Minimizing the Waiting Times of block retrieval operations in stacking facilities

- We address the Blocks Relocation Problem with Waiting Times.
- We formulate the problem by means of an integer programming model.
- We propose a look-ahead heuristic.
- The heuristic algorithm reports high-quality solutions in very short times.

This paper addresses the Blocks Relocation Problem with Waiting Times. Its objective is to retrieve a set of homogeneous blocks from a two-dimensional storage by minimizing the waiting times during their retrieval. An integer programming model and a heuristic algorithm are developed to solve this optimization problem. The mathematical model is able to solve small-size cases to optimality in reasonable computational times. Unfortunately, it requires large computational times when tackling medium and large-size scenarios. For its part, the heuristic algorithm overcomes the problems associated with the computational burden of the model by bringing forward the availability of blocks to retrieve from the storage. With this goal in mind, several look ahead strategies dedicated to perform the most promising predictive block relocation movements are proposed. The computational results disclose the proposed heuristic algorithm is able to report high-quality solutions through very short computational times, less than one second, in practical cases.