Document Type : Research Paper

Authors

Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal

Abstract

Research interests have been focused on the concept of penalizing jobs both for being early and for being tardy because not only of modern competitive industrial challenges of providing a variety of products at a very low cost by smoothing productions but also of its increasing and exciting computer applications. Here, sequencing approaches of the mixed- model just-in-time production systems is reviewed. In this note, realizing a need of critical review, a survey on the elegant mathematical models, methods and complexity of the mixed- model just-in-time sequencing problem with an insight into the existing analytical literature is given. The established research results together with open problems and possible extensions are presented. 

Keywords

 Aigbedo H., Some structural properties for the just-in-time level schedule problem, Production Planning and Control, 11, 357-362, 2000.
 Aigbedo H., and Monden Y., A parametric procedure for multicriterion sequence scheduling for just-in-time mixed-model assembly Lines, International Journal of Production Research, 35, 2543-2564, 1997.
 Balinski M., and Ramirez V., Parametric methods of apportionment, rounding and production, Mathematical Social Sciences, 37, 107-122, 1999.
 Balinski M., and Shahidi N., A simple approach to the product rate variation problem via axiomatic, Operations Research Letters, 22 (1998), 129-135.
 Balinski M. L., and Young H. P., The webster method of apportionment, Proceedings of the National Academy of Sciences, USA, 77(1), 1-4, 1980.
 Bard J. F., Shtub A., and Joshi S. B., Sequencing mixed-model assembly lines to level parts usage and minimize line length, International Journal of Production Research, 32, 10, 2431-2454, 1994.
 Bautista J., and Cano J., Minimizing work overload in mixed-model assembly lines, International Journal Production Economics, 112, 177-191, 2008.
 Bautista J., Companys R., and Corominas A., A note on the relation between the product rate variation (PRV) problem and the apportionment problem, Journal of the Operations Research Society, 47(11), 1410-1414, 1996.
 Bautista J., Companys R., and Corominas A., Heuristics and exact algorithms for solving the Monden problem, European Journal of Operations Research, 88, 101-113, 1996.
 Bautista J., Companys R., and Corominas A., Modeling and solving the production rate variation problem, TOP, 5, 2, 221-239, 1997a.
 Bautista J., Companys R., and Corominas A., Resolution of the PRV problem. Working Paper  D.I.T. 97/25, Barcelona, 1997b.
 Boysen N., Fliedner M., and Scholl A., Sequencing mixed-model assembly lines: Survey, classification and model critique, European Journal of Operations Research, 192, 2, 349-373, 2009.
 Brauner N., and Crama Y., The maximum deviation just-in-time scheduling problem, Discrete Applied Mathematics, 134, 25-50, 2004.
[ Brauner N., Jost V., and Kubiak W., On symmetric fraenkel’s and small deviations conjecture, Les Cahiers du Laboratoire Leibniz-IMAG, Grenoble, France, 54, 2004.
 Cheng L., and Ding F. Y., Modifying mixed-model assembly line sequencing methods to consider weightd variations for just-in-time production systems, IIE Transactions, 28, 919-927, 1996.
 Cho H. S., Paik C. H., Yoon H. M., and Kim H. G., A robust design of simulated annealing approach for mixed-model sequencing, Computers and Industrial Engineering, 48, 753-764, 2005.
 Corominas A., Kubiak W., and Moreno N., Response time variability, Journal of Scheduling, 10( 2), 97-110, 2007.
 Corominas A., and Moreno N., On the relations between optimal solutions for different types of min-sum balanced JIT optimisation problems, INFOR, 41(4), 333-339, 2003.
 Corominas A., and Moreno N., About relations between the optimal solutions for different types of min-sum production rate variation problem, 27 Congresso de Estadisticae Investigation Operativa Lieida, 8-11 de abril de, 2003.
 
