Single-machine scheduling of multiple projects with controllable processing times

• Published in: European journal of operational research Vol. 308; no. 3; pp. 1074 - 1090
• Main Authors: Geng, Zhichao, Yuan, Jinjiang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2023
• Subjects: Compression cost; Controllable processing times; Multiple projects; Pseudo-polynomial algorithm; Scheduling; Pseudo-polynomial algorithm; Scheduling; Controllable processing times; Multiple projects; Compression cost
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2023.01.026

•The single-machine multiple-project scheduling problems.•The processing times of jobs are controllable.•The processing cost of a project includes total compression cost and total tardiness cost of its jobs.•Two types of problems are considered: Sum problem and Restricted problem. This paper studies the single-machine multiple-project scheduling problem with controllable processing times, in which the cost of a project refers to the total compression cost of its jobs plus the weighted number of tardy jobs in a schedule satisfying some given precedence constraints. It involves four specific problems: (i) minimizing the total cost of an arbitrary number of projects, (ii) being the same as (i) except the jobs from the same project having a common due date, (iii) having a fixed number of projects and minimizing the cost of one project subject to the cost of each of other projects not exceeding a given threshold, and (iv) being the same as (iii) except all jobs having identical weights. We show that a special version of (i) in which each project has only two jobs and all jobs have unit weights and cannot be compressed is strongly NP-hard (it implies the strong NP-hardness of (i)), (ii) is weakly NP-hard and admits a pseudo-polynomial algorithm and a fully polynomial time approximation scheme, (iii) is pseudo-polynomially solvable by a two-phase transformation, and (iv) is weakly NP-hard even if there are only two projects and all jobs have identical maximum compression amounts and identical processing times.