Chapter 10 STABILITY OF OPTIMAL LINE BALANCE WITH GIVEN STATION SET Yuri N. Sotskov, Alexandre Dolgui, Nadezhda Sotskova, Frank Werner Abstract: We consider the simple assembly line balancing problem. For an optimal line balance, we investigate its stability with respect to simultaneous independent variations of the processing times of the manual operations. In particular, we prove necessary and sufficient conditions when optimality of a line balance is stable with respect to sufficiently small variations of operation times. We show how to calculate lower and upper bounds for the stability radius, i.e., the maximal value of simultaneous independent variations of operation times with definitely keeping the optimality of line balance. Key words: assembly line balance, stability analysis. 1. INTRODUCTION We consider a single-model paced assembly line, which continuously manufactures a homogeneous product in large quantities as in mass production (see [4] for definitions). An assembly line is a sequence of m linearly ordered stations, which are linked by a conveyor belt. A station has to perform the same set of operations repeatedly during the whole life cycle of the assembly line. The set of operations V, which have to be processed by all m stations within one cycle-time c, is fixed. Each operation is considered as indivisible. All the m stations start simultaneously with the processing of the sequence of their operations and buffers between stations are absent. Technological factors define a partial order on the set of operations, namely, the digraph G = (V, A) with vertices V and arcs A defines a partially ordered set of operations V = {1, 2 , . . . , n }.