Balancing and Scheduling Mixed-Model U-Shaped Production Lines

The production line considered in this paper is a U-shaped, mixed-model, asynchronous line where assembly and fabrication tasks are performed to produce a variety of different discrete products or models in a just-in-time (JIT) environment. Two important problems occur routinely with these lines. The first is the assignment of tasks to stations on the line—the line balancing problem—and the second is the selection of the sequence in which models will be produced—the model sequencing problem. The model sequence cannot be set independently of the line balance, because different models require different tasks and the same tasks have different completion times for different models, and, in the JIT environment, the model sequence cannot be set independently of the schedules of other lines and production facilities. JIT uses a pull rather than a push system of production control, which means that the model sequence at the U-shaped mixed-model final assembly line sets the schedules at the other production facilities. JIT requires these latter schedules to be “level” and this requirement imposes an additional constraint on the model sequence. The effect of these two conditions is to require that the line-balancing and model-sequencing problems be solved simultaneously. In this article, we model the joint problem and present a solution algorithm for solving instances of practical size.