Taxi planning: Branch and price decomposition

2018 ◽  
Vol 233 (9) ◽  
pp. 3395-3407
Author(s):  
Luís C Ibanez ◽  
Angel G Marín
Keyword(s):  
Flow Model ◽  
Real Data ◽  
Multicommodity Flow ◽  
Planning Problem ◽  
Branch And Price ◽  
Routing And Scheduling ◽  
Flow Capacity ◽  
Price Decomposition ◽  
Aircraft Routing And Scheduling ◽  
Model Structures

Taxi planning problem studies aircraft routing and scheduling on the airport ground. Taxi planning has been formulated using a binary multicommodity flow model in a space-time airport network. The flow capacity constraints are used to represent the conflicts among aircraft, given an airport’s capacity. Branch and price methodology has been adapted to take advantage of the integer model structures. The computational tests have been run with real data from Adolfo Suárez Madrid-Barajas airport. The tests were oriented toward comparing the new adapted branch and price with the classic Branch and Bound algorithm, trying to obtain conclusions that are useful for airport managers.

A New Resource-Constrained Multicommodity Flow Model for Conflict-Free Train Routing and Scheduling

2011 ◽  
Vol 45 (2) ◽  
pp. 212-227 ◽  
Author(s):  
G. Caimi ◽  
F. Chudak ◽  
M. Fuchsberger ◽  
M. Laumanns ◽  
R. Zenklusen
Keyword(s):  
Flow Model ◽  
Multicommodity Flow ◽  
Resource Constrained ◽  
Routing And Scheduling ◽  
Train Routing

Traffic flow model based on real data

2021 ◽  
Author(s):  
Teodora A. Mecheva ◽  
Nikolay R. Kakanakov
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Real Data ◽  
Traffic Flow Model ◽  
Model Based

Branch and Price for Chance-Constrained Bin Packing

2020 ◽  
Vol 32 (3) ◽  
pp. 547-564
Author(s):  
Zheng Zhang ◽  
Brian T. Denton ◽  
Xiaolan Xie
Keyword(s):  
Bin Packing ◽  
Real Data ◽  
Integer Program ◽  
Chance Constraints ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Closed Form Expression ◽  
Mixed Integer Program ◽  
Branch And Price ◽  
Item Size

This article describes two versions of the chance-constrained stochastic bin-packing (CCSBP) problem that consider item-to-bin allocation decisions in the context of chance constraints on the total item size within the bins. The first version is a stochastic CCSBP (SP-CCSBP) problem, which assumes that the distributions of item sizes are known. We present a two-stage stochastic mixed-integer program (SMIP) for this problem and a Dantzig–Wolfe formulation suited to a branch-and-price (B&P) algorithm. We further enhance the formulation using coefficient strengthening and reformulations based on probabilistic packs and covers. The second version is a distributionally robust CCSBP (DR-CCSBP) problem, which assumes that the distributions of item sizes are ambiguous. Based on a closed-form expression for the DR chance constraints, we approximate the DR-CCSBP problem as a mixed-integer program that has significantly fewer integer variables than the SMIP of the SP-CCSBP problem, and our proposed B&P algorithm can directly solve its Dantzig–Wolfe formulation. We also show that the approach for the DR-CCSBP problem, in addition to providing robust solutions, can obtain near-optimal solutions to the SP-CCSBP problem. We implement a series of numerical experiments based on real data in the context of surgery scheduling, and the results demonstrate that our proposed B&P algorithm is computationally more efficient than a standard branch-and-cut algorithm, and it significantly improves upon the performance of a well-known bin-packing heuristic.

A global router based on a multicommodity flow model

Integration ◽  
1987 ◽  
Vol 5 (1) ◽  
pp. 3-16 ◽  
Author(s):  
E. Shragowitz ◽  
S. Keel
Keyword(s):  
Flow Model ◽  
Multicommodity Flow

Reconstruction of False and Missing Data with First-Order Traffic Flow Model

2002 ◽  
Vol 1802 (1) ◽  
pp. 155-165 ◽  
Author(s):  
H. Haj-Salem ◽  
J. P. Lebacque
Keyword(s):  
Flow Model ◽  
Data Cleaning ◽  
Wide Spectrum ◽  
Real Data ◽  
Mathematical Structure ◽  
Traffic Data ◽  
First Order ◽  
Traffic Conditions ◽  
High Level ◽  
Real Time Application

In previous studies, two traffic data-cleaning algorithms were developed at the Institut National de Recherche sur les Transports on the basis of filtering techniques and statistical approaches. Because of their mathematical structure (linearity of the process), both algorithms present a high level of inaccuracy in the case of nonhomogeneous traffic conditions at the location of the measurement stations (for example, free flow upstream and congestion downstream, or vice versa). A new algorithm for solving the traffic data-cleaning problem on the basis of real-time application of a dynamic first-order modeling approach was devised to take into account the nonlinearity of the traffic phenomenon. The developed algorithm, named PROPAGE, was tested using real data measurements, including a wide spectrum of traffic conditions. Compared with results from previous algorithms, the results obtained were more accurate.

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