On the representation of the one machine sequencing problem in the shifting bottleneck heuristic

• Published in: European journal of operational research Vol. 182; no. 1; pp. 475 - 479
• Main Authors: Mukherjee, Saral, Chatterjee, A.K.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2007; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Bottlenecks; Due window; Exact sciences and technology; Generalized lateness objective; Heuristic; Inventory control, production control. Distribution; Job shops; Operational research and scientific management; Operational research. Management science; Scheduling; Sequential scheduling; Shifting bottleneck heuristic; Single machine; Studies; Shifting bottleneck heuristic; Scheduling; Single machine; Due window; Generalized lateness objective; Bottleneck; Job shop; Minimization; Windows; Precedence constraint; Due date; Heuristic method; Lateness; Sequencing
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2006.07.024

The Shifting Bottleneck heuristic decomposes the Job Shop problem into a series of One Machine Sequencing Problems (OMSPs) with release and due dates, precedence constraints and the minimization of maximum lateness objective. It is well known that delayed precedence constraints may exist between two operations to be performed on the same machine. We identify a new type of precedence relationship that may exist in an OMSP between the predecessor of an operation and the successor of another. The premise that an OMSP captures the sequencing relationships on other machines in the release and due date information is not valid when such precedence relationships exist. A modification of the OMSP representation is proposed based on a generalized lateness objective defined on a due window. The implications of such a representation for the OMSP solution procedure have been explored.