Common operation scheduling (COS) problems arise in real-world applications, such as industrial processes of material cutting or component dismantling. In COS, distinct jobs may share operations, and when an operation is done, it is done for all the jobs that share it. We here propose a 0-1 LP formulation with exponentially many inequalities to minimize the weighted number of tardy jobs. Separation of inequalities is in NP, provided that an ordinary min Lmaxscheduling problem is in P. We develop a branch-and-cut algorithm for two cases: one machine with precedence relation; identical parallel machines with unit operation times. In these cases separation is the constrained maximization of a submodular set function. A previous method is modified to tackle the two cases, and compared to our algorithm. We report on tests conducted on both industrial and artificial instances. For single machine and general processing times the new method definitely outperforms the other, extending in this way the range of COS applications.
Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs
Arbib, Claudio
;Servilio, Mara
2019-01-01
Abstract
Common operation scheduling (COS) problems arise in real-world applications, such as industrial processes of material cutting or component dismantling. In COS, distinct jobs may share operations, and when an operation is done, it is done for all the jobs that share it. We here propose a 0-1 LP formulation with exponentially many inequalities to minimize the weighted number of tardy jobs. Separation of inequalities is in NP, provided that an ordinary min Lmaxscheduling problem is in P. We develop a branch-and-cut algorithm for two cases: one machine with precedence relation; identical parallel machines with unit operation times. In these cases separation is the constrained maximization of a submodular set function. A previous method is modified to tackle the two cases, and compared to our algorithm. We report on tests conducted on both industrial and artificial instances. For single machine and general processing times the new method definitely outperforms the other, extending in this way the range of COS applications.File | Dimensione | Formato | |
---|---|---|---|
1-s2.0-S0305048316304856-main.pdf
accesso aperto
Descrizione: pdf
Tipologia:
Documento in Versione Editoriale
Licenza:
Dominio pubblico
Dimensione
1.9 MB
Formato
Adobe PDF
|
1.9 MB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.