Abstract
In this paper, we consider the problem of minimizing makespan of n deteriorating jobs on a single machine. Rates of deterioration are job-dependent and constant with respect to the starting times. Jobs begin to deteriorate after a common critical date ‘d.’ The concept of relaxed agreeable weights is introduced. It is shown that the problem is NP-hard. The condition of relaxed agreeable weights and the structure of the problem are used to show that our local search algorithm, to obtain a locally optimal solution, will require polynomial effort in the number of jobs.
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We are grateful to the referees for their very helpful comments.
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Gupta, A., Sharma, P. & Salwan, H. A local search algorithm: minimizing makespan of deteriorating jobs with relaxed agreeable weights. EURO J Comput Optim 6, 29–54 (2018). https://doi.org/10.1007/s13675-017-0086-2
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DOI: https://doi.org/10.1007/s13675-017-0086-2