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Doctor of Philosophy
Industrial and Systems Engineering
Date of Defense
This research is motivated by a practical application observed at a printed circuit board
(PCB) manufacturing facility. After assembly, the PCBs (or jobs) are tested in
environmental stress screening (ESS) chambers (or batch processing machines) to detect
early failures. Several PCBs can be simultaneously tested as long as the total size of all
the PCBs in the batch does not violate the chamber capacity. PCBs from different
production lines arrive dynamically to a queue in front of a set of identical ESS
chambers, where they are grouped into batches for testing. Each line delivers PCBs that
vary in size and require different testing (or processing) times. Once a batch is formed, its
processing time is the longest processing time among the PCBs in the batch, and its ready
time is given by the PCB arriving last to the batch. ESS chambers are expensive and a
bottleneck. Consequently, its makespan has to be minimized.
A mixed-integer formulation is proposed for the problem under study and compared to a
formulation recently published. The proposed formulation is better in terms of the
number of decision variables, linear constraints and run time. A procedure to compute the lower bound is proposed. For sparse problems (i.e. when job ready times are dispersed
widely), the lower bounds are close to optimum.
The problem under study is NP-hard. Consequently, five heuristics, two metaheuristics
(i.e. simulated annealing (SA) and greedy randomized adaptive search procedure
(GRASP)), and a decomposition approach (i.e. column generation) are proposed –
especially to solve problem instances which require prohibitively long run times when a
commercial solver is used. Extensive experimental study was conducted to evaluate the
different solution approaches based on the solution quality and run time.
The decomposition approach improved the lower bounds (or linear relaxation solution) of
the mixed-integer formulation. At least one of the proposed heuristic outperforms the
Modified Delay heuristic from the literature. For sparse problems, almost all the
heuristics report a solution close to optimum. GRASP outperforms SA at a higher
computational cost. The proposed approaches are viable to implement as the run time is
Vélez Gallego, Mario César, "Algorithms for Scheduling Parallel Batch Processing Machines with Non-Identical Job Ready Times" (2009). FIU Electronic Theses and Dissertations. Paper 276.