The multi-stage multi-product batch-sizing problem in the steel industry

In this paper, we consider a batch-sizing problem with multiple periods and multiple types of products that arises in the steel industry. In this problem, products of a product type are produced in series of stages to fulfill the demand. Each stage consists of a work-in-process storage with inventory capacity and a production machine with a production rate. It incurs an inventory cost in the work-in-process storage of a stage, and also incurs a setup cost whenever a production batch is formed in the first stage. The problem is to determine the formation of each production batch in each period such that the total cost of setup and inventory is minimized. For the problem, we first provide a mixed-integer quadratic programming model and then propose some optimality properties. Based on the proposed properties, we design an optimal algorithm to solve the problem in polynomial time. Finally, we report the performances of the mixed-integer quadratic programming model and the optimal algorithm based on actual production data. The computational results confirm the reliability and validity of the optimal algorithm. (C) 2019 Elsevier Inc. All rights reserved.