Background: We study one of the most important problems in production and warehouse management: the problem of determining how to allocate the initial stock and the quantity produced to bins, and then how to manage picking operations from these bins. The objective is to minimize the total cost of the bins used. Methods: We formulate an integer linear programming model able to manage the two time periods related to assignment and picking together, and to handle the FIFO picking logic. We prove that it is NP-hard, and solve it to optimality. Then, we design a tailored heuristic algorithm, inspired by the current rule of thumb used by one of the main Italian mineral water bottling companies. Results: An extensive computational experiment allows us to show that this problem can be solved to optimality in a reasonable computational time based on real-world instances, and that the heuristic provides near-optimal solutions. Conclusions: Our approach provides a contribution to modeling and solving this problem when FIFO picking operations are taken into account. Moreover, it contributes by building important bridges between theoretical understanding and practical applications.
Bertazzi et al. (Sun,) studied this question.