Abstract
This paper considers the single-machine scheduling problem with slack due date. The decision needs to determine the optimal job sequence when the due date of jobs is determined. Slack due date means that the due date is equal to its processing time plus a constant, where the constant is the decision variable. The aim is to assign the slack due date and minimize the objective function. The objective function includes the early work, late work and slack due dates. In this paper, we discuss two problems with slack due date. For the first problem, we address the range of slack due date by cost coefficients, and design a dynamic programming algorithm to solve the proposed problem. It is proved that the optimal solution can be obtained in \(O(n^3P^3 \log n)\) time. For the latter problem, we address the time-window assignment problem, and present a dynamic programming algorithm by determining the rang of due date of time window in \(O(n^4P^5\log n(1+P))\) time. Finally, a numerical example is presented to illustrate the feasibility of these algorithms.
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X.-G. Zhang Writing—supervision, conceptualization, methodology, writing—review and editing, funding acquisition. X.-M. Tang Original draft, methodology, formal analysis.
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This work was supported Project Supported by the Major Program of the National Natural Science Foundation of China (No. 11991022), the National Natural Science Foundation of China (11971443), Natural Science Foundation of Chongqing, China (No. CSTB2023NSCQ-LZX0005).
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Zhang , XG., Tang, XM. The Two Single-Machine Scheduling Problems with Slack Due Date to Minimize Total Early Work and Late Work. J. Oper. Res. Soc. China (2024). https://doi.org/10.1007/s40305-023-00528-7
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DOI: https://doi.org/10.1007/s40305-023-00528-7