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Stability analysis of an optimal balance for an assembly line with fixed cycle time. (English) Zbl 1102.90321
We address the simple assembly line balancing problem: minimize the number of stations $m$ for processing $n$ partially ordered operations $V=1, 2,\dots, n$ within the cycle time $c$. The processing time $t_i$ of operation $i\in V$ and cycle time $c$ are given. However, during the life cycle of the assembly line the values $t_i$ are definitely fixed only for the subset of automated operations $V\setminus \widetilde V$. Another subset $\widetilde V\subseteq V$ includes manual operations, for which it is impossible to fix the exact processing times during the whole life cycle of the assembly line. If $j\in\widetilde V$, then operation time $t_j$ can be different for different cycles of production process. For the optimal line balance $\bold b$ of a paced assembly line with vector $t = (t_1, t_2,\dots, t_n)$ of the operation times, we investigate stability of its optimality with respect to possible variations of the processing times $t_j$ of the manual operations $j\in\widetilde V$. In particular, we derive necessary and sufficient conditions when optimality of the line balance $\bold b$ is stable with respect to sufficiently small variations of the operation times $t_j$, $j\in\widetilde V$. We show how to calculate the maximal value of independent variations of the processing times of all the manual operations, which definitely keep the feasibility and optimality of the line balance $\bold b$.

90B30Production models
90C31Sensitivity, stability, parametric optimization
Full Text: DOI
[1] Baybars, I.: A survey of exact algorithms for the simple assembly line balancing problem. Management science 32, No. 8, 909-932 (1986) · Zbl 0601.90081
[2] Bukchin, J.; Tzur, M.: Design of flexible assembly line to minimize equipment cost. IIE transactions 32, 585-598 (2000)
[3] Dolgui, A.; Guschinski, N.; Harrath, Y.; Levin, G.: Une approche de programmation linéaire pour la conception des lignes de transfert. European journal of automated systems (APII-JESA) 36, No. 1, 11-33 (2002)
[4] A. Dolgui, N. Guschinsky, G. Levin, On problem of optimal design of transfer lines with parallel and sequential operations, in: J.M. Fuertes (Ed.), Proceedings of the 7th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA’99), Barcelona, vol. 1, 1999, pp. 329-334.
[5] Erel, E.; Sarin, S. C.: A survey of the assembly line balancing procedures. Production planning and control 9, No. 5, 414-434 (1998)
[6] Gen, M.; Tsujimura, Y.; Li, Y.: Fuzzy assembly line balancing using genetic algorithms. Computers and industrial engineering 31, No. 3/4, 631-634 (1996)
[7] Kravchenko, S. A.; Sotskov, Yu.N.; Werner, F.: Optimal schedules with infinitely large stability radius. Optimization 33, 271-280 (1995) · Zbl 0821.90067
[8] Lee, H. F.; Johnson, R. V.: A line-balancing strategy for designing flexible assembly systems. The international journal of flexible manufacturing systems 3, 91-120 (1991)
[9] Pinto, P. A.; Dannenbring, D. G.; Khumawala, B. M.: Assembly line balancing with processing alternatives: an application. Management science 29, 817-830 (1983)
[10] Sarin, S. C.; Erel, E.; Dar-El, E. M.: A methodology for solving single-model, stochastic assembly line balancing problem. OMEGA--international journal of management science 27, 525-535 (1999)
[11] Scholl, A.: Balancing and sequencing of assembly lines. (1999) · Zbl 0949.90034
[12] Scholl, A.; Klein, R.: Balancing assembly lines effectively: A computational comparison. European journal of operational research 114, 51-60 (1998) · Zbl 0949.90034
[13] Sotskov, Yu.N.: Stability of an optimal schedule. European journal of operational research 55, 91-102 (1991) · Zbl 0755.90048
[14] Yu.N. Sotskov, A. Dolgui, Stability radius of the optimal assembly line balance with fixed cycle time, in: Proceedings of the IEEE Conference ETFA’2001, 2001, pp. 623-628.
[15] Sotskov, Yu.N.; Tanaev, V. S.; Werner, F.: Stability radius of an optimal schedule: A survey and recent developments. Industrial applications of combinatorial optimization 16, 72-108 (1998) · Zbl 0936.90030
[16] Tsujimura, Y.; Gen, M.; Kubota, E.: Solving fuzzy assembly-line balancing problem with genetic algorithms. Computers and industrial engineering 29, No. 1-4, 543-547 (1995)