 Dhamala T. N., and Khadka S. R., Bottleneck product rate variation problem with absolute-deviation objective, The Nepali Mathematical Sciences Report, 27, 1-2 , 57-65, 2008.
 Dhamala T. N., and Kubiak W., A brief survey of just-in-time sequencing for mixedmodel systems, International Journal of Operations Research, 2( 2), 38-47, 2005.
 Ding F. Y., and Cheng L., An effective mixed-model assembly line sequencing heuristic for just-in -time production systems, Journal of Operations Management, 11(a), 45-50, 1993.
 Ding F. Y., and Cheng L., A simple sequencing algorithm for mixed-model assembly lines in just-in-time production systems, Operations Research Letters, 13(b), 27-36, 1993.
 Drexl A., and Kimms A., Sequencing JIT mixed-model assembly lines under stationload and part-usage constraints, Management Science, 47, 3, 480-491, 2001.
 Duplaga E. A., and Bragg D. J., Mixed-model assembly line sequencing heuristics for smoothing component parts usage: A comparative analysis. International Journal of Production Research, 36( 8), 2209-2224, 1998.
 Glover F., Maximum matchings is a convex bipartite graph, Naval Research Logistics Quarterly, 4(3), 313-316, 1967.
 Groeflin H., Luss H., Rosenwein M. B., and Wahls E. T., Final assembly sequencing for just-in-time manufacturing, International Journal of Production Research, 27(2), 199-213, 1989.
 Inman R. R., and Bulfin R. L., Sequencing JIT mixed-model assembly lines, Management Science, 37(7), 901-904, 1991.
 Jost V., Deux problemes d’approximation diophantine: Le patage proportionnel en nombers entries et les pavages equilibres de Z, DEA ROCO, Laboratoire Leibniz-IMAG, 2003.
 J´ozefowska J., J´ozefowski L., and Kubiak W., Characterization of just-in-time sequencing via apportionment, Stochastic Processes, Optimization, and Control Theory: Application in Financial Engineering, Queuing Networks, and Manufacturing SystemsSpringer US,94, 175-200, 2006.
 Korkmazel T., and Meral S., Bicriteria sequencing methods for the mixed-model assembly line in just-in-time production systems, European Journal of Operational Research, 131, 188-207, 2001.
 Kotani S., Ito T., and Ohno K., Sequencing problem for a mixed-model assembly line in the toyota production system, International Journal of Production Research, 42(23), 4955-4974, 2004.
 Kovalyov M. Y., Kubiak W., and Yeomans J. S., A computational analysis of balanced JIT optimization algorithms, Information Processing and Operational Research, 39(3), 299-316, 2001.
 Kubiak W., Minimizing variation of production rates in just-in-time systems: A survey, European Journal of Operations Research, 66, 259-271, 1993.
 Kubiak W., On small deviation conjecture, Bulletin of the Polish Academy of Sciences, 51(a), 189-203, 2003.
 Kubiak W., Cyclic just-in-time sequence are optimal, Journal of Global Optimization, 27(b), 333-347, 2003.
 Kubiak W., Fair sequences, Handbook of Scheduling, Chapman and Hall/CRC London/ Boca Raton 19-1-19-21, 2004.
 Kubiak W., Proportional optimization and fairness, International Series in Operations Research and Management Science, 127, Springer, 2009.
 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.
 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.
 Kubiak W., Steiner G., and Yeomans J. S., Optimal level schedules for mixed-model multi-level just-in-time assembly systems, Annals of Operations Research, 69, 241-259, 1997.
 Lebacque V., Jost V., and Brauner N., Simultaneous optimization of classical objectives in JIT scheduling, European Journal of Operations Research, 182, 29-39, 2007.
 Mansouri S. A., A multi-objective genetic algorithm for mixed-model sequencing on JIT assembly lines, International Journal of Operational Research, 167, 696-716, 2005.
 McMullen P. R., An efficient approach to addressing JIT sequencing problems with setups via search heuristics, Computers and Industrial Engineering, 41, 335-353, 2001.
 McMullen P. R., and Tarasewich P., A beam search heuristic method for mixed-model scheduling with setups. International Journal of Production Economics, 96, 273-283, 2005.
