Integration of Scheduling and Dynamic Optimization of Batch Processes under Uncertainty: Two-Stage Stochastic Programming Approach and Enhanced Generalized Benders Decomposition Algorithm

2013 ◽  
Vol 52 (47) ◽  
pp. 16851-16869 ◽  
Author(s):  
Yunfei Chu ◽  
Fengqi You
Keyword(s):  
Stochastic Programming ◽  
Dynamic Optimization ◽  
Benders Decomposition ◽  
Decomposition Algorithm ◽  
Batch Processes ◽  
Programming Approach ◽  
Generalized Benders Decomposition ◽  
Two Stage ◽  
Benders Decomposition Algorithm

scholarly journals A loose Benders decomposition algorithm for approximating two-stage mixed-integer recourse models

2020 ◽  
Author(s):  
Niels van der Laan ◽  
Ward Romeijnders
Keyword(s):  
Error Bounds ◽  
Benders Decomposition ◽  
Decomposition Algorithm ◽  
Mixed Integer ◽  
Large Problem ◽  
Two Stage ◽  
Convex Approximations ◽  
Integer Recourse ◽  
Benders Decomposition Algorithm ◽  
Problem Instances

Abstract We propose a new class of convex approximations for two-stage mixed-integer recourse models, the so-called generalized alpha-approximations. The advantage of these convex approximations over existing ones is that they are more suitable for efficient computations. Indeed, we construct a loose Benders decomposition algorithm that solves large problem instances in reasonable time. To guarantee the performance of the resulting solution, we derive corresponding error bounds that depend on the total variations of the probability density functions of the random variables in the model. The error bounds converge to zero if these total variations converge to zero. We empirically assess our solution method on several test instances, including the SIZES and SSLP instances from SIPLIB. We show that our method finds near-optimal solutions if the variability of the random parameters in the model is large. Moreover, our method outperforms existing methods in terms of computation time, especially for large problem instances.

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.

OPTIMAL SIZING OF IRRIGATION DELIVERY SYSTEMS USING A TWO-STAGE STOCHASTIC PROGRAMMING APPROACH

2001 ◽  
Vol 18 (4) ◽  
pp. 331-362 ◽  
Author(s):  
WALID ELSHORBAGY ◽  
KEVIN LANSEY ◽  
DONALD SLACK
Keyword(s):  
Stochastic Programming ◽  
Delivery Systems ◽  
Programming Approach ◽  
Two Stage ◽  
Optimal Sizing

scholarly journals Two-stage stochastic programming approach for the medical drug inventory routing problem under uncertainty

2019 ◽  
Vol 128 ◽  
pp. 358-370 ◽  
Author(s):  
Erfaneh Nikzad ◽  
Mahdi Bashiri ◽  
Fabricio Oliveira
Keyword(s):  
Stochastic Programming ◽  
Programming Approach ◽  
Inventory Routing ◽  
Two Stage ◽  
Routing Problem ◽  
Inventory Routing Problem ◽  
Medical Drug

Enabling smart ports through the integration of microgrids: A two-stage stochastic programming approach

2020 ◽  
Vol 258 ◽  
pp. 114022 ◽  
Author(s):  
Anahita Molavi ◽  
Jian Shi ◽  
Yiwei Wu ◽  
Gino J. Lim
Keyword(s):  
Stochastic Programming ◽  
Programming Approach ◽  
Two Stage ◽  
Smart Ports

scholarly journals Appointment Scheduling at Outpatient Clinics Using Two-Stage Stochastic Programming Approach

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 175297-175305
Author(s):  
Samira Fazel Anvaryazdi ◽  
Saravanan Venkatachalam ◽  
Ratna Babu Chinnam
Keyword(s):  
Stochastic Programming ◽  
Appointment Scheduling ◽  
Outpatient Clinics ◽  
Programming Approach ◽  
Two Stage
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