The Minimum Shift Design Problem: Theory and Practice

DOI: 10.1007/978-3-540-39658-1_54 In book: Algorithms - ESA 2003, Proceedings of the 11th Annual European Symposium, Budapest, Hungary, September 16-19, 2003, Publisher: Springer Verlag, Editors: Di Battista, Giuseppe, Zwick, Uri, pp.593-604


We study the minimum shift design problem (MSD) that arose in a commercial shift scheduling software project: Given a collection of shifts and workforce requirements for
a certain time interval, we look for a minimum cardinality subset of the shifts together with an optimal assignment of workers
to this subset of shifts such that the deviation from the requirements is minimum. This problem is closely related to the
minimum edge-cost flow problem (MECF), a network flow variant that has many applications beyond shift scheduling. We show that MSD reduces to a special case of MECF. We give a logarithmic hardness of approximation lower bound. In the second part of the paper, we present practical heuristics
for MSD. First, we describe a local search procedure based on interleaving different neighborhood definitions. Second, we describe
a new greedy heuristic that uses a min-cost max-flow (MCMF) subroutine, inspired by the relation between the MSD and MECF problems. The third heuristic consists of a serial combination of the other two. An experimental analysis shows that our
new heuristics clearly outperform an existing commercial implementation.

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    • "Given this formulation of the restricted variant of min-SHIFT DESIGN it is possible to prove the following result (the detailed proof is contained in [4]). "
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    ABSTRACT: The min-SHIFT DESIGN problem is an important scheduling problem that needs to be solved in many industrial contexts. The issue is to find a minimum number of shifts and the number of employees to be assigned to these shifts in order to minimize the deviation from the workforce requirements. Our research considers both theoretical and practical aspects of the min-SHIFT DESIGN problem. First, we establish a complexity result by means of a reduction to a network flow problem. The result shows that even a logarithmic approximation of the problem is NP-hard. However, the problem becomes poly-nomial if the issue of minimizing the number of shifts is neglected. On the basis of these results, we propose a hybrid heuristic for the problem which relies on a greedy construction phase, based on the network flow analogy, followed by a local search algorithm that makes use of multiple neighborhood relations. An experimental analysis on structured random instances shows that the hy-brid heuristic clearly outperforms an existing commercial implementation and highlights the respective merits of the composing heuristics for different perfor-mance parameters.
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    Automated Scheduling and Planning - From Theory to Practice, Edited by Etaner-Uyar, A. cSima and Özcan, Ender and Urquhart, Neil, 01/2013: pages 109-127; Springer-Verlag., ISBN: 9783642393037