Supply location and transportation planning for hurricanes: A two-stage stochastic programming framework

2019 ◽  
Vol 274 (1) ◽  
pp. 108-125 ◽  
Author(s):  
Jomon A. Paul ◽  
Minjiao Zhang
Keyword(s):  
Stochastic Programming ◽  
Transportation Planning ◽  
Two Stage ◽  
Programming Framework

Interval-parameter robust optimization for environmental management under uncertainty

2009 ◽  
Vol 36 (4) ◽  
pp. 592-606 ◽  
Author(s):  
Y.P. Li ◽  
G.H. Huang
Keyword(s):  
Stochastic Programming ◽  
Robust Optimization ◽  
Decision Makers ◽  
Interval Parameter ◽  
Two Stage ◽  
Uncertainty Interval ◽  
Second Stage ◽  
Programming Framework ◽  
Different Levels

In this study, an interval-parameter robust optimization (IPRO) method is developed through incorporating techniques of interval-parameter programming and robust optimization within a two-stage stochastic programming framework. The IPRO improves upon the two-stage stochastic programming methods by allowing uncertainties presented as both intervals and random variables to be handled in the optimization system. Moreover, in the modeling formulation, penalties are exercised with the recourse against any infeasibility, and robustness measures are introduced to examine the variability of the second-stage costs that are above the expected level. The IPRO is generally suitable for risk-aversive planners under high-variability conditions. The developed method is applied to a case of long-term waste management under uncertainty. Interval solutions under different robustness levels have been generated. They cannot only be used for analyzing various policy scenarios that are related to different levels of economic penalties when the pre-regulated waste allocation allowances are violated, but also help decision makers to analyze the interrelationships between the penalties and their variabilities.

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

Top ◽  
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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