Heuristics for Minimizing the Number of Tardy Jobs on a Single Machine With Release Time

Abstract

This paper considers the problem of minimizing the number of tardy jobs with release time on a single machine. Given that the problem has been classified as strongly NP-Hard, three heuristics (EOO, HR2, and HR3) are proposed for this problem. They are compared with a heuristic by Dauzere-Perez (selected from the literature). Randomly-generated problems ranging from 3 to 500 jobs are solved. Experimental results show that one of the proposed heuristics (EOO) outperforms other heuristics, both in terms of quality of solution (effectiveness) and speed of execution (efficiency). OPSOMMINGDie navorsing behandel die ministering van voltooiingstyd van die aantal draaltake by 'n enkele werktuig. As aanvaar word dat die problem geklassifiseer word as hoofsaaklike NP-hard, word voorgestel dat die vraagstuk bestudeer word deur gebruik te maak van drie heuristiese metodes (EOO, HR2, HR3). Die metodes word vergelyk ten opsigte van vertoning met die Dauzere-Perez-metode. Toevalsgegenereerde probleme wat strek vanaf 3 tot 500 draaltake word behandel. Die eksperimentele werk lewer bewys dat die EOO-metode ander metodes die loef afsteek ten opsigte van oplossingsgoedheid en -snelheid.

Demand Categorisation, Forecasting, and Inventory Control for Intermittent Demand Items

“…The HR7 heuristic systematically combines the AEO and EOO heuristics. (For details of the HR7 heuristic and the BB method, see Oyetunji [17] and Oyetunji and Oluleye [19], page 149, respectively.) The HR7 outperformed the best (HR6) of the heuristics proposed by Oyetunji and Oluleye [18], hence its selection for evaluation.…”

“…This is probably due to the fact that the problem is NP-Hard in the strong sense. Therefore, to compare the performances of the proposed heuristics, a heuristic (HR7) was selected from Oyetunji [17] as well as a branch and bound (BB) method implemented by Oyetunji and Oluleye [19]. The HR7 heuristic systematically combines the AEO and EOO heuristics.…”

“…A normalisation scheme (which converts the values of one criterion to the other) was also put forward. Three heuristics (HR4, HR5, and HR6) were proposed by Oyetunji and Oluleye [19] for the bi-criteria problem of simultaneously minimising the total completion time (Ctot) and the number of tardy jobs (NT) on a single machine with release dates. The bi-criteria problem of minimising the total completion time (Ctot) and number of tardy jobs (NT) on a single machine with release dates was modeled as hierarchical minimisation problems by Oyetunji and Oluleye [20].…”

“…The effort put into single criterion scheduling problems since the pioneering work of Johnson [7] has paid off. Today a number of solution methods proposed for the bi-criteria and multi-criteria scheduling problems have been either a direct modification or an amalgamation of solution methods to single criterion scheduling problems [19,23].…”

“…The total cost of a schedule is not a function of one objective, but rather a function of two or more objectives [4]. Since realising this fact, many researchers [6,13,15,21,22,23] have worked on bi-criteria and multi-criteria scheduling problems. The effort put into single criterion scheduling problems since the pioneering work of Johnson [7] has paid off.…”