Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Routing open shop with two nodes, unit processing times and equal number of jobs and machines. / Golovachev, Mikhail; Pyatkin, Artem V.
Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings. ed. / Michael Khachay; Panos Pardalos; Yury Kochetov. Springer-Verlag GmbH and Co. KG, 2019. p. 264-276 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11548 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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TY - GEN
T1 - Routing open shop with two nodes, unit processing times and equal number of jobs and machines
AU - Golovachev, Mikhail
AU - Pyatkin, Artem V.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In the Routing Open Shop problem n jobs are located in the nodes of an edge-weighted graph G=(V,E) and m machines must process all jobs in such a way that each machine processes only one job at a time and each job is processed by only one machine at a time. The goal is to minimize the makespan, i. e. the time when the last machine comes back to the initial node called a depot (at the beginning all machines are in the depot). This problem is NP-hard even when the graph contains only two nodes. In this paper we consider the case of G=K2 when all processing times and travel times are unit. We pose the conjecture that the problem is polynomially solvable in this case, i.e. that the makespan depends only on the number of machines and the loads of the nodes and can be calculated in time O(log mn). We provide some bounds on the makespan for the case of m=n depending on the loads distribution.
AB - In the Routing Open Shop problem n jobs are located in the nodes of an edge-weighted graph G=(V,E) and m machines must process all jobs in such a way that each machine processes only one job at a time and each job is processed by only one machine at a time. The goal is to minimize the makespan, i. e. the time when the last machine comes back to the initial node called a depot (at the beginning all machines are in the depot). This problem is NP-hard even when the graph contains only two nodes. In this paper we consider the case of G=K2 when all processing times and travel times are unit. We pose the conjecture that the problem is polynomially solvable in this case, i.e. that the makespan depends only on the number of machines and the loads of the nodes and can be calculated in time O(log mn). We provide some bounds on the makespan for the case of m=n depending on the loads distribution.
KW - Complexity
KW - Makespan bounds
KW - Polynomial time
KW - Routing Open Shop
KW - Scheduling
KW - Unit processing times
KW - COMPLEXITY
KW - ALGORITHM
UR - http://www.scopus.com/inward/record.url?scp=85067656044&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-22629-9_19
DO - 10.1007/978-3-030-22629-9_19
M3 - Conference contribution
AN - SCOPUS:85067656044
SN - 9783030226282
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 264
EP - 276
BT - Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings
A2 - Khachay, Michael
A2 - Pardalos, Panos
A2 - Kochetov, Yury
PB - Springer-Verlag GmbH and Co. KG
T2 - 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019
Y2 - 8 July 2019 through 12 July 2019
ER -
ID: 20643507