A branch-first, cut-second approach for locomotive assignment

Article Abstract:

A methodological and computational solution to the locomotive assignment problem that significantly reduces integrality gaps in the integer programming formulation is developed. The locomotive assignment problem involves giving trains just enough power to meet its schedule at minimum cost. The solution involves branching decisions that define the projection of the problem on a low-dimensional subspace. The facets of the polyhedron describing a restricted complaint can then be derived. This strategy applies to networks with only two types of locomotives to those with several. This shows that the method can be used to solve large scale real world problems. The effectiveness of this method can be seen in its successful application in the weekly strategic problem of the firm Canadian National Railways Co.

Railroad Rolling Stock Manufacturing, Railroad equipment, Locomotives, Operations Research, Methods, Analysis, Railroad equipment industry, Canadian National Railway Co.

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Daily aircraft routing and scheduling

Article Abstract:

The daily aircraft routing and scheduling problem (DARSP) is examined. The problem is important for airlines since the fleet schedule determines a significant portion of airline cost estimates, including the fixed cost for each aircraft, salaries of crew members and cost of the fuel consumed. Two models for the DARSP are presented, namely, a Set Partitioning type formulation and a time constrained multicommodity network flow formulation. Integer solutions are derived through the use of a branch-and-bound algorithm. Optimal branching strategies compatible with the column generation technique are also proposed, The strategies were developed by capitalizing on the relationship between the two formulations.

Airlines

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Lagrangian relaxation methods for solving the minimum fleet size multiple traveling salesman problem with time windows

Article Abstract:

The problem of finding the minimum number of vehicles required to visit a set of nodes once is considered. The fleet is subject to time window constraints and is located at a common depot. An optimal solution to this problem is presented that uses the augmented Lagrangian method. In one Lagrangian relaxation studied, time constraints are relaxed, which produces easily solved network sub-problems, but the bound obtained by the relaxation is weak. Constraints requiring each node to be visited are relaxed in the second Lagrangian relaxation, producing excellent bounds.

Usage, Algorithms, Lagrange equations

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