Group-scheduling problems in electronics manufacturing

This dissertation addresses the "multi-machine carryover sequence-dependent group-scheduling problem with anticipatory setups," which arises in the printed circuit board (PCB) manufacturing. Typically, in PCB manufacturing different board types requiring similar components are grouped together to reduce setup times and increase throughput. The challenge is to determine the sequence of board groups as well as the sequence of individual board types within each group. The two separate objectives considered are minimizing the makespan and minimizing the mean flow time.; In order to quickly solve the problem with each of the two objectives, highly effective metasearch heuristic algorithms based on the concept known as tabu search are developed. Advanced features of tabu search, such as the long-term memory function in order to intensify/diversify the search and variable tabu-list sizes, are utilized in the proposed heuristics.; In the absence of knowing the actual optimal solutions, another important challenge is to assess the quality of the solutions identified by the proposed meta-heuristics. For that purpose, methods that identify strong lower bounds both on the optimal makespan and the optimal mean flow time are proposed. The quality of a heuristic solution is then quantified as its percentage deviation from the lower bound. Based on the minimum possible setup times, this dissertation develops a lower bounding procedure, called procedure Minsetup, that is capable of identifying tight lower bounds.; Even tighter lower bounds are identified using a mathematical programming decomposition approach. Novel mathematical programming formulations are developed and a branch-and-price (B&P) algorithm is proposed and implemented. A Dantzig-Wolfe reformulation of the problem that enables applying a column generation algorithm to solve the linear programming relaxation of the master problem is presented. Single-machine subproblems are designed to identify new columns if and when necessary. To enhance the efficiency of the algorithm, approximation algorithms are developed to solve the subproblems. Effective branching rules partition the solution space of the problem at a node where the solution is fractional. In order to alleviate the slow convergence of the column generation process at each node, a stabilizing technique is developed. Finally, several implementation issues such as constructing a feasible initial master problem, column management, and search strategy, are addressed.; The results of a carefully designed computational experiment for both low-mix high-volume and high-mix low-volume production environments confirm the high performance of tabu search algorithms in identifying extremely good quality solutions with respect to the proposed lower bounds.