Lagrangian domain reductions for the single machine earliness–tardiness problem with release dates

• Published in: European journal of operational research Vol. 201; no. 1; pp. 45 - 54
• Main Authors: Detienne, Boris, Pinson, Éric, Rivreau, David
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.02.2010; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Branch & bound algorithms; Branch-and-Bound; Computer Science; Elimination rules; Exact method; Exact sciences and technology; Heuristik; Inventory control, production control. Distribution; Just in Time; Lagrange multiplier; Lagrangian relaxation; Operational research and scientific management; Operational research. Management science; Operations Research; Optimization; Production scheduling; Produktionsplanung; Release dates; Scheduling; Scheduling Just-in-time Elimination rules Lagrangian relaxation Exact method; Scheduling, sequencing; Scheduling-Verfahren; Studies; Scheduling; Just-in-time; Lagrangian relaxation; Elimination rules; Exact method; Lagrangian; Branch and bound method; Expert system; Windows; Due date; Lagrange multiplier; Just in time; Relaxation method; Single machine
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2009.02.005

This paper presents new elimination rules for the single machine problem with general earliness and tardiness penalties subject to release dates. These rules, based on a Lagrangian decomposition, allow to drastically reduce the execution windows of the jobs. We measure the efficiency of these properties by integrating them in a branch-and-bound. Tests show that instances with up to 70 jobs without release dates, and up to 40 jobs with release dates, can be optimally solved within 1000 seconds.