Complexity of cyclic job shop scheduling problems for identical jobs with no-wait constraints

A. A. Romanova^a, V. V. Servakh<sup>b

a</sup> Omsk State University, 55a Mir Avenue, 644077 Omsk, Russia
^b Omsk Branch of Sobolev Institute of Mathematics, 13 Pevtsov Street, 644099 Omsk, Russia

Abstract: We consider the cyclic job shop problem with no-wait constraints which consists in minimizing the cycle time. We assume that a single product is produced on a few machines. A job is processed by performing a given set of operations in a predetermined sequence. Each operation can be performed on exactly one machine. We consider the problem of minimization the cycle time with no-wait constraints between some pairs of sequential operations and investigate the complexity of the problem and some of its subproblems. In general, the problem is proved to be strongly NP-hard. In the case when the job is processed without downtime between operations, polynomial solvability is proved and the two algorithms are proposed. Also we develop an algorithm for the general case which is pseudopolynomial if the number of admissible downtime is fixed. The case of a single no-wait constraint is polynomially solvable. The problem with two no-wait constraints becomes NP-hard. We found effectively solvable cases and propose the corresponding algorithms. Illustr. 4, bibliogr. 14.

Keywords: scheduling theory, cyclic job shop, identical jobs, computational complexity theory, polynomial algorithm, pseudopolynomial algorithm.

UDC: 519.8

Received: 27.08.2018
Revised: 29.07.2019
Accepted: 28.08.2019

DOI: 10.33048/daio.2019.26.629