Linear programming modelling of the finishing hot rolling programme for low carbon steel coils

In this paper a mathematical model was developed to optimize the finishing rolling of hot rolled coils by increasing the productivity of the rolling programme, to help achieve the required level of quality assurance and to facilitate production planning and control in the hot rolling mill. A brief account of the technological and planning aspects of the hot rolling processes and mills relevant to strip steel is given. Linear (mixed integer) programming is used to formulate the objective function and the various types of constraints of the model. The model takes into consideration, the general aspects pertinent to hot rolling of low carbon steel and the characteristics of the hot rolling mills as stipulated by the operational codes and guidelines of the relevant establishment. Owing to the flexibility offered by linear programming the model can incorporate any modifications and/or additional requirements, if any, in case of other types of steel and/or other types of mills. The full modelling of the problem required the incorporation of some zero/one variable constraints. Owing to the complexity involved and the need to keep the model as simple as possible, it was decided to exclude these constraints and deal with them externally. HYPER LINDO PC was used to solve the programme. Using available data, in the case under consideration the model showed astonishing results in achieving the objectives. Taking into account the effect on the overall productivity as well as quality improvement, the investigation showed that a net improvement in conforming output to the effect of around 43%, could have been obtained had the model been used in the case under consideration.