## Computer Aided Scheduling of Switching Engines (2003)

Venue: | MATHEMATICS—KEY TECHNOLOGY FOR THE FUTURE: JOINT PROJECTS BETWEEN UNIVERSITIES AND INDUSTRY |

Citations: | 5 - 2 self |

### BibTeX

@INPROCEEDINGS{Lübbecke03computeraided,

author = {Marco E. Lübbecke and Uwe T. Zimmermann},

title = {Computer Aided Scheduling of Switching Engines},

booktitle = {MATHEMATICS—KEY TECHNOLOGY FOR THE FUTURE: JOINT PROJECTS BETWEEN UNIVERSITIES AND INDUSTRY},

year = {2003},

pages = {690--702},

publisher = {CASPT}

}

### OpenURL

### Abstract

Scheduling the switching engines of an industrial railroad is a formidable and responsible task, closely related to the well-studied pickup and delivery problem with time windows. Aiming at an efficient usage of resources the need arose for a computer aided scheduling tool as support for the human dispatcher. We sketch a set partitioning formulation of this problem to be solved via column generation. The pricing subproblem is hard in the theoretical sense but can be solved by means of a combination of heuristics and exact algorithms. A trade-off between mathematical rigor and practicability becomes apparent and is extensively discussed. Our computational experience with an academic prototype implementation is encouraging. We succeed in obtaining practically acceptable solutions for instances of more than forty customers and six vehicles.

### Citations

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Citation Context .... That is, branch-and-bound, an implicit enumeration scheme to solve integer programs, must be enabled to generate additional columns if required. The resulting algorithm is known as branch-and-price =-=[1]-=-. The general proceeding is to iterativelysx the binary variables to zero or one in a binary tree manner. Again, evaluating each solution is impracticable, hence one strives to keep the search tree as... |

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Citation Context ...re locally most valuable, while the extension itself is calculated at an inferior level. The theoretical principle underlying this idea can be best explained adopting an economic viewpoint, see e.g., =-=[-=-8]. Dierent branches of a large company independently take decisions on how much to use shared scarce resources in order to maximize the company's overall prot. The branches inform a central coordinat... |

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Citation Context ...onsiderable mathematical experience and intuition are required in order to identify the non-obvious. A natural mixed-integer formulation of the Engine Scheduling Problem (ESP), following the lines of =-=[5,12]-=-, with explicit decisions on engine assignments, request sequences, service times, and tonnage requirements, respectively, turned out to be highly symmetric [7]. That is, in a sense, each decision car... |

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Citation Context ... The general strategy is, starting from empty tours, to successively append yet unvisited locations to partial tours, always preserving feasibility with respect to tonnage and time window constraints =-=[3,4,5]-=-. In our algorithm, we combine this technique with the fact that feasible tours are severely restricted in their combinatorial structure, cf. Fig. 2. Indeed, we proceed by iteratively concatenating en... |

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Citation Context ...obtaining integer solutions. There is no doubt that without the concerted interaction of heuristics and exact methods a solution even of smaller instances would not have been possible. The monographs =-=[8,11]-=- and the recent synopsis [2] on various acceleration techniques are valuable sources of information. Computational Experience As indicated earlier, our concept of request is more general than the one ... |

21 |
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Citation Context ...ere is no doubt that without the concerted interaction of heuristics and exact methods a solution even of smaller instances would not have been possible. The monographs [8,11] and the recent synopsis =-=[2]-=- on various acceleration techniques are valuable sources of information. Computational Experience As indicated earlier, our concept of request is more general than the one used in practice. Hence, all... |

17 |
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Citation Context ...roblem (ESP), following the lines of [5,12], with explicit decisions on engine assignments, request sequences, service times, and tonnage requirements, respectively, turned out to be highly symmetric =-=[7-=-]. That is, in a sense, each decision carries too few information; similar solutions are reproducible in many dierent ways. Such circumstance embodies the danger that a reasonably directed search for ... |

17 |
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(Show Context)
Citation Context ...onsiderable mathematical experience and intuition are required in order to identify the non-obvious. A natural mixed-integer formulation of the Engine Scheduling Problem (ESP), following the lines of =-=[5,12]-=-, with explicit decisions on engine assignments, request sequences, service times, and tonnage requirements, respectively, turned out to be highly symmetric [7]. That is, in a sense, each decision car... |

9 |
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(Show Context)
Citation Context ...he topography of the tracks, peculiarities of single customers, weather conditions, service agreements, priorities, and many more complete the picture. For a much more detailed discussion we refer to =-=[9,10-=-]. Current information and disposition systems merely map reality onto the screen, oering an ecient administration e.g., by means of a graphical display of the track layout. The actual disposition, ho... |

7 | Engine routing and scheduling at industrial in-plant railroads. Transportation Sci
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(Show Context)
Citation Context ...he topography of the tracks, peculiarities of single customers, weather conditions, service agreements, priorities, and many more complete the picture. For a much more detailed discussion we refer to =-=[9,10-=-]. Current information and disposition systems merely map reality onto the screen, oering an ecient administration e.g., by means of a graphical display of the track layout. The actual disposition, ho... |

4 |
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(Show Context)
Citation Context ... The general strategy is, starting from empty tours, to successively append yet unvisited locations to partial tours, always preserving feasibility with respect to tonnage and time window constraints =-=[3,4,5]-=-. In our algorithm, we combine this technique with the fact that feasible tours are severely restricted in their combinatorial structure, cf. Fig. 2. Indeed, we proceed by iteratively concatenating en... |

3 |
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Citation Context ...rable speedup of the pricing algorithm. In [9,10] we discuss possible renements of LB. For an exhaustive presentation of the application of such bounds in implicit enumeration strategies we refer to [=-=6-=-]. Integer Solutions It must be stated clearly that all our eorts so far only lead to an optimal solution of the linear relaxation of (SP) which may be fractional. Even worse, there is no guarantee th... |