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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 in the automatic casting lines. 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 two computational intelligence algorithms for simultaneous grouping and scheduling tasks and presents the results achieved by these algorithms for example test problems.

Mathematical programming, constraint programming and computational intelligence techniques, presented in the literature in the field of operations research and production management, are generally inadequate for planning real-life production process. These methods are in fact dedicated to solving the standard problems such as shop floor scheduling or lot-sizing, or their simple combinations such as scheduling with batching. Whereas many real-world production planning problems require the simultaneous solution of several problems (in addition to task scheduling and lot-sizing, the problems such as cutting, workforce scheduling, packing and transport issues), including the problems that are difficult to structure. The article presents examples and classification of production planning and scheduling systems in the foundry industry described in the literature, and also outlines the possible development directions of models and algorithms used in such systems.

The paper presents a novel Iterated Local Search (ILS) algorithm to solve multi-item multi-family capacitated lot-sizing problem with setup costs independent of the family sequence. The model has a direct application to real production planning in foundry industry, where the goal is to create the batches of manufactured castings and the sequence of the melted metal loads to prevent delays in delivery of goods to clients. We extended existing models by introducing minimal utilization of furnace capacity during preparing melted alloy. We developed simple and fast ILS algorithm with problem-specific operators that are responsible for the local search procedure. The computational experiments on ten instances of the problem showed that the presence of minimum furnace utilization constraint has great impact on economic and technological conditions of castings production. For all test instances the proposed heuristic is able to provide the results that are comparable to state-of-the art commercial solver.