 Merengo C., Nava F., and Pozzetti A., Balancing and sequencing manual mixed-model assembly lines, International Journal of Production Research, 37(12), 2835-2860, 1999.
 Miltenburg J., Level schedules for mixed-model assembly lines in just-in-time production systems, Management Science, 35(2), 192-207, 1989.
 Miltenburg J., and Goldstein T., Developing production schedules which balance part usage and smooth production loads for just-in-time production systems, Naval Research Logistics, 38, 893-910, 1991.
 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.
 Miltenburg J., Steiner G., and Yeomans J. S., A dynamic programming algorithm for scheduling mixed-model, just-in-time production systems, Mathematical Computer Modeling, 13( 3), 57-66, 1990.
 Monden Y., Toyota production systems, Industrial Engineering and Management Press, Norcross, GA, 1983.
 Moreno N., and Corominas A., Solving the minsum product rate variation problem as an assignment problem, International Journal of Flexible Manufacturing Systems, 18(a), 269-284, 2006.
 Scholl A., Klein R., and Domschke W., Pattern based vocabulary building for effectively sequencing mixed-model assembly lines, Journal of Heuristics, 4, 359-381, 1998.
 Solnon C., Cung V. D., Nguyen A., and Artigues C., The car sequencing problem: Overview of state-of-the-art methods and industrial case-study of the ROADEF’2005 challenge problem. European Journal of Operational Research, 191(3), 912-927, 2008.
  Steiner G., and Yeomans J. S., Level schedules for mixed-model, just-in-time processes, Management Science, 39(6), 728-735, 1993.
 Steiner G., and Yeomans J. S., A bicriterion objective for levelling the schedule of a mixed-model, JIT assembly process. Mathematical and Computer Modelling, 20,123-134, 1994.
 Steiner G., and Yeomans J. S., Optimal level schedules in mixed-model multi-level JIT assembly systems with pegging, European Journal of Operations Research, 95, 38-52, 1996.
 Still J. w., A class of new methods for congressional apportionment, SIAM Journal Applied Mathematics, 37, 401-418, 1979.
 Sumichrast R. T., and Russell R. S., Evaluating mixed-model assembly line sequencing heuristics for just-in-time production systems, Journal of Operations Management, 9(3), 371 – 390, 1990.
 Sumichrast R. T., Russell R. S., and Taylor B. W., A comparative analysis of sequencing procedures for mixed-model assembly lines in a just-in-time production system, International Journal of Production Research, 30(1), 199-214, 1992.
 Tavakkoli-Moghaddam R., and Rahimi-Vahed A. R., Multi-criteria sequencing problem for a mixed-model assembly line in a JIT production system, Applied Mathematics and Computation, 181, 1471-1481, 2006.
 Tijdeman R., The chairman assignment problem, Discrete Mathematics, 32(a), 323-330, 1980.
 Vuillon L., Balanced words. Rapports de Recherche-006, LIAFA CNRS, Universite Paris 7, 2003.
 Xiaobo Z., and Ohno K., Algorithms for sequencing mixed models on an assembly line in a JIT production system, Computers Industrial Engineering, 32(1), 47-56, 1997.
 Yavuz M., and Akcali E., Production smoothing in just-in-time manufacturing systems: a review of the models and solution approaches, International Journal of Production Research, 45(16), 3579-3597, 2007.
 Yavuz M., and Tufekci S., The single-level batch production smoothing problem: An analysis and a heuristic solution, Department of Industrial and Systems Engineering, University of Florida, 05, 2004b.
 Yavuz M., and Tufekci S., Bounded dynamic programming solution to the batching problem in mixed-model just-in-time manufacturing systems, International Journal of Production Economics, 103, 841-862, 2006.
 Yavuz M., and Tufekci S., Dynamic programming solution to the batching problem in just-in-time flowshops, Computing Industrial Engineering, 51(b), 416-432, 2007.
 Zeramdini Z., Aigbedo H., and Monden Y., Bicriteria sequencing for just-in-time mixed-model assembly lines, International Journal of Production Research, 38, 15, 3451-3470, 2000.