Allocation of tasks to stations in small-batch assembly with learning: basic concepts

SUMMARY

Conventional line balancing deals with the processing of large batches with fixed operation times, such that the throughput rate is maximized. Solution procedures are predicted upon equal allocation of work to stations along the line. When batches are small, operation times exhibit learning effects, and not all stations are employed at the beginning and end of the batch process. Thus a totally different approach must be taken. The objective is to minimize the throughput time of a finite batch. In this article we show that optimal solutions are based upon allocation of work to stations in decreasing proportions, so that more work is allocated to the first station than to the last. A number of theorems are presented to support and illustrate the decreasing proportions principle; and two heuristics, one based upon simplified linear programming model, and the other on the geometric mean ratio of successive task times, are developed to find task-to-station allocations that yield minimum throughput times for the small-batch problem. A comparison with equal allocation of work (under learning conditions) is made, and the properties of the task allocations and resultant schedules are discussed.