TY - JOUR
T1 - The minimum shift design problem
T2 - theory and practice
AU - Gaspero, Luca Di
AU - Gärtner, Johannes
AU - Kortsarz, Guy
AU - Musliu, Nysret
AU - Schaerf, Andrea
AU - Slany, Wolfgang
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2003
Y1 - 2003
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0142183780&partnerID=8YFLogxK
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AN - SCOPUS:0142183780
SN - 0302-9743
VL - 2832
SP - 593
EP - 604
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
ER -