The problem considered in the paper is motivated by production planning in a foundry equipped with the furnace and casting line, which
provides a variety of castings in various grades of cast iron/steel for a large number of customers. The quantity of molten metal does not
exceed the capacity of the furnace, the load is a particular type of metal from which the products are made. The goal is to create the order
of the melted metal loads to prevent delays in delivery of goods to customers. This problem is generally considered as a lot-sizing and
scheduling problem. The paper describes a mathematical programming model that formally defines the optimization problem and its
relaxed version that is based on the conception of rolling-horizon planning