Multi-Product Multi-Stage Multi-Period Resource Allocation for Minimizing Batch-Processing Steel Production Cost

Rational allocation of resources can improve the profit margin of a steel enterprise. This paper deals with a multi-product multi-stage multi-period resource allocation problem. In it, product manufacturing involves multiple continuous production stages, each of which has parallel machines. According to process requirements, the tasks assigned to a machine need to be produced in batches. The process route of a product is a sequential combination of machines each of which is to be selected from a stage. The process route for each product and the batching rules of each machine are known in advance. Multi-period production means that the tasks released before a planning period can be processed in any of its periods. The demand for each product type in each period and the capacity of each machine are predetermined. Considering a customer's demand, we optimally allocate machines for products in each planning period to achieve their efficient utilization. The objective is to minimize the sum of various costs related to transportation, resources, unmet demand, and product inventory. A mixed integer linear program is developed for the concerned problem. A fix-and-optimize heuristic with variable neighborhood size is newly designed to obtain high-quality solutions. Its solutions are compared with those of CPLEX (a commercial software) given a fixed solution time. Experimental results show that it can accurately solve small-scale instances and find better solutions than CPLEX for most large-scale instances. Comparison experiments are conducted and the results show that the proposed algorithm has excellent accuracy, speed, and stability in addressing the concerned problem. Note to Practitioners - As demand for steel products gradually shows a trend towards multiple varieties, small batches, and personalized customization, it increases the difficulty for practitioners to rationally allocate resources for their production in a steel enterprise. It is hard to achieve rational material and machine resource allocation subject to complex constraints for processing multiple products in multiple production stages and periods. To deal with a multi-product multi-stage multi-period resource allocation problem, it is essential to design efficient and stable algorithms. A fix-and-optimize heuristic with variable neighborhood size is thus proposed for addressing it. The method can decompose the problem into a series of subproblems according to a decomposition scheme. They are iteratively solved. In this work, our goal is to help practitioners to deal with the challenging resource allocation problem in a short time. The effectiveness of the proposed algorithm is validated and tested by comparing its results with those of a commercially available exact solver called CPLEX on various problem instances. Extensive experimental results demonstrate its effectiveness. It can quickly solve small-scale instances with no statistically significant difference from the optimal solutions obtained by CPLEX. When addressing large-scale instances, the proposed algorithm shows better solution performance than CPLEX in a given running time. The algorithm is flexible, accurate, and fast, which implies its great application potential for resource allocation in steel enterprises.