Stochastic Modelling of Times to Temperature for Furnaces Supplying Titanium Blooms to a Rolling Mill at TIMET

In conjunction with TIMET at Waunarlwydd (Swansea, UK) a model has been developed that will optimise the scheduling of various blooms to their eight furnaces so as to minimise the time taken to roll these blooms into the finished mill products. This production scheduling model requires reliable data on times taken for the various furnaces that heat the slabs and blooms to reach the temperatures required for rolling. These times to temperature are stochastic in nature and this paper identifies the distributional form for these times using the generalised F distribution as a modelling framework. The times to temperature were found to be similarly distributed over all furnaces. The identified distributional forms were incorporated into the scheduling model to optimise a particular campaign that was run at TIMET Swansea. Amongst other conclusion it was found that, compared to the actual campaign, the model produced a schedule that reduced the makespan by some 35%.