Balancing / Sequencing Mixed-Model Lines

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Purposes of Mixed-Model Sequencing.
Algorithms for Mixed-Model Sequencing.
First Blender Algorithm.
Reciprocal of Production Ratio Algorithm.
Percentage of Production Ratio Algorithm.
Goal Chasing Algorithm I.
Goal Chasing Algoorithm II.
Miltenburg Heuristics.

Reading Lists:
Articles - Balancing Mixed-Model Line.
Articles - Mixed-Model Sequencing.
Books.

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Last Updated: October 22, 1996.

Purposes of Mixed-Model Sequencing

Mixed-model sequencing is a key element of just-in-time (JIT) production. It is often applied by companies to maintain diversified small-lot production to satisfy customers' demand for a variety of products, without holding large inventories. There are two main purposes of using mixed-model sequencing strategy:

Leveling the load (total assembly time) on each process within the line. This goal recognizes that all products do not have the same operation time at each work station on the line, and some workstations might have a longer than average cycle time.
Keeping a constant spped in consuming each part on the line. This second goal attempts to keep the quantity of each part used by the mixed-model assembly line per unit time constant.

According to Professor Monden at University of Tsukuba, Japan, the Toyota Co. considered the second goal to be more important and critical then the first one for a JIT production system.

Algorithms for Mixed-Model Sequencing

The importance of the order in which models are assembly on a mixed-model line has been recognized by practitioners and academics alike. Many algorithms have been proposed to solve the problem. Some common referred algorithms are:

First Blender Algorithm (by Unidentified Japanese Researcher or Company).
Reciprocal of Production Ratio Algorithm (by Unidentified Japanese Researcher or Company).
Percentage of Production Ratio Algorithm (by Unidentified Japanese Researcher or Company).
Goal Chasing Algorithm I (by Toyota Co., Japan. See Monden 1993).
Goal Chasing Algorithm II (by Toyota Co.,Japan. See Monden 1993).
Goal Coordination Method (by Toyota Co., Japan. See Monden 1993).
Miltenburg Heuristic I, II, and III (Miltenburg et. al., 1989, 1991, 1992).
Quick and Dirty Sequencing Method (Inman Bulfin 1992).
Time Spread Method (Sumichrast et. al. 1992)

Reading Lists

The topic of mixed-model sequencing has attract much attention by both academics and practitioners and has been extensively studied over the past decade. Thus, the references cited below may not be a complete list.

Articles:

Balancing Mixed-Model Lines:

Chakravarty, A. K. and Shtub, V., "Balancing Mixed Model Lines with In-Process Inventories," Management Science, 31, 9 (1985), pp. 1161-1174.
DarEl, E. M. and Cucuy, S., "Optimal MixedModel Sequencing for Balanced Assembly Line," OMEGA: The Int. J. of Mgmt. Sci., 5, 3 (1977), pp. 333-342.
Macaskill, J. L. C., "Production Line Balances for Mixed-Model Lines," Management Science, 19, 4 (1972), pp. 423-434.
Macaskill, J. L. C., "Computer Simulation for MixedModel Production Line," Management Science, 20, 3 (1973), pp. 341-348.
Roberts, S. D. and Villa, C. D., "On a Multiproduct Assembly Line Balancing Problem," AIIE Transactions, 2, 4 (1970), pp. 361-364.
Thomopoulos, N. T., "Line Balancing-Sequencing for Mixed Model Assembly," Management Science, 14, 2 (1967), pp. B59-75.
Thomopoulos, N. T., "Mixed Model Line Balancing with Smoothed Station Assignments," Management Science, 16, 9 (1970), pp. 593-603.
Vrat, P. and Virani, A., "A Cost Model for Optimal Mixed of Balanced Stochastic Assembly Line and the Modular Assembly System for a Customer Oriented Production System," Int. J. of Prod. Res., 14, 4 (1976), pp. 445-463.

Mixed-Model Sequencing:

Bard, J. F., Dar-El, E. and Shtub, A., "An Analytic Framework for Sequencing Mixed Model Assembly Lines," Int. J. of Prod. Res., 30, 1 (1992), pp. 35-48.
Berkley, B. J., "Simulation Tests of FCFS and SPT Sequencing in Kanban Systems," Decision Sciences.
Bruns, L. D. and Daganzo, C. F., "Assembly Line Job Sequencing Principles," Int. J. of Prod. Res. 25, 1 (1987), pp. 71-99.
Cakir, A. and Inman, R. R., "Modified Goal Chasing for Products with Non-Zero/One Bills of Materials," Int. J. of Prod. Res., 31, 1 (1993), pp. 107-115.
DarEl, E. M. and Cother, R. F., "Assembly Line Sequencing for Model Mix," Int. J. of Prod. Res., 13, 5 (1975), pp. 463-477.
DarEl, E. M. and Nadivi, A., "A Mixed-Model Sequencing Application," Int. J. of Prod. Res., 19, 1 (1981), pp. 69-84.
DarEl, E. M. and Rabinovitch, M., "Optimal Planning and Scheduling of Assembly Lines," Int. J. of Prod. Res., 26, 9 (1988), pp. 1433-1450.
Ding, F. Y. and Cheng, L., "An Effective Mixed-Model Assembly Line Sequencing Heuristic for Just-in-Time Production Systems," J. of Operations Management, 11 (1993), pp. 45-50.
ElTamimi, A. M., Suliman, S. M. and Williams, D. F., "A Simulation Study of Part Sequencing in a Flexible Assembly Cell," Int. J. of Prod. Res., 27, 10 (1989), pp. 1769-1793.
Groeflin, H., Luss, H., Rosenwein, M. B., and Wahls, E. T., "Final Assembly Sequencing for Just-in-Time Manufacturing," Int. J. of Prod. Res., 27, 2 (1989), pp. 199-213.
Hall, R. W., "Leveling the Scheduling," Zero Inventory Philosophy and Practices: APICS Seminar Proceedings, pp. 111-119.
Inman, R. R. and Bulfin, R. L., "Sequencing JIT Mixed-Model Assembly Lines," Management Science, 37, 7 (1991), pp. 901-904.
Inman, R. R. and Bulfin, R. L., "Quick and Dirty Sequencing for Mixed-Model Multi-Level JIT Systems," Int. J. of Prod. Res., 30, 9 (1992), pp. 2011-2018.
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 (1991), PP. 121-122.
Lee, S. Y. and Kim, C. B., "A Study on MRP-Based JIT System," Proceedings of the 3rd Int. Conf. on Just in Time Manufacturing, (June 1988), pp. 211-220.
Miltenburg, J., "Level Schedules for Mixed-Model Assembly Lines in JustinTime Production Systems," Management Science, 35, 2 (February 1989), pp. 192-207.
Miltenburg, J., "A Theoretical Basis for Scheduling Mixed-Model Production Lines," Management Science, 35 (1989), pp. 192-207.
Miltenburg, J. and Sinnamon, G., "Scheduling Mixed-Model MultiLevel Just-in-Time Production Systems," Int. J. of Prod. Res., 27, 9 (1989), pp. 1487-1509.
Miltenburg, J. and Goldstein, T., "Developing Production Schedules with Balance Part Usage and Smooth Production Loads for Just-in-Time Production Systems," Naval Research Logistics, 38 (1991), pp. 893-910.
Miltenburg, J. and Sinnamon, G., "Algorithms for Scheduling MultiLevel Just-in-Time Production Systems," IIE Transactions, 24, 2 (1992), pp. 121-130.
Okamura, K. and Yamashina, H., "A Heuristic Algorithm for the Assembly Line Model-Mix Sequencing Problem to Minimize the Risk of Stopping the Conveyer," Int. J. of Prod. Res., 17,3 (1979), pp. 233-247.
Pleschberger, T. E. and Hitomi, K,, "Flexible Final-Assembly Sequencing Method for a JIT Manufacturing Environment," Int. J. Prod. Res., 31, 5 (1993), pp. 1189-1199.
Steiner, G. and Yeomans, S., "Level Schedules for Mixed-Model, Just-in-Time Processes," Management Science, 39, 6 (June 1993), pp. 728-735.
Sumichrast, R. T. and Russell, R. S., "Evaluating Mixed-Model Assembly Line Sequencing Heuristics for Just-in-Time Production systems," J. of Operations Management, 9, 3 (1990), pp. 371-390.
Sumichrast, R. T., Russell, R. S. and Taylor, III, B. W., "A Comparative Analysis of Sequencing Procedures for Mixed-Model Assembly Lines in a Just-in-Time Production System," Int. J. of Prod. Res., 30, 1 (1992), pp. 199-214.
Yano, C. A. and Rachamadugu, R., "Sequencing to Minimize Work Overload in Assembly Lines with Product Options," Management Science, 37, 5 (May 1991), pp. 572-586.

Books:

Monden, Y., Toyota Production System: An Integrated Approach to Just-In-Time, Second Edition, Industrial Engineering and Management Press, Norcross, GA, 1993. Chapters 16, 17 and appendix 2.

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Mail your comments to: Dr. Chao-Hsien Chu chu@ist.psu.edu.