•Introduction of an integrated lot-sizing and storage selection problem.•Consideration of multiple suppliers with individual, total, and hybrid discounts.•Modelling of heterogeneous storage facilities.•Proposal of a powerful heuristic for solving realistic instances. In this paper we consider the sourcing process of a production facility from the process industry. The production facility sources raw materials from a set of suppliers that offer different discount schemes. For storing raw materials, heterogeneous storage facilities can be used, which vary with respect to their associated costs and capacities. We formulate the corresponding planning problem of selecting suppliers and storage facilities as well as determining order quantities and transport flows under the discount schemes offered by the suppliers. For solving large problem instances, a heuristic based on kernel search is proposed and evaluated in a real world case study. The case study reveals that supplier selection and storage selection are highly interdependent decisions. By integrating both perspectives, significant savings can be generated. It turns out that single-sourcing is the dominant strategy for most raw materials. However, the selection of the optimal suppliers depends on both the prices offered by the suppliers as well as the associated logistics costs for transportation and stock-holding.