Relocations in container depots for different handling equipment types: Markov models

Abstract This paper proposes a family of Markov models to analytically characterize the distribution of the number of relocations per retrieval in a container depot. We focus on empty container yards, which, while ubiquitous in worldwide logistics, have rarely been studied in the literature, as most prior research has addressed container movements in ports. We build on the few models available in the literature by: 1) expanding the assumed material handling equipment type (we consider three of the most common types used in practice); and 2) allowing for container arrivals during the retrieval process. These aspects are rarely considered but are particularly relevant for empty container depot practices. We show the effect of various yard configurations and material handling equipment types on the probability distribution of the number of relocations. Our approach can also consider time periods of imbalance by assuming an arrival rate greater than or less than the retrieval rate. The results of these models can be used in planning yard layouts, selecting material handling equipment, and determining staffing and overtime levels. Specifically, container relocations during retrievals directly contribute to operational costs, and so accurate models estimating those are required for any planning purposes. While we focus on empty container yards, the models can be applicable to port side container areas as well, particularly ones in developing countries where overhead yard cranes are not employed as often. Therefore, this paper contributes to both the literature and the practice of container depots.