Algorithms for scheduling parallel batch processing machines with non-identical job ready times

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 very short. ^

A meta -analysis of empirical research studies on resilience among students at -risk for school failure

Being at-risk is a growing problem in the U.S. because of disturbing societal trends such as unemployment, divorce, substance abuse, child abuse and neglect, and the new threat of terrorist violence. Resilience characterizes individuals who rebound from or adapt to adversities such as these, and academic resilience distinguishes at-risk students who succeed in school despite hardships. ^ The purpose of this research was to perform a meta-analysis to examine the power of resilience and to suggest ways educators might improve academic resilience, which was operationalized by satisfactory test scores and grades. In order to find all studies that were relevant to academic resilience in at-risk kindergarten through 12th-grade students, extensive electronic and hardcopy searches were conducted, and these resulted in a database of 421 articles. Two hundred eighty seven of these were rejected quickly, because they were not empirical research. Upon further examination, another 106 were rejected for not meeting study protocol criteria. Ultimately, 28 studies were coded for study level descriptors and effect size variables. ^ Protective factors for resilience were found to originate in physical, psychological, and behavioral domains on proximal/intraindividual, transitional/intrafamilial, or distal/extrafamilial levels. Effect sizes (ESs) for these were weighted and the means for each level or category were interpreted by commonly accepted benchmarks. Mean effect sizes for proximal (M = .27) and for transitional (M = .15) were small but significant. The mean effect size for the distal level was insignificant. This supported the hypotheses that the proximal level was the source of most protective factors for academic resilience in at-risk students followed by the transitional level. The distal effect size warranted further research particularly in light of the small number of studies (n = 11) contributing effect sizes to that category. A homogeneity test indicated a search for moderators, i.e., study variables affecting outcomes, was justified. “Category” was the largest moderator. Graphs of weighted mean effect sizes in the physical, psychological, and behavioral domains were plotted for each level to better illustrate the findings of the meta-analysis. Suggestions were made for combining resilience development with aspects of positive psychology to promote resilience in the schools. ^