The stochastic container relocation problem with flexible service policies

This paper investigates the Stochastic Container Relocation Problem in which a flexible service policy is adopted in the import container retrieval process. The flexible policy allows the terminal operators to determine the container retrieval sequence to some extent, which provides more opportunity for reducing the number of relocations and the truck waiting times. A more general probabilistic model that captures customers’ arrival preference is presented to describe the randomness for external truck arrivals within their appointed time windows. Being a multi-stage stochastic sequential decision-making problem, it is first formulated into a stochastic dynamic programming (SDP) model to minimize the expected number of relocations. Then, the SDP model is extended considering a secondary objective representing the truck waiting times. Tree search-based algorithms are adapted to solve the two models to their optimality. Heuristic algorithms are designed to seek high-quality solutions efficiently for larger problems. A discrete-event simulation model is developed to evaluate the optimal solutions and the heuristic solutions respectively on two performance metrics. Extensive computational experiments are performed based on instances from literature to verify the effectiveness of the proposed models and algorithms

The Stochastic Container Relocation Problem

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the assumption of knowing the full retrieval order of containers is particularly unrealistic in real operations. This paper studies the stochastic CRP (SCRP), which relaxes this assumption. A new multi-stage stochastic model, called the batch model, is introduced, motivated, and compared with an existing model (the online model). The two main contributions are an optimal algorithm called Pruning-Best-First-Search (PBFS) and a randomized approximate algorithm called PBFS-Approximate with a bounded average error. Both algorithms, applicable in the batch and online models, are based on a new family of lower bounds for which we show some theoretical properties. Moreover, we introduce two new heuristics outperforming the best existing heuristics. Algorithms, bounds and heuristics are tested in an extensive computational section. Finally, based on strong computational evidence, we conjecture the optimality of the “Leveling” heuristic in a special “no information” case, where at any retrieval stage, any of the remaining containers is equally likely to be retrieved next

Column Generation for the Container Relocation Problem

Container terminals offer transfer facilities to move containers from vessels to trucks, trains and barges and vice versa. Within the terminal the container yard serves as a temporary buffer where incoming containers are piled up in stacks. Only the topmost container of each stack can be accessed. If another container has to be retrieved, containers stored above it must be relocated first. Containers need to be transported to a ship or to trucks in a predefined sequence as fast as possible. Generally, this sequence does not match the stacking order within the yard. Therefore, a sequence of retrieval and relocation movements has to be determined that retrieves containers from the bay in the prescribed order with a minimum number of relocations. This problem is known as the container relocation problem. We apply an exact and a heuristic column generation approach to this problem. First results are very promising since both approaches provide very tight lower bounds on the minimum number of relocations