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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 $$\mathbf b$$ 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 $$\mathbf b$$ 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 $$\mathbf b$$.

##### MSC:
 90B30 Production models 90C31 Sensitivity, stability, parametric optimization
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##### References:
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