Two-stage Distributionally Robust Optimization for Cross-dock Door Design

TL;DR

This paper introduces a novel two-stage distributionally robust optimization model for cross-dock door design, addressing uncertainty and combinatorial complexity, and proposes heuristics that outperform standard solvers.

Contribution

It develops the first two-stage distributionally robust model for cross-dock door design, incorporating scenario clustering and min-max heuristics for improved computational performance.

Findings

Proposed heuristics outperform Cplex and Gurobi in computational tests.

The model effectively handles uncertainty in door design and commodity flow.

Scenario clustering improves solution bounds and computational efficiency.

Abstract

The cross-dock door design problem consists of deciding the strip and stack doors and nominal capacity of an entity under uncertainty. Inbound commodity flow from origin nodes is assigned to the strip doors, it is consolidated in the entity, and the outbound flow is assigned to the stack ones for being delivered to destination nodes, at a minimum cost. The problem combines three highly computational difficulties, namely, NP-hard combinatorics, uncertainty in the main parameters and their probability distribution. Distributionally robust optimization is considered to deal with these uncertainties. Its related two-stage mixed binary quadratic model is presented for cross-dock problem-solving; the first stage decisions are related to the design of the entity; the second stage ones are related to the assignment of the commodity flow to the doors in a finite set of scenarios for the ambiguity set members. The goal is to minimize the highest total cost in the ambiguity set, subject to the constraint system for each of those members and the stochastic dominance risk averse functional. As far as we know, the challenging problem that results has not been addressed before, although its application field is a very broad one. Given the problem-solving difficulty, a scenario cluster decomposition and a min-max based matheuristic are proposed for obtaining lower and upper bounds, respectively. A computational study validates the proposal; it overperformances the straightforward use of the state-of-the-art solvers Cplex and Gurobi.