Maximizing the robustness for simple assembly lines with fixed cycle time and limited number of workstations

Abstract

This paper deals with an optimization problem that arises when a new paced simple assembly line has to be designed subject to a limited number of available workstations, cycle time constraint, and precedence relations between necessary assembly tasks. The studied problem, referred to as SALPB-S, consists in assigning the set of tasks to workstations so as to find the most robust line configuration (or solution) under task time variability. The robustness of solution is measured via its stability radius, i.e., as the maximal amplitude of deviations for task time nominal values that do not violate the solution feasibility. In this work, the concept of stability radius is considered for two well-known norms: ℓ1 and ℓ∞. For each norm, the problem is proven to be strongly NP-hard and a mixed-integer linear program (MILP) is proposed for addressing it. To accelerate the seeking of optimal solutions, an upper bound on the stability radius is devised and integrated into the corresponding MILP. Computational results are reported on a collection of instances derived from classic benchmark data used in the literature for the Simple Assembly Line Balancing Problem.