Cross-Dock Door Design under Uncertainty: A two-stage DRO-based lower- and upper-bounding scheme

Mathematics > Optimization and Control [Submitted on 2 Jun 2025 (v1), last revised 18 Jun 2026 (this version, v2)] Title:Cross-Dock Door Design under Uncertainty: A two-stage DRO-based lower- and upper-bounding scheme View PDF HTML (experimental)Abstract:The stochastic cross-dock door design problem entails determining the number of doors and their nominal capacities under uncertainty. The inbound flow of commodities from origin nodes is assigned to the entry doors consolidated in the platform, and the outbound flow is assigned to the exit doors to be delivered to the destination nodes. This problem combines three high computational difficulties, namely, NP-hard quadratic combinatorics, uncertainty in the main parameters, and ambiguity in their probability distribution. Distributionally robust optimization is considered to deal with these uncertainties. A two-stage mixed binary quadratic model is presented, where the first stage decisions are related to the design of the platform and the second stage ones are related to the assignment of the commodity flow to the doors in the members of the ambiguity set. The goal is to minimize the highest total cost in the ambiguity set, subject to the constraint system for each of those members. In addition to the risk-neutral version, a risk-averse formulation is presented. Given the difficulty of this problem, a min-max matheuristic scheme based on a scenario cluster decomposition is proposed for obtaining lower and upper bounds. A computational study is conducted to compare the solutions provided by the straightforward use of the state-of-the-art solvers CPLEX and Gurobi, as well as to validate the proposed matheuristic scheme. Submission history From: Maria Araceli Garin [view email][v1] Mon, 2 Jun 2025 13:57:17 UTC (289 KB) [v2] Thu, 18 Jun 2026 07:52:51 UTC (147 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.