An Introduction to Two-Stage Stochastic Mixed-Integer Programming

2017 ◽  
pp. 1-27 ◽  
Author(s):  
Simge Küçükyavuz ◽  
Suvrajeet Sen
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Mixed Integer ◽  
Two Stage ◽  
Stochastic Mixed Integer Programming

scholarly journals Two-Stage Stochastic Mixed-Integer Programming with Chance Constraints for Extended Aircraft Arrival Management

2020 ◽  
Vol 54 (4) ◽  
pp. 897-919
Author(s):  
Ahmed Khassiba ◽  
Fabian Bastin ◽  
Sonia Cafieri ◽  
Bernard Gendron ◽  
Marcel Mongeau
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Benders Decomposition ◽  
Chance Constraints ◽  
Mixed Integer ◽  
Chance Constrained Programming ◽  
Management Problem ◽  
Two Stage ◽  
Acceleration Techniques ◽  
Stochastic Mixed Integer Programming

The extended aircraft arrival management problem, as an extension of the classic aircraft landing problem, seeks to preschedule aircraft on a destination airport a few hours before their planned landing times. A two-stage stochastic mixed-integer programming model enriched by chance constraints is proposed in this paper. The first-stage optimization problem determines an aircraft sequence and target times over a reference point in the terminal area, called initial approach fix (IAF), so as to minimize the landing sequence length. Actual times over the IAF are assumed to deviate randomly from target times following known probability distributions. In the second stage, actual times over the IAF are assumed to be revealed, and landing times are to be determined in view of minimizing a time-deviation impact cost function. A Benders reformulation is proposed, and acceleration techniques to Benders decomposition are sketched. Extensive results on realistic instances from Paris Charles-de-Gaulle airport show the benefit of two-stage stochastic and chance-constrained programming over a deterministic policy.

A bi-level programming for transportation services procurement based on combinatorial auction with fuzzy random parameters

2018 ◽  
Vol 30 (5) ◽  
pp. 1162-1182 ◽  
Author(s):  
Fang Yan ◽  
Yanfang Ma ◽  
Cuiying Feng
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Traditional Approach ◽  
Algorithm Analysis ◽  
Mixed Integer ◽  
Content Type ◽  
Winner Determination ◽  
Stochastic Mixed Integer Programming ◽  
Maximum Utility ◽  
Algorithm Comparison

Purpose The purpose of this paper is to study a transportation service procurement bid construction problem from a less than a full truckload perspective. It seeks to establish stochastic mixed integer programming to allow for the proper bundle of loads to be chosen based on price, which could improve the likelihood that carrier can earn its maximum utility. Design/methodology/approach The authors proposes a bi-level programming that integrates the bid selection and winner determination and a discrete particle swarm optimization (PSO) solution algorithm is then developed, and a numerical simulation is used to make model and algorithm analysis. Findings The algorithm comparison shows that although GA could find a little more Pareto solutions than PSO, it takes a longer time and the quality of these solutions is not dominant. The model analysis shows that compared with traditional approach, our model could promote the likelihood of winning bids and the decision effectiveness of the whole system because it considers the reaction of the shipper. Originality/value The highlights of this paper are considering the likelihood of winning the business and describing the conflicting and cooperative relationship between the carrier and the shipper by using a stochastic mixed integer programming, which has been rarely examined in previous research.

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