Optimization of a molten iron scheduling problem with uncertain processing time using variable neighborhood search algorithm

Punctuality of the steel-making scheduling is important to save steel production costs, but the processing time of the pretreatment process, which connects the iron- and steel-making stages, is usually uncertain. This paper presents a distributionally robust iron-steel allocation (DRISA) model to obtain a robust scheduling plan, where the distribution of the pretreatment time vector is assumed to belong to an ambiguity set which contains all the distributions with given first and second moments. This model aims to minimize the production objective by determining the iron-steel allocation and the completion time of each charge, while the constraints should hold with a certain probability under the worst-case distribution. To solve problems in large-scale efficiently, a variable neighborhood algorithm is developed to obtain a near-optimal solution in a short time. Experiments based on actual production data demonstrate its efficiency. Results also show the robustness of the DRISA model, i.e., the adjustment and delay of the robust schedule derived from the DRISA model are less than the nominal one.