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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 $\bold b$.

MSC:
90B30Production models
90C31Sensitivity, stability, parametric optimization
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References:
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