×

zbMATH — the first resource for mathematics

The product rate variation problem and its relevance in real world mixed-model assembly lines. (English) Zbl 1159.90359
Summary: Production processes in a wide range of industries rely on modern mixed-model assembly systems, which allow an efficient manufacture of various models of a common base product on the same assembly line. In order to facilitate a just-in-time supply of materials, the literature proposes various sequencing problems under the term “level scheduling”, which all aim at evenly smoothing the part consumption induced by the production sequence over time. Among these approaches, the popular product rate variation (PRV) problem is considered to be an appropriate approximate model, if either (i) all products require approximately the same number and mix of parts or (ii) part usages of all products are (almost completely) distinct. These statements are (iii) further specified by analytical findings, which prove the equivalence of product and material oriented level scheduling under certain conditions. These three prerequisites commonly cited in the literature when justifying the practical relevance of the PRV are evaluated by means of three simple computational experiments and are then discussed with regard to their relevance in practical settings. It is concluded that the PRV is in fact inappropriate for use in today’s real world mixed-model assembly systems.

MSC:
90B30 Production models
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bard, J.F.; Shtub, A.; Joshi, S.B., Sequencing mixed-model assembly lines to level parts usage and minimize line length, International journal of production research, 32, 2431-2454, (1994) · Zbl 0902.90071
[2] Bautista, J.; Companys, R.; Corominas, A., Heuristics and exact algorithms for solving the monden problem, European journal of operational research, 88, 101-113, (1996) · Zbl 0913.90159
[3] Boysen, N.; Fliedner, M.; Scholl, A., Assembly line balancing: which model to use when?, International journal of production economics, 111, 509-528, (2008)
[4] Boysen, N.; Fliedner, M.; Scholl, A., Sequencing mixed-model assembly lines to minimize part inventory cost, OR spectrum, 30, 611-633, (2008) · Zbl 1193.90017
[5] Boysen, N.; Fliedner, M.; Scholl, A., Sequencing mixed-model assembly lines: survey, classification and model critique, European journal of operational research, 192, 349-373, (2009) · Zbl 1157.90405
[6] Corominas, A.; Kubiak, W.; Palli, N.M., Response time variability, Journal of scheduling, 10, 97-110, (2007) · Zbl 1154.90433
[7] Dhamala, T.N.; Kubiak, W., A brief survey of just-in-time sequencing for mixed-model systems, International journal of operations research, 2, 38-47, (2005) · Zbl 1115.90337
[8] Drexl, A.; Kimms, A., Sequencing JIT mixed-model assembly lines under station-load and part-usage constraints, Management science, 47, 480-491, (2001) · Zbl 1232.90110
[9] Duplaga, E.A.; Hahn, C.K.; Hur, D., Mixed-model assembly line sequencing at hyundai motor company, Production and inventory management journal, 37, 20-26, (1996)
[10] Grigoriev, A.; van de Klundert, J.J., On the high multiplicity traveling salesman problem, Discrete optimization, 3, 50-62, (2006) · Zbl 1110.90074
[11] Joo, S.-H.; Wilhelm, W.E., A review of quantitative approaches in just-in-time manufacturing, Production planning & control, 4, 207-222, (1993)
[12] Kubiak, W., Minimizing variation of production rates in just-in-time systems: A survey, European journal of operational research, 66, 259-271, (1993) · Zbl 0771.90051
[13] Kubiak, W., Fair sequences, ()
[14] Kubiak, W.; Sethi, S., A note on schedules for mixed-model assembly lines in just-in-time production systems, Management science, 37, 121-122, (1991) · Zbl 0727.90033
[15] Kubiak, W.; Steiner, G.; Yeomans, J.S., Optimal level schedules for mixed-model, multi-level just-in-time assembly systems, Annals of operations research, 69, 241-259, (1997) · Zbl 0880.90061
[16] Lebacque, V.; Jost, V.; Brauner, N., Simultaneous optimization of classical objectives in JIT scheduling, European journal of operational research, 182, 29-39, (2007) · Zbl 1128.90526
[17] Mather, H., Competitive manufacturing, (1989), Englewood Cliffs
[18] Meyr, H., Supply chain planning in the German automotive industry, OR spectrum, 26, 447-470, (2004) · Zbl 1069.90033
[19] Miltenburg, J., Level schedules for mixed-model assembly lines in just-in-time production systems, Management science, 35, 192-207, (1989) · Zbl 0666.90040
[20] Monden, Y., Toyota production system: an integrated approach to just-in-time, (1998), Engineering & Management Press Norcross
[21] Pine, B.J., Mass customization: the new frontier in business competition, (1993), Harvard Business School Press Boston
[22] Röder, A.; Tibken, B., A methodology for modeling inter-company supply chains and for evaluating a method of integrated product and process documentation, European journal of operational research, 169, 1010-1029, (2006) · Zbl 1079.90534
[23] Sarker, B.R.; Pan, H., Designing a mixed-model, open-station assembly line using mixed-integer programming, Journal of the operational research society, 52, 545-558, (2001) · Zbl 1131.90021
[24] Steiner, G.; Yeomans, S., Level schedules for mixed-model just-in-time processes, Management science, 39, 728-735, (1993) · Zbl 0783.90047
[25] Sumichrast, R.T.; Clayton, E.R., Evaluating sequences for paced, mixed-model assembly lines with JIT component fabrication, International journal of production research, 34, 3125-3143, (1996) · Zbl 0928.90031
[26] Tsai, L.-H., Mixed-model sequencing to minimize utility work and the risk of conveyor stoppage, Management science, 41, 485-495, (1995) · Zbl 0832.90052
[27] Zhu, J.; Ding, F.-Y., A transformed two-stage method for reducing the part-usage variation and a comparison of the product-level and part-level solutions in sequencing mixed-model assembly lines, European journal of operational research, 127, 203-216, (2000) · Zbl 0979.90048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.