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Stability of the Optimal Line Balance: Case of a Fixed Number of Stations

by Sotskov, Y.N., Dolgui, A., Sotskova, N., Werner, F..

Series: 2002-20, Preprints

90B30 Production models
90C31 Sensitivity, stability, parametric optimization

We consider the following simple assembly line balancing problem. Minimize the cycle-time
of processing n partially ordered operations on m linearly ordered stations.
The real processing times of the operations and the set of stations are given.
During the life cycle of the assembly line the processing times are definitely
fixed only for the subset of so-called automated operations. Another subset includes manual operations for which it is
impossible to fix the exact processing times during the life cycle of the assembly line.
For the optimal line balance of a paced assembly line with vector t of operation times, we investigate
the stability of its optimality with respect to possible variations of the processing times of the manual operations.
In particular, we prove necessary and sufficient conditions
when optimality of the line balance is stable with respect
to sufficiently small variations of the processing times.

Assembly; Line Balance; Optimality; Stability

This paper was published in:
Proceedings of the ACS'02 - SCM confe