A dynamic multi-commodity inventory and facility location problem in steel supply chain network design

Logistics network design is a major strategic issue due to its impact on the efficiency and responsiveness of the supply chain. This paper focuses on strategic and tactical design of steel supply chain (SSC) networks. Ever-increasing demand for steel products enforces the steel producers to expand their production and storage capacities. The main purpose of the paper includes preparing a countrywide production, inventory, distribution, and capacity expansion plan to design an SSC network. The SSC networks consist of iron ore mines as suppliers, raw steel producer companies as producers, and downstream steel companies as customers. Demand is assumed stochastic with normal distribution and known at the beginning of planning horizon. To achieve the service level of interest, a potential production capacity along with two kinds of safety stocks including emergency and shared safety stocks are suggested by the authors. A mixed integer nonlinear programming (MINLP) model and a mixed integer linear programming (MILP) model are presented to design dynamic multi-commodity SSC networks. To evaluate the performance of the MILP model, a real case of SSC network design is solved. Furthermore, solving two proposed models by using a commercial solver for a set of numerical test cases shows that the MILP model outperforms MINLP in medium- and large-scale problems in terms of computational time. Finally, the complexity of the linear model is investigated by relaxing some major assumptions.