On the integer programming formulation for the relaxed restricted container relocation problem

In a recent paper entitled “A new binary formulation of the restricted container relocation problem based on a binary encoding of configurations”, Galle, Barnhart and Jaillet (2018) introduced a new variant of the container relocation problem (CRP), named the relaxed restricted CRP, where every container can be relocated at most once for retrieving each target container. The authors also proposed a binary integer programming model for formulating the relaxed restricted CRP. In this paper, it is first shown that the proposed model contains two deficiencies in formulating the “last in, first out” (LIFO) policy. These deficiencies will cause the solutions obtained by the model to correspond to infeasible configurations or infeasible relocation sequences. Then, the LIFO policy is analyzed in detail and reformulated as linear constraints correctly. Lastly, the corrected integer programming formulation is presented. Computational experiments show that the corrected model dramatically reduces complexity and improves performance.