Two-Stage Stochastic Programming Models for the Extended Aircraft Arrival Management Problem with Multiple Pre-Scheduling Points

2021 ◽  
Author(s):  
Ahmed Khassiba ◽  
Sonia Cafieri ◽  
Fabian Bastin ◽  
Marcel Mongeau ◽  
Bernard Gendron
Keyword(s):  
Stochastic Programming ◽  
Programming Models ◽  
Management Problem ◽  
Two Stage

scholarly journals An Integrated Problem of p-Hub Location and Revenue Management with Multiple Capacity Levels under Disruptions

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Yan-Ting Hou ◽  
Jia-Zhen Huo ◽  
Feng Chu
Keyword(s):  
Stochastic Programming ◽  
Revenue Management ◽  
Programming Model ◽  
Profit Maximization ◽  
Transportation Cost ◽  
Sample Average Approximation ◽  
Management Problem ◽  
Hub Location ◽  
Two Stage ◽  
Airline Tickets

This paper considers an integrated hub location and revenue management problem in which a set of capacities is available from which one can be chosen for each hub and the disruption is considered in a star-star shaped airline network. We propose a two-stage stochastic programming model to maximize the profit of the network in which the cost of installing the hubs at different levels of capacities, the transportation cost, and the revenue obtained by selling airline tickets are considered. To provide flexible solutions, a hybrid two-stage stochastic programming-robust optimization model is developed by putting relative emphasis on a weighted sum of profit maximization. Furthermore, a sample average approximation approach is used for solving the stochastic programming formulation and a genetic algorithm approach is applied for both formulations. Numerical experiments are conducted to verify the mathematical formulations and compare the performance of the used approaches.

scholarly journals Application of stochastic programming to electricity generation planning in South Africa

ORiON ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 88-125
Author(s):  
M Bashe ◽  
M Shuma-Iwisi ◽  
MA Van Wyk
Keyword(s):  
South Africa ◽  
Stochastic Programming ◽  
Electricity Generation ◽  
Programming Model ◽  
Programming Models ◽  
Planning Problem ◽  
Two Stage ◽  
Generation Planning ◽  
Stochastic Programming Model ◽  
Minimum Costs

A two-stage stochastic programming model is used to solve the electricity generation planning problem in South Africa for the period 2013 to 2050, in an attempt to minimise expected cost. Costs considered are capital and running costs. Unknown future electricity demand is the source of uncertainty represented by four scenarios with equal probabilities. The results show that the main contributors for new capacity are coal, wind, hydro and gas/diesel. The minimum costs obtained by solving the two-stage stochastic programming models range from R2 201 billion to R3 094 billion.

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.

scholarly journals A simple heuristic for reducing the number of scenarios in two-stage stochastic programming

2010 ◽  
Vol 34 (8) ◽  
pp. 1246-1255 ◽  
Author(s):  
Ramkumar Karuppiah ◽  
Mariano Martín ◽  
Ignacio E. Grossmann
Keyword(s):  
Stochastic Programming ◽  
Two Stage ◽  
Simple Heuristic
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