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Scheduling Jobs with Releases Dates and Delivery Times on M Identical Non-idling Machines

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