A common due-date assignment problem with job rejection on parallel uniform machines

Gur Mosheiov and Assaf Sarig

International Journal of Production Research, 2024, vol. 62, issue 6, 2083-2092

Abstract: We study a common due-date assignment problem on two parallel uniform machines. The jobs are assumed to have identical processing times, and job-dependent and asymmetric earliness and tardiness unit costs. The scheduler may process only a subset of the jobs, i.e. the option of job-rejection is allowed. The objective function consists of three cost components: the total earliness-tardiness cost of all scheduled jobs, the cost of the common due-date, and total rejection cost. For a given number of rejected jobs and a given due-date, the problem is reduced to a non-standard linear assignment problem. Consequently, the optimal solution is shown to be obtained in polynomial time in the number of jobs. The case of a given (possibly restrictive) due-date, the extension to a setting of more than two machines, and a number of special cases, are also discussed.

Date: 2024
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DOI: 10.1080/00207543.2023.2217277

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