Grouping PCB Assembly Jobs with Feeders of Several Types

A variant of the classical job grouping problem (JGP) in printed circuit board (PCB) assembly is considered. Studies on JGPs have assumed a single feeder from which the components are retrieved and then placed on the PCB. Recent advances in technology have made it possible to use several different kinds (types) of feeders at the same time. In a JGP, the aim is to group the PCBs so that the cardinality of the grouping is minimal and each group can be processed without rearranging the contents of the feeder. In the job grouping problem with several feeder types (JGP-T) the goal is the same but instead of one linear feeder we have several feeders and each component is associated with a given feeder type which restricts its placement. We give a mathematical formulation for the JGP-T and show that it is hard to solve to optimality for problems of practical size. The connections of JGP-T to known problems are discussed. We also propose several efficient heuristics and compare their results against optimal solutions.

[1]  Timo Knuutila,et al.  Grouping of PCB assembly jobs in the case of flexible feeder units , 2005 .

[2]  Morven Leese,et al.  Book Review: Mathematical Classification and Clustering (Nonconvex Optimization and Its Applications, Vol. 11) , 2003 .

[3]  O. Nevalainen,et al.  Three perspectives for solving the job grouping problem , 1999 .

[4]  Fabián A. Chudak,et al.  Improved approximation algorithms for a capacitated facility location problem , 1999, SODA '99.

[5]  Yves Crama,et al.  Worst-case performance of approximation algorithms for tool management problems , 1999 .

[6]  Frits C. R. Spieksma,et al.  Production planning in automated manufacturing , 1994 .

[7]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[8]  Frits C. R. Spieksma,et al.  Minimizing the number of tool switches on a flexible machine , 1994 .

[9]  Mika Johnsson,et al.  Job Grouping in Surface Mounted Component Printing , 1999 .

[10]  C. H. Aikens,et al.  Facility location models for distribution planning , 1985 .

[11]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[12]  Christopher S. Tang,et al.  Models Arising from a Flexible Manufacturing Machine, Part I: Minimization of the Number of Tool Switches , 1988, Oper. Res..

[13]  Boris Mirkin,et al.  Mathematical Classification and Clustering , 1996 .

[14]  Avraham Shtub,et al.  Role of similarity measures in PCB grouping procedures , 1992 .

[15]  Yves Crama,et al.  A column generation approach to job grouping for flexible manufacturing systems , 1994 .

[16]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .