# A hybrid Lagrangean metaheuristic for the two-machine cross-docking flow shop scheduling problem

## TL;DR

This paper introduces a hybrid Lagrangean metaheuristic to optimize truck scheduling in cross-docking centers, significantly improving efficiency in minimizing makespan compared to existing methods.

## Contribution

It proposes a novel hybrid Lagrangean metaheuristic approach for the two-machine flow shop scheduling problem with precedence constraints in cross-docking, outperforming current solutions.

## Key findings

- Outperforms existing methods on small and large instances
- Efficiently generates upper and lower bounds within polynomial time
- Reduces makespan in cross-docking truck scheduling

## Abstract

Cross-docking is a logistics strategy that minimizes the storage and picking functions of conventional warehouses. The objective is to unload the cargo from inbound trucks and directly load it into outbound trucks, with little or no storage. The success of the strategy depends on an efficient transshipment operation. This work undertakes a study of truck scheduling in a cross-docking center. The problem is modeled as a two-machine flow shop scheduling problem with precedence constraints, with the objective of minimizing the makespan. The proposed method is based on a Lagrangean relaxation solved by a Volume algorithm over a time-indexed formulation. We use polynomial time heuristics for generating efficient upper and lower bounds in a computationally efficient time, outperforming current results in the literature for small and large size instances.