Vehicle scheduling in public transit and Lagrangean pricing

Article Abstract:

A study was conducted to analyze the solution of the linear programming relaxation of multi-commodity flow determination of the multiple-depot vehicle scheduling problems resulting from public mass transit. Column generation techniques were utilized to carry out the analysis. A new column generation method based on Lagrangean relaxations of the multicommodity flow framework was then developed to examine the solution. It effectively activated arcs of complete paths. Results indicated that the column generation method can effectively solve the linear programming relaxation of the multicommodity flow formulation of the scheduling problem. Findings also showed that the method can generate minimal linear programming solutions that do not support yield minimum operation weights.

Local and Suburban Transportation, Local Transit, Urban Transit Systems, Management Dynamics NEC, Research, Linear programming, Usage, Management techniques, Lagrangian functions

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A fast taboo search algorithm for the job shop problem

Article Abstract:

A fast and easily implementable approximation algorithm for determining a minimum makespan in a job shop is proposed. The algorithm is based on a taboo search (TS) approach with a specific neighborhood definition which uses a critical path and blocks of operations notions. Computational studies indicate that the algorithm can find shorter makespans than the best approximation approaches and can run in shorter time. The algorithm can also solve the well-known 10 x 10 hard benchmark problem within 30 seconds on a personal computer. Modifications of the classical TS approach are also presented. The proposed method can also be applied to other scheduling problems, such as flow shop and open shop, with the minimum value of the maximum penalty criterion.

Methods, Analysis, Algorithms, Machine shops

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