Minimizing the mean flow time in a two-machine group-scheduling problem with carryover sequence dependency

This paper addresses the two-machine group-scheduling problem for minimizing the mean flow time with carryover sequence dependency, typically encountered in the manufacture of printed circuit boards (PCBs) in electronics manufacturing. A procedure, namely Minsetup, is developed to determine a lower bound for the mean flow time, and an efficient solution algorithm based on tabu search is also developed to solve the problem. The algorithm is implemented on a tabu tree, and the steps associated with it are further demonstrated by solving a representative example from industry. The analysis is further directed at two different types of PCB manufacturers. The first type focuses on producing board types that are similar and in high volume during the production period, as in bulk orders for PCBs used in cellular phones and personal computers. The second type focuses on producing board types that are somewhat dissimilar and in low volume during the production period, as in PCBs used in medical equipment and the like. A carefully planned statistical experiment is performed on problem instances of both types to assess the effectiveness of the lower bounding mechanism and the solution algorithm. The results reveal that the proposed lower bounding technique is very effective in being able to justify that the best solution obtained with the proposed solution algorithm has an average measurable quality of approximately 13% and 8% or lower for problem types 1 and 2, respectively. (C) 2003 Published by Elsevier Science Ltd.