A three-dimensional, time-minimizing (bottleneck) assignment problem consists of assigning n jobs to n workers to be performed on n machines under different forms of feasibility conditions so that the different functions of the individual times taken by a worker to finish a job on a given machine are minimized. The usual assumption made in such a problem is that all the jobs can be commenced simultaneously. In this paper, two special structured precedence constraints on jobs are considered, which necessitate modifications in this assumption. Further, the main purpose here is to develop branch-and-bound-type algorithms for solving the corresponding problems and to illustrate them by a numerical example.
