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The development of optimization models for planning and scheduling is one of the most useful tools for improving productivity of a large number of manufacturing companies. This paper presents a mixed-integer programming model for scheduling steelmaking-continuous casting production. We first review the recent works in continuous casting planning. We focus on a model inspired from an application of steelmaking-continuous casting by Arcelor Group in Liege, Belgium. The process scheduling is characterized by several constraints: job grouping, technological interdependence, no dead time inside the same group of jobs and dynamic processing time of jobs. We present a formulation with mixed-integer linear programming which can be solved using standard software packages. Finally, we treat a few examples to illustrate this application and we conclude this paper with some comments and directions for future extensions.

The development of optimization models for planning and scheduling is one of the most useful tools for improving productivity of a large number of manufacturing companies. Nowadays, factory management looks for high-quality, low-costs just-in-time (JIT), value-added products for specific purposes. In steel manufacturing, for example, many international iron and steel corporations are devoted to developing computer integrated manufacturing systems to improve their global competition, particularly with strong competitors in China, South Korea, etc. Researchers and practitioners have developed and implemented many methods of planning and scheduling of steel production. Most of these methods use expert systems (Suh et al., 1998), heuristics (Cowling, 1995; Cowling and Rezig, 2000; Lopez et al., 1998) and mathematical programming (Chen and Wang, 1997; Lee, 2000) to generate feasible solutions. In this paper we study a model of steelmaking-continuous casting (SCC). The SCC is usually the bottleneck in iron and steel production; it is characterized by several constraints: job grouping, technological interdependence, no dead time inside the same group of jobs and dynamic processing time of jobs. We present a formulation with mixed-integer linear programming which can be solved using standard software packages. The rest of this paper is organized as follows. In Section 2 we will give a brief overview of the methods used for planning and scheduling in SCC production. In Section 3, we will describe the product environment for the SCC process. Section 4 proposes a mixed integer linear programming model for SCC planning. A few examples illustrate this model in Section 5 and the paper is concluded with some comments and directions for future extensions.

In this paper, we focused on a model inspired from an application of steelmaking-continuous casting by Arcelor Group in Liege, Belgium. We introduced the steelmaking-continuous casting problem. We modeled the problem with a mixed integer programming formulation, solvable using standard software packages (OMPartners). Practical examples showed that using the mathematical model for the continuous casting planning can lead to a significant reduction of the overall production time in SCC process. In the future some extensions will be considered. • Even if the “company solution” is build to treat only two sequences, chosen pragmatically a priori, it can be interesting to model simultaneously the schedule of several sequences on each CC. At this time, it will be necessary to integrate in the optimization model the order in which each sequence will be treated on each CC. To do this, we can think either to extend the mathematical programming model by using additional binary variables expressing the permutation of the sequences on each CC or to embed the present model into a meta-heuristic (for instance simulated annealing or tabu search) treating this permutation aspect. • Even if the converters constitute a bottleneck of the system, it can happen that idle time can be necessary between two successive charges, especially between the last charge of a sequence and the first charge of the next sequence. Such extension will also be analyzed in the future.