The blocks relocation problem with item families minimizing the number of reshuffles

In this paper, we consider the process of unloading items from a storage (e.g., a warehouse, depot, etc.). The items are stored in stacks where only the topmost item of each stack can be directly accessed. Each item belongs to a certain family indicating the main type of the item. For a given sequence of families, it has to be decided which item of each demanded family is unloaded from the storage with the objective to minimize the total number of reshuffles. Besides new complexity results, we propose IP formulations and a two-stage simulated annealing algorithm. Computational results are presented for real-world data from a company, benchmark instances from the literature and randomly generated instances with different characteristics.