A scheduling problem arising in the iron and steel industry is discussed. It concerns the medium planning and the short-term scheduling of three tools: continuous-casting, strip mill and finishing, these three belonging to the hot unit of an iron and steel company. The strip mill is more constrained than the other two, it is therefore called the pivot, the continuous-casting tool is called the upstream tool and the finishing tool is called the downstream tool. A hierarchical approach consisting of two levels is designed. At each level of this hierarchy, the pivot is scheduled first followed by the other tools under the constraints of the pivot schedule. Methods are proposed to solve scheduling problems arising from this approach. Each of the methods is an approximation scheme because of the NP-hardness of the scheduling problems. Some of the approximation schemes are local search methods (simulated annealing improved by some specific techniques), others are specific constructive methods built to solve given problems. An interesting criterion is the following: the schedule of the pivot being given, the schedule of the upstream tool must begin as late as possible and the schedule of the downstream must end as soon as possible in order to minimize the inventory cost between the tools while minimizing the other costs of manufacturing such as the number of profile changes, the number of block changes, etc. The pivot medium-term solving is the most developed part of this paper and it is tested on some generated examples; the generator description and the numerical results are presented.