Assembly Line Balancing with Parallel Stations and Shared Resources: A Cycle-Relative Constraint Programming Approach

Abstract

This paper addresses an assembly line balancing problem that combines task assignment, scheduling, and allocation of parallel workstations to minimize cycle time, subject to precedence and shared resource constraints. A key complexity in periodic production environments is the presence of cyclic resource constraints which arise when workers (resources) move between workstations within the same cycle. This scenario is particularly prevalent in large-scale manufacturing industries with long cycle times, such as aerospace assembly. Existing constraint programming (CP) models for this problem schedule tasks on an absolute time horizon. However, this approach relies on modulo operators to project task intervals into a cycle window, which hinders constraint propagation, and makes extending the model beyond fixed factory layouts difficult. We propose a novel cycle-relative CP formulation that addresses both shortcomings. Our model dynamically determines the optimal placement of parallel workstations and defines task decision variables directly within the cycle window, eliminating the need for modulo operators. Experimental evaluations demonstrate the cycle-relative model’s superiority, consistently finding equal or better solutions faster than the temporal approach. Furthermore, a direct engine comparison shows that OptalCP outperforms CP Optimizer on these models across the vast majority of instances.