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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 $V=1,2,\cdots ,n$ 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 $V\setminus \stackrel{˜}{V}$. Another subset $\stackrel{˜}{V}\subseteq V$ includes manual operations, for which it is impossible to fix the exact processing times during the whole life cycle of the assembly line. If $j\in \stackrel{˜}{V}$, then operation time ${t}_{j}$ can be different for different cycles of production process. For the optimal line balance $𝐛$ of a paced assembly line with vector $t=\left({t}_{1},{t}_{2},\cdots ,{t}_{n}\right)$ 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 $j\in \stackrel{˜}{V}$. In particular, we derive necessary and sufficient conditions when optimality of the line balance $𝐛$ is stable with respect to sufficiently small variations of the operation times ${t}_{j}$, $j\in \stackrel{˜}{V}$. 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 $𝐛$.
MSC:
 90B30 Production models 90C31 Sensitivity, stability, parametric optimization