Abstract
In the open shop scheduling with bioperational jobs each job consists of two unit operations with a delay between the end of the first operation and the beginning of the second one. Nowait requirement enforces that the delay between operations is equal to 0. Noidle means that there is no idle time on any machine. We model this problem by the interval incidentor (1, 1)coloring (IIR(1, 1)coloring) of a graph with the minimum number of colors which was introduced and researched extensively by Pyatkin and Vizing. An incidentor is a pair (v, e), where v is a vertex and e is an edge incident to v. In the incidentor coloring of a graph the colors of incidentors at the same vertex must differ. The interval incidentor (1, 1)coloring is a restriction of the incidentor coloring by two additional requirements:colors at any vertex form an interval of integers and the colors of incidentors of the same edge differ exactly by one. In the paper we proposed the polynomial time algorithm solving the problem of IIR(1, 1)coloring for graphs with degree bounded by 4, i.e., we solved the problem of minimum makespan open shop scheduling of bioperational jobs with nowait & noidle requirements with the restriction that each machine handles at most 4 job.
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Copyright (AGHUST, Kraków, Poland, 2017)Details
 Category:
 Conference activity
 Type:
 publikacja w wydawnictwie zbiorowym recenzowanym (także w materiałach konferencyjnych)
 Title of issue:
 DMMS 2017 & ZTS XX Proceedings strony 65  72
 Language:
 English
 Publication year:
 2017
 Bibliographic description:
 Pastuszak K., Małafiejski M., Ocetkiewicz K.: NoWait & NoIdle Open Shop Minimum Makespan Scheduling with Bioperational Jobs// DMMS 2017 & ZTS XX Proceedings / ed. Prof. Tadeusz Sawik, PhD, ScD AGH University of Science and Technology Faculty of Management Kraków: Agencja ReklamowoWydawnicza „Ostoja”, Cianowice, ul. Niebyła 17, 32043 Skała , 2017, s.6572
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