Authors:
Fatma Hermès
1
and
Khaled Ghédira
2
Affiliations:
1
High Institute of Computer Sciences (ISI) and Tunis El Manar University, Tunisia
;
2
High Institute of Management (ISG) and Tunis University, Tunisia
Keyword(s):
Scheduling, Identical Parallel Machines, Non-idling Constraint, Release Dates, Delivery Times, Makespan.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Evolutionary Computation and Control
;
Formal Methods
;
Informatics in Control, Automation and Robotics
;
Intelligent Control Systems and Optimization
;
Optimization Algorithms
;
Planning and Scheduling
;
Simulation and Modeling
;
Symbolic Systems
Abstract:
This paper considers the problem of scheduling jobs with release dates and delivery times on identical
machines where the machines must work under the non-idling constraint. Indeed, each machine must
process all the jobs affected to it continuously without any intermediate delays. The objective is to minimize
the makespan. This problem is strongly NP-hard since its particular case on only one machine has been
proved to be strongly NP-hard (Chrétienne, 2008). Furthermore, the complexity of the considered problem
where the jobs are unit-time remains an open question (Chrétienne, 2014). Recently, the particular case on
only one non-idling machine has been studied and some efficient classical algorithms proposed to solve the
classic one machine scheduling problem (i.e without adding the non-idling constraint) have been easily
extended to solve its non-idling version (see (Chrétienne, 2008), (Carlier et al., 2010) and (Kacem and
kellerer, 2014)). In this paper, we propose some
heuristics to solve the considered machines problem
under the non-idling constraint. We first suggest a generalization of the well known rule of Jackson
(Jackson, 1955) in order to construct feasible schedules. This rule gives priority to the ready jobs with the
greatest delivery time. Then, we extend Potts algorithm (Potts, 1980) which has been proposed to solve the
one machine problem. Finally, we present the results of a computational study which shows that the
proposed heuristics are fast and yields in most tests schedules with relative deviation which is on average
equal to 0,4%.
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