The stability radius of an optimal line balance with maximum efficiency for a simple assembly line

Abstract

We consider a simple assembly line balancing problem in which each element of the partially ordered set of assembly operations must be assigned to one element of the set of workstations used for processing the operations. An objective is minimizing the product of the number of workstations used in the line balance and the cycle time of the line balance among all admissible line balances. An admissible line balance is a partition of all assembly operations into at least two workstations without violating the precedence relations among the assembly operations. We assume that during the lifespan of the assembly line, the duration of each manual operation may deviate from an initially estimated value, while the duration of each automated operation is deterministic. We conduct the stability analysis of an optimal line balance. First, we derive a sufficient and necessary condition for an optimal line balance to be stable. Second, we show that the stability radius of an optimal line balance could be infinitely large. We also establish some lower and upper bounds for a finite stability radius. Third, we derive formulae that are needed and develop an algorithm for obtaining the stability radius of an optimal line balance.