A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines

• Published in: European journal of operational research Vol. 202; no. 3; pp. 646 - 653
• Main Authors: Huynh Tuong, Nguyen, Soukhal, Ameur, Billaut, Jean-Charles
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-05-2010; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Algorithms; Applied sciences; Computer Science; Deadlines; Dynamic programming; Exact sciences and technology; Inventory control, production control. Distribution; Job shops; Mathematical programming; Operational research and scientific management; Operational research. Management science; Operations Research; Optimization algorithms; Parallel machines; Production scheduling; Scheduling; Scheduling Single machine Parallel machines Dynamic programming; Scheduling, sequencing; Single machine; Studies; Parallel machines; Scheduling; Dynamic programming; Single machine; Management science; Total weighted tardiness; Resource allocation; Functional equation; NP hard problem; Task scheduling; Sequencing; Due date
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2009.06.033

This paper deals with a scheduling problem of independent tasks with common due date where the objective is to minimize the total weighted tardiness. The problem is known to be ordinary NP-hard in the case of a single machine and a dynamic programming algorithm was presented in the seminal work of Lawler and Moore [E.L. Lawler, J.M. Moore, A functional equation and its application to resource allocation and sequencing problems, Management Science 16 (1969) 77–84]. In this paper, this algorithm is described and discussed. Then, a new dynamic programming algorithm is proposed for solving the single machine case. These methods are extended for solving the identical and uniform parallel-machine scheduling problems.