Integrated production, distribution and scheduling in the aluminium industry: a continuous-time MILP model and decomposition method

This article deals with the multi-stage production–shipping and distribution–scheduling problem in the aluminium industry. Related processes take place in worldwide operating networks with multiple sites in each stage. The aim is to coordinate production activities and material flows worldwide months in advance and exactly to the day, so that temporary storage of intermediate products is reduced network wide or even set to zero. This paper includes a further development of the multi-stage production-shipping and distribution-scheduling problem including in-time supplies of all production sites (MSPSDS-IS). However, the in-time supplies at the sites often result in network-wide temporary storage before and/or after site production. In contrast, it should be possible that either stock-free material flows within the entire network or site-specific storage times are prescribed. The previous modelling is not able to meet these aforementioned requirements as it can be considered as special case of the generalised approach developed in the following. Therefore, a substantially extended continuous-time MILP model is presented. Furthermore, extensive computational experiments with a high-performance computer indicate that a modified version of the relax-and-fix heuristic, which was applicable to the MSPSDS-IS, also results in high-quality solutions and remarkable reductions in computation times.