Integer programming approach to the printed circuit board grouping problem

A printed circuit board (PCB) grouping problem arising from the electronics industry is considered. Given a surface-mounting device with a number of component feeders and several types of PCBs to be produced, the problem is how to group the PCBs so that the total set-up time for component feeders is minimized. The problem is formulated as an integer-programming problem and a column generation approach is proposed to solve it. In this approach, the original problem is decomposed into a master problem and a column-generation subproblem. Starting with a few columns in the master problem, new columns are generated successively by solving the subproblem optimally. To solve the subproblem, a branch-and-cut approach is used. To solve the master problem, a branch-and-bound algorithm is used with the generated columns. However, a branching strategy is also proposed that maintains consistency in the column-generation procedure after branching. Computational experiments show that the solution approach gives high-quality solutions in reasonable computing time.

[1]  Giovanni Rinaldi,et al.  A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems , 1991, SIAM Rev..

[2]  Frits C. R. Spieksma,et al.  Throughput rate optimization in the automated assembly of printed circuit boards , 1991 .

[3]  Sungsoo Park,et al.  An Integer Programming Approach to the PCB Grouping Problem , 2003 .

[4]  E. Andrew Boyd,et al.  Polyhedral Results for the Precedence-Constrained Knapsack Problem , 1990, Discret. Appl. Math..

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

[6]  Avraham Shtub,et al.  Grouping methods for printed circuit board assembly , 1991 .

[7]  Sungsoo Park,et al.  Lifting Cover Inequalities for the Precedence-constrained Knapsack Problem , 1997, Discret. Appl. Math..

[8]  Avraham Shtub,et al.  Grouping components in printed circuit board assembly with limited component staging capacity and single card setup: Problem characteristics and solution procedures , 1997 .

[9]  T. T. Narendran,et al.  Grouping PCBs for set-up reduction: a maximum spanning tree approach , 1996 .

[10]  George L. Nemhauser,et al.  Solving binary cutting stock problems by column generation and branch-and-bound , 1994, Comput. Optim. Appl..

[11]  A. Kusiak.  The generalized group technology concept , 1987 .

[12]  Sabah U. Randhawa,et al.  An integer programming application to solve sequencer mix problems in printed circuit board production , 1985 .

[13]  Tien-Chien Chang,et al.  PCB assembly setup reduction using group technology , 1991 .

[14]  K. Rajkumar,et al.  A heuristic for sequencing PCB assembly to minimize set-up times , 1998 .

[15]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[16]  Marco Perona,et al.  Cell formation in PCB assembly based on production quantitative data , 1993 .

[17]  Oded Maimon,et al.  Group set-up for printed circuit board assembly , 1989 .

[18]  Oded Maimon,et al.  Set-up saving schemes for printed circuit boards assembly , 1993 .

[19]  R. Sokal,et al.  Principles of numerical taxonomy , 1965 .

[20]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[21]  George L. Nemhauser,et al.  Min-cut clustering , 1993, Math. Program..

[22]  Sungsoo Park,et al.  Efficient operation of a multi-functional surface mounting device , 1997 .