Skip to main content
Log in

Group-scheduling problems in electronics manufacturing

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

This paper addresses the flowshop group-scheduling problems typically encountered in the assembly of printed circuit boards in electronics manufacturing. A mathematical programming model is formulated to capture the characteristics inherent to group-scheduling problems experienced in electronics manufacturing as well as those common to a wide range of group-scheduling problems encountered in other production environments. Several heuristics, each incorporating different components that underlie the tabu search concept, are developed to solve this strongly NP-hard problem effectively in a timely manner. In order to investigate the quality of the heuristic solutions with respect to tight lower bounds, an effective and efficient decomposition approach is developed. The problem is decomposed into a master problem and single-machine subproblems, and a column generation algorithm is developed to solve the linear programming relaxation of the master problem. Branching schemes, compatible with the column generation subproblems, are employed to partition the solution space when the solution to the linear programming relaxation is not integral. Furthermore, tabu search based fast heuristics are implemented to solve the subproblems, and an effective stabilization method is developed to accelerate the column generation approach. An experimental design with both fixed and random factors accompanied by rigorous statistical analyses of computational tests conducted on randomly generated test problems as well as on a large size real industry problem confirm the high performance of the proposed approach in identifying quality lower bounds and strongly suggest its flexibility and applicability to a wide range of real problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+
from $39.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Amini, M. M., & Racer, M. A. (1994). Rigorous computational comparison of alternative solution methods for the generalized assignment problem. Management Science, 40(7), 868–890.

    Article  Google Scholar 

  • Anon. (2003). ILOG Branch&Price&Cut and shortest path optimizers prototype manual. Mountain View: Ilog Inc.

    Google Scholar 

  • Anon. (2004a). ILOG CPLEX 9.0 reference manual. Mountain View: Ilog Inc.

    Google Scholar 

  • Anon. (2004b). SAS: The SAS system for Windows. Cary: SSAS Institute Inc.

    Google Scholar 

  • Balakrishnan, A., & Vanderbeck, F. (1999). A tactical planning model for mixed-model electronics assembly operations. Operations Research, 47(3), 395–409.

    Article  Google Scholar 

  • Barnhart, C., Johnson, E., Nemhauser, G., Savelsbergh, M., & Vance, P. (1998). Branch-and-Price: Column generation for solving huge integer programs. Operations Research, 46, 316–329.

    Article  Google Scholar 

  • Barr, R. S., Golden, B. L., Kelly, J. P., Resende, M. G. C., & Stewart, W. R. (1995). Designing and reporting on computational experiments with heuristic methods. Journal of Heuristics, 1, 9–32.

    Article  Google Scholar 

  • Bulbul, K., Kaminsky, P., & Yano, C. (2004). Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs. Naval Research Logistics, 51, 407–445.

    Article  Google Scholar 

  • Chen, Z. L., & Powell, W. (1999). Solving parallel machine scheduling problems by column generation. INFORMS Journal on Computing, 11, 78–94.

    Article  Google Scholar 

  • Coffin, M., & Saltzman, M. J. (2000). Statistical analysis of computational tests of algorithms and heuristics. INFORMS Journal on Computing, 12(1), 24–44.

    Article  Google Scholar 

  • Crama, Y., van de Klundert, J. J., & Spieksma, F. C. R. (2002). Production planning problems in printed circuit board assembly. Discrete Applied Mathematics, 123, 339–361.

    Article  Google Scholar 

  • du Merle, O., Villeneuve, D., Desrosiers, J., & Hansen, P. (1999). Stabilized column generation. Discrete Mathematics, 194, 229–237.

    Article  Google Scholar 

  • Eom, D. H., Shin, H. J., Kwun, I. H., Shim, J. K., & Kim, S. S. (2002). Scheduling jobs on parallel machines with sequence-dependent family set-up times. International Journal on Advanced Manufacturing Technology, 19, 926–932.

    Article  Google Scholar 

  • Garey, M. R., Johnson, D. S., & Sethi, R. R. (1976). The complexity of flowshop and jobshop scheduling. Mathematics of Operations Research, 36, 767–777.

    Google Scholar 

  • Gelogullari, C. A. (2005). Group scheduling problems in electronics manufacturing. Doctoral dissertation, Oregon State University, Corvallis, OR, USA.

  • Glover, F., & Laguna, M. (1997). Tabu search. Boston: Kluwer Academic.

