Solving a mixed integer linear program with times setup for the steel-continuous casting planning and scheduling problem

In this paper, we present a novel model that generalise the steelmaking continuous casting planning and scheduling problem. The model includes three stages: converters namely CV, refining stands namely RS and continuous castings namely CC. The obtained problem can be formulated as a mathematical program with typical constraints, namely the times setup constraints. We develop a mixed integer linear program (MILP) to schedule several sequences of charges for more than two continuous castings devices. The aim is: (i) on one hand, to schedule a list of several sequences that are already ordered for each continuous casting with times setup between two successive sequences, (ii) on the other hand, to determine the optimal order of the successive sequences. We use a benchmark and randomly generated instances to test the model and solved by mean of the commercial software solver Cplex v12.5. These problems span a variety of instances varying from small to large sized instances with different intrinsec parameters as the availability date for a converter CV or the variation intervals of the start time for the first charge at the continuous casting CC stage. We analyse the efficiency of the proposed model based on the CPU time and show the time limitations of the model for large instances. Also, we show the robustness of the model when modifying the initial (starting) state.