This paper studies the problem of multi-plant manganese alloy production. The problem consists of finding the optimal furnace feed of ores, fluxes, coke, and slag that yields output products which meet customer specifications, and to optimally decide the volume, composition, and allocation of the slag. To solve the problem, a nonlinear pooling problem formulation is presented upon which the bilinear terms are reformulated using the Multiparametric Disaggregation Technique (MDT). This enables global optimisation by means of commercial software for mixed integer linear programs. We demonstrate the model and solution approach through case studies from a Norwegian manganese alloy producer. The computational study shows that the model and proposed optimisation approach can solve problem sizes of up to ten furnaces to a small optimality gap, that global optimization approach with MDT scales well with larger, real problem instances, and that the model outperforms the current operational practice.

本文研究了多厂锰合金的生产问题。问题在于找到矿石，熔剂，焦炭和炉渣的最佳炉料，以产生满足客户要求的输出产品，并以最佳方式确定炉渣的量，组成和分配。为了解决该问题，提出了一种非线性合并问题公式，使用多参数分解技术（MDT）在该公式上重新构造了双线性项。这使得可以通过商业软件对混合整数线性程序进行全局优化。我们通过来自挪威锰合金生产商的案例研究演示了模型和解决方案方法。计算研究表明，该模型和所提出的优化方法可以解决多达十个炉子的问题尺寸，并保持较小的最优间隙；