Chapter

The Minimum Shift Design Problem: Theory and Practice

01/1970; 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

ABSTRACT 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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Keywords

approximation lower
 
certain time interval
 
commercial shift scheduling software project
 
existing commercial implementation
 
experimental analysis
 
interleaving different neighborhood definitions
 
local search procedure
 
MCMF
 
MECF problems
 
min-cost max-flow
 
minimum edge-cost flow problem
 
minimum shift design problem
 
new greedy heuristic
 
optimal assignment
 
second part
 
serial combination
 
shift scheduling
 
shifts
 
special case
 
workforce requirements