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Network flow models for intraday personnel scheduling problems

Brucker, Peter; Qu, Rong

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Peter Brucker

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Professor of Computer Science


Personnel scheduling problems can be decomposed into two stages. In the first stage for each employee the working days have to be fixed. In the second stage for each day of the planning period an intraday scheduling problem has to be solved. It consists of the assignment of shifts to the employees who have to work on the day and for each working period of an employee a task assignment such that the demand of all tasks for personnel is covered. In Robinson et al. (Burke and Trick (Eds.), Proceedings of the 5th International Conference on the Practice and Theory of Automated Timetabling, 18th August–20th August 2004, Pittsburgh, PA, USA, pp. 561–566, 2005), the intraday problem has been formulated as a maximum flow problem. The assumptions are that, employees are qualified for all tasks, their shifts are given, and they are allowed to change tasks during the day.

In this work, we extend the network flow model to cover the case where not all employees are qualified to perform all tasks. The model is further extended to be able to calculate shifts of employees for the given day, assuming that an earliest starting time, a latest finishing time, and a minimal working time are given. Labour cost can be also taken into account by solving a minimum cost network flow problem.

Journal Article Type Article
Publication Date Jan 1, 2014
Deposit Date Feb 19, 2015
Publicly Available Date Feb 19, 2015
Journal Annals of Operations Research
Print ISSN 0254-5330
Electronic ISSN 0254-5330
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 218
Issue 1
Keywords Personnel scheduling, Assignment problem, Network flows
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Publisher URL
Additional Information The final publication is available at Springer via


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