Stability analysis of an optimal balance for an assembly line with fixed cycle time

Abstract

We address the simple assembly line balancing problem: minimize the number of stations m for processing n partially ordered operations V = {1, 2, …, n} within the cycle time c. The processing time t i of operation i ∈ 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 ⧹ V ∼ . Another subset V ∼ ⊆ 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 ∈ 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 = ( t 1, t 2, …, t n ) 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 ∈ 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 ∈ 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 .