Abstract
Optimal schedules in the job shop problem with preemption and with the objective of minimizing an arbitrary regular function of operation completion times are studied. It is shown that for any instance of the problem there always exists an optimal schedule that meets several remarkable properties. Firstly, each changeover date coincides with the completion time of some operation, and so, the number of changeover dates is not greater than the total number of operations, while the total number of interruptions of the operations is no more than the number of operations minus the number of jobs. Secondly, every changeover date is “super-integral”, which means that it is equal to the total processing time of some subset of operations. And thirdly, the optimal schedule with these properties can be found by a simple greedy algorithm under properly defined priorities of operations on machines. It is also shown that for any instance of the job shop problem with preemption allowed there exists a finite set of its feasible schedules which contains at least one optimal schedule for any regular objective function (from the continuum set of regular functions).
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Supported by the Russian Foundation for Basic Research (grants no. 08-01-00370 and 08-06-92000-HHC) and by Federal Target Grant “Scientific and educational personnel of innovation Russia” for 2009–2013 (government contract No. 14.740.11.0362).
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Sevastyanov, S.V., Chemisova, D.A. & Chernykh, I.D. On some properties of optimal schedules in the job shop problem with preemption and an arbitrary regular criterion. Ann Oper Res 213, 253–270 (2014). https://doi.org/10.1007/s10479-012-1290-3
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DOI: https://doi.org/10.1007/s10479-012-1290-3