◽

Vol 9 (4) ◽

pp. 316

Author(s):

Nadide Caglayan ◽

Sule Itir Satoglu

Keyword(s):

Decision Support ◽

Stochastic Programming ◽

Programming Model ◽

Decision Support Tool ◽

Data Driven ◽

Two Stage ◽

Support Tool ◽

Transportation Time ◽

Multi Objective ◽

Stochastic Programming Model

Disaster management is a process that includes mitigation, preparedness, response and recovery stages. Operational strategies covering all stages must be developed in order to alleviate the negative effects of the disasters. In this study, we aimed at minimizing the number of casualties that could not be transported to the hospitals after the disaster, the number of additional ambulances required in the response stage, and the total transportation time. Besides, we assumed that a data-driven decision support tool is employed to track casualties and up-to-date hospital capacities, so as to direct the ambulances to the available hospitals. For this purpose, a multi-objective two-stage stochastic programming model was developed. The model was applied to a district in Istanbul city of Turkey, for a major earthquake. Accordingly, the model was developed with a holistic perspective with multiple objectives, periods and locations. The developed multi-objective stochastic programming model was solved using an improved version of the augmented ε-constraint (AUGMECON2) method. Hence, the Pareto optimal solutions set has been obtained and compared with the best solution achieved according to the objective of total transportation time, to see the effect of the ambulance direction decisions based on hospital capacity availability. All of the decisions examined in these comparisons were evaluated in terms of effectiveness and equity. Finally, managerial implication strategies were presented to contribute decision-makers according to the results obtained. Results showed that without implementing a data-driven decision support tool, equity in casualty transportation cannot be achieved among the demand points.

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Optimal purchasing strategies for large power consumers by two-stage stochastic programming with linear partial information

Electrical Engineering and Information Technology ◽

10.2495/ceeit140201 ◽

2014 ◽

Author(s):

Xue Wang ◽

Xinshun Ma

Keyword(s):

Stochastic Programming ◽

Partial Information ◽

Two Stage ◽

Large Power ◽

Linear Partial Information

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A column-and-constraint generation algorithm for two-stage stochastic programming problems

Top ◽

10.1007/s11750-021-00593-2 ◽

2021 ◽

Author(s):

Denise D. Tönissen ◽

Joachim J. Arts ◽

Zuo-Jun Max Shen

Keyword(s):

Stochastic Programming ◽

Benders Decomposition ◽

Equivalent Model ◽

Computational Time ◽

Two Stage ◽

Generation Algorithm ◽

Constraint Generation ◽

Deterministic Equivalent ◽

Location Routing ◽

Relative Tolerance

AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

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