A mathematical formulation and efficient heuristics for the dynamic container relocation problem

The container relocation problem (CRP) is concerned with emptying a single yard-bay which contains J containers each following a given pickup order so as to minimize the total number of relocations made during their retrieval process. The CRP can be modeled as a binary integer programming (IP) problem and is known to be NP-hard. In this work, we focus on an extension of the CRP to the case where containers are both received and retrieved from a single yard-bay, and call it the dynamic container relocation problem. The arrival (departure) sequences of containers to (from) the yard-bay is assumed to be known a priori. A binary IP formulation is presented for the problem. Then, we propose three types of heuristic methods: index based heuristics, heuristics using the binary IP formulation, and a beam search heuristic. Computational experiments are performed on an extensive set of randomly generated test instances. Our results show that beam search heuristic is very efficient and performs better than the other heuristic methods.