Personnel Planning with Multi-tasking and Structured Qualifications
We present a fairly involved ILP-model for a complex personnel planning problem arising from a real-world application. Two main aspects distinguish the problem from standard models: (i) Several tasks may be executed by the same person simultaneously. Howe
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Abstract We present a fairly involved ILP-model for a complex personnel planning problem arising from a real-world application. Two main aspects distinguish the problem from standard models: (i) Several tasks may be executed by the same person simultaneously. However, this multi-tasking is subject to certain complicated conditions. (ii) Qualification of personnel is complex and totally inhomogeneous. We introduce a representation for both issues that is at the same time fairly general and still easy enough to operate for the personnel manager.
1 Introduction In a standard personnel assignment problem, every person can fulfill every given task, therefore the planning problem boils down to covering the required time periods by a feasible roster. If each person is assigned a certain skill level on an ordinal scale and each task requires a minimal skill level (a frequent scenario e.g. in hospitals), a feasible plan has to make sure that each person assigned to a task has at least the required skill level. Due to space restrictions we refer the reader to the surveys [1, 2, 4], instead of giving a detailed literature review. In this contribution we consider a much more complicated setting: each person has a certain portfolio of unordered, categorical skills and can only fulfill tasks it is qualified for. Hence, each person has to be considered individually and the personnel structure is very inhomogeneous. The main innovation of our problem is the feature that a person might fulfill several tasks at the same time. This is a major deviation from classical personnel planning literature although complex skill levels were considered T. Kreiter (B) · U. Pferschy · J. Schauer Department of Statistics and Operations Research, University of Graz, Universitaetsstrasse 15, E3, 8010 Graz, Austria e-mail: [email protected] U. Pferschy e-mail: [email protected] J. Schauer e-mail: [email protected] © Springer International Publishing Switzerland 2017 K.F. Dœrner et al. (eds.), Operations Research Proceedings 2015, Operations Research Proceedings, DOI 10.1007/978-3-319-42902-1_81
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e.g. in [3]. Moreover, the possibility of combining tasks is again highly non-uniform and depends both on the individual task and the considered person.
2 Representation of Task Combinations The possibility of combining tasks, i.e. of carrying out more than one task at the same time by the same person, requires compatibility of tasks and ability of persons to perform the corresponding work by multi-tasking. Each of these two aspects has to be characterized and represented in a suitable way.
2.1 Representation of Task Compatibility The simple exclusion of one person performing two tasks with overlapping time windows can be represented by a conflict matrix with cjk = 1 indicating that tasks j and k require different persons. However, the practical planning problem this work originates from also contains a number of tasks which require little operative work. Instead, they mainly consist of monitoring
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