*Article* **Vehicle Routing Optimization with Cross-Docking Based on an Artificial Immune System in Logistics Management**

**Shih-Che Lo \* and Ying-Lin Chuang**

Department of Industrial Management, National Taiwan University of Science and Technology, Taipei City 106335, Taiwan

**\*** Correspondence: sclo@mail.ntust.edu.tw; Tel.: +886-2-2737-6351

**Abstract:** Background: Manufacturing companies optimize logistics network routing to reduce transportation costs and operational costs in order to make profits in an extremely competitive environment. Therefore, the efficiency of logistics management in the supply chain and the quick response to customers' demands are treated as an additional source of profit. One of the warehouse operations for intelligent logistics network design, called cross-docking (CD) operations, is used to reduce inventory levels and improve responsiveness to meet customers' requirements. Accordingly, the optimization of a vehicle dispatch schedule is imperative in order to produce a routing plan with the minimum transport cost while meeting demand allocation. Methods: This paper developed a two-phase algorithm, called sAIS, to solve the vehicle routing problem (VRP) with the CD facilities and systems in the logistics operations. The sAIS algorithm is based on a clustering-first and routinglater approach. The sweep method is used to cluster trucks as the initial solution for the second phase: optimizing routing by the Artificial Immune System. Results: In order to examine the performance of the proposed sAIS approach, we compared the proposed model with the Genetic Algorithm (GA) on the VRP with pickup and delivery benchmark problems, showing average improvements of 7.26%. Conclusions: In this study, we proposed a novel sAIS algorithm for solving VRP with CD problems by simulating human body immune reactions. The experimental results showed that the proposed sAIS algorithm is robustly competitive with the GA on the criterion of average solution quality as measured by the two-sample t-test.

**Keywords:** logistics management; artificial immune systems; vehicle routing problem; cross-docking

**MSC:** 68W01; 90B06; 97R40
