A location-routing problem for cross-docking networks: A biogeography-based optimization algorithm

- An integrated model for location-routing problem in a distribution network with cross-docking centers is proposed.
- In the distribution network, loads can be transported via direct shipment in addition to cross-docking strategy.
- In cross docking it is possible to have routes between suppliers.
- A metaheuristic algorithm based on Biogeography-based optimization (BBO) is proposed.

This paper considers a location-routing problem in a distribution network with a set of part suppliers, cross-docking centers and assembly plants known as customers. We develop a mixed integer non-linear programming formulation for the problem in which the location for establishing the cross-docks is determined while simultaneously a fleet of vehicles are applied to transport goods from suppliers to the assembly plants via two transportation strategies: direct shipment and shipment through cross-dock (indirect shipment). In the second strategy, it is possible to have routes between suppliers. Not considering two problems of location and distribution planning simultaneously would result in increasing the costs of supplying parts since the transportation strategy has a huge effect on location of cross-docks. In the other words, if some loads can be directly shipped, then this kind of loads should not be taken into account in determining cross-docks location. Thus, a location- routing problem is presented for cross-docking system in this paper. The goal is to determine the location of cross-docks, allocating suppliers to them and routing decisions, so that the location cost and total shipping cost in the network are minimized, considering variable cost of servicing parts passed through cross-docks. The proposed model is NP-hard based on literature. Thus, a metaheuristic algorithm named Biogeography-based optimization (BBO) is utilized to solve the problem. In order to evaluate its efficiency, BBO results are compared with those of PSO, which is a well-known algorithm in the literature. Solving numerical examples for small size problem instances illustrates that the solving approach performs with a negligible gap relative to GAMS, while it performs much better than PSO in most cases in terms of total cost of the network and computational time.

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