    Google Scholar 

  • Gopalakrishnan, M., Ding, K., Bourjolly, J. M., & Mohan, S. (2001). A tabu-search heuristic for the capacitated lot sizing problem with set-up carryover. Management Science, 47, 851–863.

    Article  Google Scholar 

  • Hayrinen, T., Johnsson, M., Jahletta, T., Smed, J., & Nevalainen, O. (2000). Scheduling algorithms for computer-aided line balancing in printed circuit board assembly. Production Planning and Control, 11, 497–510.

    Article  Google Scholar 

  • Hooker, J. N. (1994). Needed: An empirical science of algorithms. Operations Research, 42(3), 201–212.

    Article  Google Scholar 

  • Johnson, M., & Smed, J. (2001). Observations on PCB assembly optimization. Electronic Packaging and Production, 28, 1871–1883.

    Google Scholar 

  • Kanet, J. J., & Sridharan, V. (2000). Scheduling with inserted idle time: problem taxonomy and literature review. Operations Research, 48, 99–110.

    Article  Google Scholar 

  • Leon, V. J., & Peters, B. A. (1996). Replanning and analysis of partial setup strategies in printed circuit board assembly systems. International Journal of Flexible Manufacturing Systems, 8, 389–412.

    Article  Google Scholar 

  • Logendran, R., & Sonthinen, A. (1997). A tabu search-based approach for scheduling job-shop type flexible manufacturing systems. Journal of the Operational Research Society, 48, 264–277.

    Article  Google Scholar 

  • Logendran, R., & Subur, F. (2004). Unrelated parallel machine scheduling with job splitting. IIE Transactions, 6(4), 359–372.

    Article  Google Scholar 

  • Maimon, O., & Schtub, A. (1991). Grouping methods for printed circuit boards. International Journal of Production Research, 29, 1370–1390.

    Article  Google Scholar 

  • McGinnis, L. F., Ammons, J. C., Carlyle, M., Cranmer, L., Depuy, G. W., Ellis, K. P. Tovey, C. A. & Xu, H. (1992). Automated process planning for printed circuit card assembly. IIE Transactions, 24, 18–30.

    Article  Google Scholar 

  • Montgomery, D. C. (2005). Design and analysis of experiments. New York: Wiley.

    Google Scholar 

  • Rossetti, M. D., & Stanford, K. J. A. (2003). Group sequencing a PCB assembly system via an expected sequence dependent setup heuristic. Computers and Industrial Engineering, 45(1), 231–254.

    Article  Google Scholar 

  • Savelsbergh, M. (1997). A branch-and-price algorithm for the generalized assignment problem. Operations Research, 45, 831–841.

    Article  Google Scholar 

  • Schaller, J. E. (2001). A new lower bound for the flow shop group scheduling problem. Computers and Industrial Engineering, 41, 151–161.

    Article  Google Scholar 

  • Smed, J., Salonen, K., Johnsson, M., Johletta, T., & Nevalainen, O. (2004). Grouping PBCs with minimum feeder changes. International Journal of Flexible Manufacturing Systems, 15, 19–35.

    Article  Google Scholar 

  • Sox, C. R., & Gao, Y. (1999). The capacitated lot sizing problem with setup carry-over. IIE Transactions, 31, 173–181.

    Google Scholar 

  • Strusevic, V. A. (2000). Group technology approach to the open shop scheduling problem with batch setup times. Operations Research Letters, 26, 181–192.

    Article  Google Scholar 

  • Suerie, C., & Stadtler, H. (2003). The capacitated lot-sizing problem with linked lot sizes. Management Science, 49, 1039–1054.

    Article  Google Scholar 

  • Tang, C. S., & Denardo, E. V. (1988). Models arising from a flexible manufacturing machine, part 1: Minimization of the number of tool switches. Operations Research, 36, 767–777.

    Article  Google Scholar 

  • Van den Akker, J., Hoogeven, J., & Van de Velde, S. (1999). Parallel machine scheduling by column generation. Operations Research, 47, 862–872.

    Article  Google Scholar 

  • Vanderbeck, F., & Wolsey, L. (1996). An exact algorithm for IP column generation. Operations Research Letters, 19, 151–159.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rasaratnam Logendran.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gelogullari, C.A., Logendran, R. Group-scheduling problems in electronics manufacturing. J Sched 13, 177–202 (2010). https://doi.org/10.1007/s10951-009-0147-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-009-0147-3