Thanks to the rapidly advancing development of (commercial) MILP software and hardware components, pseudo-polynomial formulations have been established as a powerful tool for solving cutting and packing problems in recent years. In this paper, we focus on the one-dimensional skiving stock problem (SSP), where a given inventory of small items has to be recomposed to obtain a maximum number of larger objects, each satisfying a minimum threshold length. In the literature, different modeling approaches for the SSP have been proposed, and the standard flow-based formulation has turned out to lead to the best trade-off between efficiency and solution time. However, especially for instances of practically meaningful sizes, the resulting models involve very large numbers of variables and constraints, so that appropriate reduction techniques are required to decrease the numerical efforts. For that reason, this paper introduces two improved flow-based formulations for the skiving stock problem that are able to cope with much larger problem sizes. By means of extensive experiments, these new models are shown to possess significantly fewer variables as well as an average better computational performance compared to the standard arcflow formulation.

Improved flow-based formulations for the skiving stock problem / Martinovic, J.; Delorme, M.; Iori, M.; Scheithauer, G.; Strasdat, N.. - In: COMPUTERS & OPERATIONS RESEARCH. - ISSN 0305-0548. - 113:(2020), pp. 1-18. [10.1016/j.cor.2019.104770]

Improved flow-based formulations for the skiving stock problem

Iori M.;
2020

Abstract

Thanks to the rapidly advancing development of (commercial) MILP software and hardware components, pseudo-polynomial formulations have been established as a powerful tool for solving cutting and packing problems in recent years. In this paper, we focus on the one-dimensional skiving stock problem (SSP), where a given inventory of small items has to be recomposed to obtain a maximum number of larger objects, each satisfying a minimum threshold length. In the literature, different modeling approaches for the SSP have been proposed, and the standard flow-based formulation has turned out to lead to the best trade-off between efficiency and solution time. However, especially for instances of practically meaningful sizes, the resulting models involve very large numbers of variables and constraints, so that appropriate reduction techniques are required to decrease the numerical efforts. For that reason, this paper introduces two improved flow-based formulations for the skiving stock problem that are able to cope with much larger problem sizes. By means of extensive experiments, these new models are shown to possess significantly fewer variables as well as an average better computational performance compared to the standard arcflow formulation.
19-ago-2019
113
1
18
Improved flow-based formulations for the skiving stock problem / Martinovic, J.; Delorme, M.; Iori, M.; Scheithauer, G.; Strasdat, N.. - In: COMPUTERS & OPERATIONS RESEARCH. - ISSN 0305-0548. - 113:(2020), pp. 1-18. [10.1016/j.cor.2019.104770]
Martinovic, J.; Delorme, M.; Iori, M.; Scheithauer, G.; Strasdat, N.
File in questo prodotto:
File Dimensione Formato  
7067.pdf

accesso aperto

Descrizione: Versione pre print
Tipologia: Pre-print dell'autore (bozza pre referaggio)
Dimensione 473.83 kB
Formato Adobe PDF
473.83 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1186980
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact