  In a commonly-used version of the Simple Assembly Line Balancing Problem
(SALBP-1) tasks are assigned to stations along an assembly line with a fixed
cycle time in order to minimize the required number of stations. It has
traditionally been assumed that the total work needed for each product unit has
been partitioned into economically indivisible tasks. However, in practice, it
is sometimes possible to divide particular tasks in limited ways at additional
time penalty cost. Despite the penalties, task division where possible, now and
then leads to a reduction in the minimum number of stations. Deciding which
allowable tasks to divide creates a new assembly line balancing problem, TDALBP
(Task Division Assembly Line Balancing Problem). We propose a mathematical
model of the TDALBP, an exact solution procedure for it and present promising
computational results for the adaptation of some classical SALBP instances from
the research literature. The results demonstrate that the TDALBP sometimes has
the potential to significantly improve assembly line performance.
