Industrial Engineering and Computer Sciences Division (G2I

Industrial Engineering and Computer Sciences Division (G2I)
A SINGLE MACHINE SCHEDULING PROBLEM
WITH POSITION-DEPENDENT PROCESSING
TIMES AND PRECEDENCE CONSTRAINTS
A. DOLGUI, V. GORDON, V. STRUSEVICH
February 2009
RESEARCH REPORT
2009-500-001
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Centre G2I
Génie Industriel et Informatique
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Industrial Engineering and Computer Sciences
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Ecole Nationale Supérieure des Mines de Saint-Etienne
Centre G2I
158, Cours Fauriel
42023 SAINT-ETIENNE CEDEX 2
France
A Single Machine Scheduling Problem with Position-Dependent Processing
Times and Precedence Constraints
Alexandre Dolgui1, Valery Gordon1, and Vitaly Strusevich3*
1
Centre for Industrial Engineering and Computer Science
Ecole Nationale Supérieure des Mines de Saint-Etienne
158, Cours Fauriel, 42023 Saint Etienne, France
2
United Institute of Informatics Problems
National Academy of Sciences of Belarus
Surganova 6, 220012 Minsk, Belarus
3
School of Computing and Mathematical Sciences
University of Greenwich
Old Royal Naval College, Park Row, Greenwich, SE10 9LS London, UK
Abstract. In many real-life situations the processing conditions in scheduling models cannot be
viewed as given constants since they vary over time thereby affecting actual durations of jobs. We
consider single machine scheduling problems of minimizing the makespan in which the processing
time of a job depends on its position (with either cumulative deterioration or exponential learning).
It is often found in practice that some products are manufactured in a certain order implied, for example, by technological, marketing or assembly requirements. This can be modeled by imposing
precedence constraints on the set of jobs. We consider scheduling models with positional deterioration or learning under precedence constraints that built up iteratively from prime partially ordered
sets of width bounded by some fixed value (this class of precedence constraints includes, in particular, series-parallel precedence constraints). We show that objective functions of the considered problems satisfy job module property and possess the recursion property. As a result, the problems under
consideration are solvable in polynomial time.
Keywords: Scheduling; Precedence constraints; Deterioration; Learning; Positionally dependent
processing time.
*
Corresponding author, e-mail address: [email protected], tel: +44 (0)20 8331 8662, fax: +44
(0)20 8331 8665.
Ecole Nationale Supérieure des Mines de Saint-Etienne
Centre G2I
158, Cours Fauriel
42023 SAINT-ETIENNE CEDEX 2
www.emse.fr