Document Type: Research Paper

Authors

Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal

Abstract

The product rate variation problem minimizes the variation in the rate at which different models of a common base product are produced on the assembly lines with the assumption of negligible switch-over cost and unit processing time for each copy of each model. The assumption of significant setup and arbitrary processing times forces the problem to be a two phase problem. The first phase determines the size and the number of batches and the second one sequences the batches of models. In this paper, the bottleneck case i.e. the min-max case of the problem with a generalized objective function is formulated. A Pareto optimal solution is proposed and a relation between optimal sequences for the problem with different objective functions is investigated. 

Keywords

[1]  Brauner N., and Crama Y., The maximum deviation just-in-time scheduling problem, Discrete Applied Mathematics, 134, 25-50, 2004.

[2]  Brauner N., Jost V., and Kubiak W., On symmetric Fraenkel’s and small deviations  conjecture, Les Cahiers du Laboratoire Leibniz-IMAG, 54, Grenoble, France, 2004.

[3]  Dhamala T. N., and Khadka S. R., A review on sequencing approaches for mixed-model just-in-time production system, Iranian Journal of Optimization, 1, 3, 266-290, 2009.

[4]  Dhamala T. N., Khadka S. R., and Lee M. H., A note on bottleneck product rate variation problem with square-deviation objective, International Journal of Operations Research, 7(1), 1-10, 2010.

[5]  Khadka  S. R., and Dhamala T. N., Optimality of the bottleneck product rate variation problem with a general objective, Submitted, 2010.

[6]  Kubiak  W., Minimizing variation of production rates in just-in-time systems: A survey, European Journal of Operational Research, 66, 259-271, 1993.

[7]  Kubiak  W., On small deviation conjecture, Bulletin of the Polish Academy of Sciences, 51, 189-203, 2003.

[8]  Kubiak W., Proportional optimization and fairness, International Series in Operations Research and management Science, Springer, 2009.

[9]  Kubiak W., and Sethi S., A note on level schedules for mixed-model assembly lines in just-in-time production systems, Management Science, 37, 1, 121-122, 1991.

[10]  Kubiak W., and Sethi S., Optimal just-in-time schedules for flexible transfer lines, The International Journal of Flexible Manufacturing Systems, 6, 137-154, 1994.

[11]  Kubiak W., and Yavuz M., Just-in-time smoothing through batching, Manufacturing and Service Operations Management, 10(3), 506-518, 2008.

[12]  Miltenburg J., Level schedules for mixed-model assembly lines in just-in-time production systems, Management Science, 35(2), 192-207, 1989.

[13]  Miltenburg J., and Sinnamon G., Scheduling mixed-model multi-level just-in-time production systems, International Journal of Production Research, 27(9), 1487-1509, 1989.

[14]  Moreno N., and Corominas A., Solving the minmax product rate variation problem (PRVP) as a bottleneck assignment problem, Computers and Operations Research, 33, 928-939, 2006.

[15]  Steiner G., and Yeomans J. S., Level schedules for mixed-model, just-in-time processes, Management Science, 39(6), 728-735, 1993.

[16]  Yavuz M., Akcali E., and Tufekci S., Optimizing production smoothing decisions via batch selection for mixed-model just-in-time manufacturing systems with arbitrary setup and processing times, International Journal of Production Research, 44(15), 3061-3081, 2006.

[17]  Yavuz  M., and Tufekci S., An analysis and solution to the single-level batch production smoothing problem, International Journal of Production Research, 45(17), 3893-3916, 2007.