Total completion time minimization in two-machine flow shop scheduling problems with a fixed job sequence

• Published in: Discrete optimization Vol. 9; no. 1; pp. 29 - 39
• Main Authors: Hwang, F.J., Kovalyov, M.Y., Lin, B.M.T.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2012
• Subjects: Dynamic programming; Fixed sequence; Total completion time; Two-machine flow shop; Dynamic programming; Fixed sequence; Total completion time; Two-machine flow shop
• ISSN: 1572-5286; 1873-636X
• DOI: 10.1016/j.disopt.2011.11.001

This paper addresses scheduling n jobs in a two-machine flow shop to minimize the total completion time, subject to the condition that the jobs are processed in the same given sequence on both machines. A new concept of optimal schedule block is introduced, and polynomial time dynamic programming algorithms employing this concept are derived for two specific problems. In the first problem, the machine-2 processing time of a job is a step increasing function of its waiting time between the machines, and a decision about machine-1 idle time insertion has to be made. This problem is solved in O(n2) time. In the second problem, the jobs are processed in batches and each batch is preceded by a machine-dependent setup time. An O(n5) algorithm is developed to find an optimal batching decision.