Efficient Lagrangian Heuristics for the Two-Stage Flow Shop with Job Dependent Buffer Requirements

• Published in: Combinatorial Algorithms Vol. 10765; pp. 312 - 324
• Main Authors: Gu, Hanyu, Memar, Julia, Zinder, Yakov
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2018; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Buffer; Flow shop; Lagrangian relaxation; Total weighted completion time
• ISBN: 3319788248; 9783319788241
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-78825-8_26

The paper is concerned with minimisation of total weighted completion time for the two-stage flow shop with a buffer. In contrast to the vast literature on this topic, the buffer requirement varies from job to job and a job occupies the buffer continuously from the start of its first operation till the completion of its second operation rather than only between operations. Such problems arise in supply chains requiring unloading and loading of minerals and in some multimedia systems. The problem is NP-hard and the straightforward integer programming approach is impossible even for modest problem sizes. The paper presents a Lagrangian relaxation based decomposition approach that allows to use for each problem, obtained by this decomposition, a very fast algorithm. Several Lagrangian heuristics are evaluated by means of computational experiments.