Schedule Execution for Two-Machine Job-Shop to Minimize Makespan with Uncertain Processing Times

Abstract

This study addresses a two-machine job-shop scheduling problem with fixed lower and upper bounds on the job processing times. An exact value of the job duration remains unknown until completing the job. The objective is to minimize a schedule length (makespan). It is investigated how to best execute a schedule, if the job processing time may be equal to any real number from the given (closed) interval. Scheduling decisions consist of the off-line phase and the on-line phase of scheduling. Using the fixed lower and upper bounds on the job processing times available at the off-line phase, a scheduler may determine a minimal dominant set of schedules (minimal DS), which is based on the proven sufficient conditions for a schedule dominance. The DS optimally covers all possible realizations of the uncertain (interval) processing times, i.e., for each feasible scenario, there exists at least one optimal schedule in the minimal DS. The DS enables a scheduler to make the on-line scheduling decision, if a local information on completing some jobs becomes known. The stability approach enables a scheduler to choose optimal schedules for most feasible scenarios. The on-line scheduling algorithms have been developed with the asymptotic complexity O(n2) for n given jobs. The computational experiment shows the effectiveness of these algorithms.

Applying a Hybrid Model to Solve the Job-Shop Scheduling Problem with Preventive Maintenance, Sequence-Dependent Setup Times and Unknown Processing Times

“…Based on our literature research, no papers have been found considering a job-shop with sequence-dependent setup times and preventive maintenance, where the processing times are unknown at the beginning. Previously mentioned Sotskov et al (2020) shows the most comparable research with having uncertain products times until the product is produced, without sequence-dependent setup times and preventive maintenance. Naderi et al (2009) investigates sequence-dependent setup times and preventive maintenance in job-shop scheduling, however they considered all processing times to be known at the start.…”

“…This still considers much information known in advance of the production process, which is unrealistic due to many factors that can influence the actual processing times. Sotskov et al (2020) researched a two-machine job-shop with uncertain processing times but did not consider maintenance or sequence-dependent setup times. Lou et al (2012) researched reactive scheduling, using an initial schedule, based on unexpected events in the simulation environment.…”

A JSSP solution for production planning optimization combining industrial engineering and evolutionary algorithms

“…The flexible JSSP extends the deterministic JSSP by allowing a machine operation to be processed by one machine out of a set of machines, thereby adding the problem of assigning each operation to a specific machine (routing) [41]. Stochastic JSSPs introduce parameters dealing with probability conditions, for instance, machine breakdown or processing time [16]. Since real-world JSSP times often don't have deterministic value, fuzzy values (processing times, due date, ranking) have been incorporated into JSSP, hence the name fuzzy JSSP [43].…”

Advances and Novel Approaches in Discrete Optimization

“…Sotskov et al [17] consider the two-machine job-shop scheduling problem with interval processing times and makespan minimization. The focus of this paper is how to execute a schedule in the best way.…”