TY - GEN

T1 - Sufficient conditions of polynomial solvability of the two-machine preemptive routing open shop on a tree

AU - Chernykh, Ilya

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The routing open shop problem with preemption allowed is a natural combination of the metric TSP problem and the classical preemptive open shop scheduling problem. While metric TSP is strongly NP-hard, the preemptive open shop is polynomially solvable for any (even unbounded) number of machines. The previous research on the preemptive routing open shop is mostly focused on the case with just two nodes of the transportation network (problem on a link). It is known to be strongly NP-hard in the case of an unbounded number of machines and polynomially solvable for the two-machine case. The algorithmic complexity of both two-machine problem on a triangular network and a three-machine problem with two nodes are still unknown. The problem with a general transportation network is a generalization of the metric TSP and therefore is strongly NP-hard. We describe a wide polynomially solvable subclass of the preemptive routing open shop on a tree. This class allows building an optimal schedule with at most one preemption in linear time. For any instance from that class optimal makespan coincides with the standard lower bound. Therefore, the result, previously known for the problem on a link, is generalized on a special case on an arbitrary tree. The algorithmic complexity of the general case of the two-machine problem on a tree remains unknown.

AB - The routing open shop problem with preemption allowed is a natural combination of the metric TSP problem and the classical preemptive open shop scheduling problem. While metric TSP is strongly NP-hard, the preemptive open shop is polynomially solvable for any (even unbounded) number of machines. The previous research on the preemptive routing open shop is mostly focused on the case with just two nodes of the transportation network (problem on a link). It is known to be strongly NP-hard in the case of an unbounded number of machines and polynomially solvable for the two-machine case. The algorithmic complexity of both two-machine problem on a triangular network and a three-machine problem with two nodes are still unknown. The problem with a general transportation network is a generalization of the metric TSP and therefore is strongly NP-hard. We describe a wide polynomially solvable subclass of the preemptive routing open shop on a tree. This class allows building an optimal schedule with at most one preemption in linear time. For any instance from that class optimal makespan coincides with the standard lower bound. Therefore, the result, previously known for the problem on a link, is generalized on a special case on an arbitrary tree. The algorithmic complexity of the general case of the two-machine problem on a tree remains unknown.

KW - Overloaded edge

KW - Overloaded node

KW - Polynomially solvable subclass

KW - Preemption

KW - Routing open shop

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=85061206621&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-10934-9_7

DO - 10.1007/978-3-030-10934-9_7

M3 - Conference contribution

AN - SCOPUS:85061206621

SN - 9783030109332

T3 - Communications in Computer and Information Science

SP - 97

EP - 110

BT - Optimization and Applications - 9th International Conference, OPTIMA 2018, Revised Selected Papers

A2 - Kochetov, Yury

A2 - Khachay, Michael

A2 - Evtushenko, Yury

A2 - Malkova, Vlasta

A2 - Posypkin, Mikhail

A2 - Jacimovic, Milojica

PB - Springer-Verlag GmbH and Co. KG

T2 - 9th International Conference on Optimization and Applications, OPTIMA 2018

Y2 - 1 October 2018 through 5 October 2018

ER -