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. No-wait requirement enforces that the delay between operations is equal to 0. No-idle 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 no-wait & no-idle requirements with the restriction that each machine handles at most 4 job.
LicenseCopyright (AGH-UST, Kraków, Poland, 2017)
- Conference activity
- publikacja w wydawnictwie zbiorowym recenzowanym (także w materiałach konferencyjnych)
- Title of issue:
- DMMS 2017 & ZTS XX Proceedings strony 65 - 72
- Publication year:
- Bibliographic description:
- Pastuszak K., Małafiejski M., Ocetkiewicz K.: No-Wait & No-Idle 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 Reklamowo-Wydawnicza „Ostoja”, Cianowice, ul. Niebyła 17, 32-043 Skała , 2017, s.65-72
- Bibliography: test
- Giaro, K. (2003). Task scheduling by graph coloring (in Polish). D.Sc. Dissertation. Gdansk University of Technology. open in new tab
- Giaro, K. (1997). The complexity of consecutive D-coloring of bipartite graphs: 4 is easy, 5 is hard. Ars Combinatoria 47, pp. 287-300.
- Gonzalez, T., Sahni, S. (1976). Open shop scheduling to minimize finish time. Journal of the ACM, pp. 665- 679. open in new tab
- Graham, R., Lawler, E., Lenstra, J., Rinnooy Kan, A. (1979). Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey. Proceedings of the Advanced Research Institute on Discrete Optimization and Systems Applications of the Systems Science Panel of NATO and of the Discrete Optimization Symposium., pp. 287-326. open in new tab
- Hanson, D., Loten, C. O. M., Toft, B. (1998). On interval coloring of biregular bipartite graphs. Ars ombinatoria, pp. 23-32.
- Małafiejska, A. (2016). Wybrane problemy i modele końcówkowego kolorowania grafów (in Polish). Raport Tech. WETI 3/2016, Politechnika Gdańska (2016), pp. 1-19.
- Melynikov, L., Pyatkin, A., Vizing, V. (2000). On the (k, l)-coloring of incidentors (in Russian). Diskretn. Anal. Issled. Oper. 1, pp. 29-37.
- Pyatkin, A. V. (1997a). Some optimization problems of scheduling the transmission of messages in a local communication network. Operations Research and Discrete Analysis, pp. 227-232, 1997. open in new tab
- Pyatkin, A. (1997b). The incidentor coloring problems and their applications, Ph.D. Dissertation (in Russian). Institute of Mathematics SB RAS, Novosibirsk. open in new tab
- Pyatkin, A. V. (2002). The incidentor coloring of multigraphs and its applications. Electronic Notes in Discrete Mathematics, pp. 103-104.
- Pyatkin, A. (2004). Upper and lower bounds for an incidentor (k,l)-chromatic number (in Russian). Diskretn. Anal. Issled. Oper., 1, pp. 93-102.
- Pyatkin, A., Vizing, V. (2006). Incidentor coloring of weighted multigraphs. Discrete Applied Mathematics, 120, pp. 209-217.
- Pyatkin, A. (2013). Incidentor coloring: Methods and results. Graph Theory and Interactions, Durham. open in new tab
- Pyatkin, A. (2015). On an Interval (1,1)-Coloring of Incidentors of Interval Colorable Graphs. Journal of Applied and Industrial Mathematics, 9, pp. 271-278. open in new tab
- Vizing, V. (2000). On Incidentor Coloring in a Partially Directed Multigraph. Fuzzy Sets and Systems, pp. 141-147. open in new tab
- Vizing, V. (2003). Interval colorings of the incidentors of an undirected multigraph (in Russian). Diskretn. Anal. Issled. Oper. pp. 14-40. open in new tab
- Vizing, V. (2005). On the (p, q)-coloring of incidentors of an undirected multigraph (in Russian). Diskretn. Anal. Issled. Oper. 1, pp. 23-39. open in new tab
- Vizing, V. (2007). On Bounds for the Incidentor Chromatic Number of a Directed Weighted Multigraph. Journal of Applied and Industrial Mathematics, 1, pp. 504-508. open in new tab
- Vizing, V. (2009). On Incidentor Coloring in a Hypergraph. Journal of Applied and Industrial Mathematics, 3, pp. 144-147. open in new tab
- Vizing, V. (2012). Multicoloring the Incidentors of a Weighted Undirected Multigraph. Journal of Applied and Industrial Mathematics, 6, pp. 514-521. open in new tab
- Vizing, V. (2014). Multicoloring the Incidentors of a Weighted Directed Multigraph. Journal of Applied and Industrial Mathematics, 8, pp. 604-608. open in new tab
- Verified by:
- Gdańsk University of Technology
seen 75 times