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A linear mixed-integer model FOR A PURCHASING PROBLEM INVOLVING DISCOUNT STRUCTURES

APPLIED MATHEMATICAL modelLING 1983年第5期7卷 372-373页

作者： SINCLAIR, M Department of Applied Mathematics University of Stellenbosch Stellenbosch 7600 South Africa

In a recent paper a quadratic mixed-integer programming model was presented for an industrial purchasing problem involving complicated discount structures. The solution method presented in the paper for this model involved the solution of a series of quadratic zero-one programming problems. The disadvantages of such an approach are immediately obvious to anyone familiar with the state-of-the-art of solution methods for nonlinear integer programming problems. In this paper a linear model is constructed for the same problem and its computational advantages over the nonlinear model are discussed.

关键词： mathematical model linear mixed-integer programming model

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Integrated multi-track station layout design and train scheduling models on railway corridors

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2016年 69卷 91-119页

作者： Qi, Jianguo Yang, Lixing Gao, Yuan Li, Shukai Gao, Ziyou Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

The dwelling capacity of the station (mainly determined by its multi-track layout) is a practically significant factor to influence the quality of the train schedules, especially in a busy railway corridor with heterogeneous trains and complex operations. To improve the passing capacity and transportation efficiency, this paper focuses on a network design problem over a railway corridor, in which some critical stations are considered to enlarge the number of siding tracks or platforms within the budget constraints. To evaluate the quality of design strategies, the construction cost and total travel time in the corresponding optimal train schedule are adopted as evaluation indexes. Based on two specific modeling methodologies, two types of optimization models are particularly formulated with different considerations. One is a single-level linear mixed-integer programming (S-LMIP) model based on the space-time network representation method;the other is a bi-level programming model associated with the platform choice-based method, where the upper level of the proposed model aims to design new siding tracks/platforms in the candidate stations, and the lower level is a train scheduling model with assigning the tracks for each train at each station. The commercial software GAMS with CPLEX solver and local searching based heuristic with integrated CPLEX solver are respectively employed to solve the near-optimal solutions for these two types of models. Finally, two sets of examples, in which a sample railway corridor and the Wuhan-Guangzhou high-speed railway corridor are adopted as the experimental environments, are implemented to illustrate the performance and effectiveness of the proposed approaches. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Train scheduling Multi-track station layout design linear mixed-integer programming model Bi-level optimization model Local search algorithm

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