Calculation of the stability radius of an optimal line balance

For an assembly line, it is necessary to minimize the cycle time for processing a partially ordered set of operations V = {1, . . . , n} on a set of m linearly ordered working stations. The number m of stations and the initial processing times t = (t1, . . . , tn) of the operations V are given. However, for a subset Ṽ ⊆ V of the manual operations j ∈ Ṽ , it is impossible to fix the processing times tj for the whole life cycle of the assembly line. On the other hand, for each automated operation i ∈ V \ Ṽ , the processing time ti is fixed. We investigate the stability of an optimal line balance b0 of the assembly line with respect to variations of the processing times tj , j ∈ Ṽ . It is shown how to calculate the stability radius ρb0(t) of an optimal line balance b0, i.e., the maximal value of simultaneous independent variations of the processing times of the manual operations with keeping the optimality of the line balance b0. We survey known results on the stability radius of an optimal line balance for a dual problem which is to minimize the number m of the working stations for the given cycle time.