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An LP-based heuristic for Inspector Scheduling

  • We present a heuristic based on linear programming (LP) for the integrated tour and crew roster planning of toll enforcement inspectors. Their task is to enforce the proper paying of a distance-based toll on German motorways. This leads to an integrated tour planning and duty rostering problem; it is called Toll Enforcement Problem (TEP). We tackle the TEP by a standard multi-commodity flow model with some extensions in order to incorporate the control tours. The heuristic consists of two variants. The first, called Price & Branch, is a column generation approach to solve the model’s LP relaxation by pricing tour and roster arc variables. Then, we compute an integer feasible solution by restricting to all variables that were priced. The second is a coarse-to-fine approach. Its basic idea is projecting variables to an aggregated variable space, which is much smaller. The aim is to spend as much algorithmic effort in this coarse model as possible. For both heuristic procedures we will show that feasible solutions of high quality can be computed even for large scale industrial instances.
Author:Gerwin Gamrath, Markus Reuther, Thomas Schlechte, Elmar SwaratORCiD
Document Type:In Proceedings
Parent Title (English):Proceedings of the 13th International Conference on the Practice and Theory of Automated Timetabling - PATAT 2021: Volume I
First Page:77
Last Page:86
Year of first publication:2021
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