A new binary formulation of the restricted Container Relocation Problem based on a binary encoding of configurations

© 2017 Elsevier B.V. The Container Relocation Problem (CRP), also called Block Relocation Problem (BRP), 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. The restricted CRP enforces that only containers blocking the target container can be relocated. We improve upon and enhance an existing binary encoding and using it, formulate the restricted CRP as a binary integer programming problem in which we exploit structural properties of the optimal solution. This integer programming formulation reduces significantly the number of variables and constraints compared to existing formulations. Its efficiency is shown through computational results on small and medium sized instances taken from the literature

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