Abstract
A branch & bound algorithm is presented for a very general scheduling problem withn jobs andm machines. Each job consists of a set of operations. Each operation has to be processed on a dedicated machine. There may be arbitrary precedence relations between the operations. The set of all operations is partitioned into groups. If on a machine an operation belonging to groupG g is processed immediately after an operation belonging to groupG f there is a setup ofs fg time units. We assume thats fg=0 iff=g and that thes fg satisfy the triangle inequality. Computational results for this general problem as well as for special cases like the job-shop problem and the open-shop problem are reported.
Zusammenfassung
Es wird ein Branch & Bound-Algorithmus für ein sehr allgemeines Scheduling Problem mitn Jobs undm Maschinen vorgestellt. Jeder Job besteht aus einer Menge von Operationen, die auf einer ausgewählten Maschine bearbeitet werden müssen. Zwischen den Operationen sind beliebige Vorrangbeziehungen möglich. Ferner werden die Operationen in Gruppen aufgeteilt. Wenn auf einer Maschine eine Operation der GruppeG g unmittelbar nach einer Operation der GruppeG f bearbeitet wird, ist eine Rüstzeit vons fg Zeiteinheiten notwendig. Wir setzen voraus, daßs fg=0 fürf=g und daß dies fg die Dreiecksungleichung erfüllen. Sowohl für dieses allgemeine Problem als auch für Spezialfälle wie das Job-Shop Problem und das Open-Shop Problem werden Rechenergebnisse vorgestellt.
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Supported by the Deutsche Forschungsgemeinschaft (Project JoPTAG) and by INTAS (Project 93–257)
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Brucker, P., Thiele, O. A branch & bound method for the general-shop problem with sequence dependent setup-times. OR Spektrum 18, 145–161 (1996). https://doi.org/10.1007/BF01539706
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DOI: https://doi.org/10.1007/BF01539706
Key words
- General-shop problem
- sequence dependent setup-times
- branch & bound method
- block approach
- immediate selection
- job-shop
- open-shop
- disjunctive graph model