Time-indexed formulation and polynomial time heuristic for a multi-dock truck scheduling problem in a cross-docking centre

•This work deals with truck scheduling in a cross-docking facility.•A time-indexed formulation is proposed and compared against previous models.•A polynomial time heuristic is proposed and extensively tested.•The heuristic outperformed current results in the literature.

Cross-docking is a logistic solution bringing significant cost reductions and simplifying operations of distribution centres. The success of this strategy relies on an efficient transhipment operation. This article undertakes a study of truck scheduling in a cross-docking facility. The problem is formulated as a two-stage hybrid flow-shop problem, subject to cross-docking constraints with the objective of minimising the makespan. We propose a time-indexed mixed integer linear programming formulation and a polynomial time heuristic. Results show that the heuristic outperformed current results in the literature for moderate and large size instances.