Revisit the scheduling problem with assignable or generalized due dates to minimize total weighted late work

Rubing Chen, Yuan Gao, Zhichao Geng and Jinjiang Yuan

International Journal of Production Research, 2023, vol. 61, issue 22, 7630-7648

Abstract: We revisit the single-machine scheduling for minimising the total weighted late work with assignable due dates (ADD-scheduling) and generalised due dates (GDD-scheduling). In particular, we consider the following three problems: (i) the GDD-scheduling problem for minimising the total weighted late work, (ii) the ADD-scheduling problem for minimising the total weighted late work, and (iii) the ADD-scheduling problem for minimising the total late work. In the literature, the above three problems are proved to be NP-hard, but their exact complexity (unary NP-hardness or pseudo-polynomial-time solvability) are unknown. In this paper, we address these open problems by showing that the first two problems are unary NP-hard and the third problem admits pseudo-polynomial-time algorithms. For the third problem, we also present a 2-approximation solution and a fully polynomial-time approximation scheme. Computational experiments show that our algorithms and solutions are efficient. When the jobs have identical processing times, we further present more efficient polynomial-time algorithms.

Date: 2023
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DOI: 10.1080/00207543.2022.2160502

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