# Two-Stage Metaheuristic Algorithms for Order-Batching and Routing Problems
## 6 Conclusions  
In this study, we investigated how warehouses can effectively divide received orders into batches, obtain efficient picking routes for each batch to achieve the shortest total distance, and consequently, reduce costs and enhance competitiveness. In small-scale problems, the exhaustion method may be applied to determine the optimal solution, but as the number of orders increases and the problems become more complex, an algorithm becomes indispensable for efficiently obtaining solutions. The basic limitation of this study is that the same order cannot be divided into different batches, and the capacity of the picking vehicle will be greater than that of any single order; therefore, this study is more applicable to retail items purchased by general consumers, that is, small- and medium-sized online shopping retail warehouses or traditional retail warehouses with a large number of items. Each order contains several items, and the quantity of each item is only one to several pieces. Furthermore, all orders are known in advance and order insertion/removal are not allowed. This means that the algorithm for static problems is considered. This is mainly because most of the picking is a daily routine, and therefore, in the general retail industry, there is rarely a need to adjust the order in time. For this order-batching and picking-route problem, we mainly introduce two-stage SA and VNS algorithms based on a set of neighborhood search algorithms. The concept is clear and easy to understand, and the solution speed is excellent. In addition, for such research, it is easy to extend to various single-solution-based algorithms such as tabu search and iterated local search because the concept of the algorithm is clear. Moreover, with even a little adjustment, it is easy to apply methods to swarm intelligence algorithms. Five initial order-batching methods are proposed; we further tested these solutions under eight scenarios and with three random seeds. The results revealed that the BFD method yielded favorable results under all scenarios. In addition, the chain length and perturbation factors of the solutions were considered. Finally, the SA and VNS algorithms were incorporated into the solution comparisons. The algorithm processes were divided into two stages: The first stage involved batching, and the second stage involved optimizing the route. Under various scenarios, the VNS algorithm returned more favorable solutions  
Figure 6: Error ratio of objective value associated with 40 orders. Figure 7: Error ratio of objective value associated with 80 orders. than did the SA algorithm; moreover, the VNS algorithm demonstrated a faster solving speed. By contrast, the SA algorithm exhibited a slow solving speed in large-scale problems and converged slowly. This study takes the conventional rectangular warehouse layout as an example layout. However, in practical applications, the layouts of almost all warehouses are different. This does not affect the algorithm design of order batching, but only affects the optimal picking distance between any two points in the order-picking-route problem. The distance between any two points can be obtained by calculating the minimum distance between any two points in advance, that is, it does not affect the implementation of the overall algorithm. Therefore, in practical applications, for the retail industry, small- and medium-sized online shopping retail warehouses or traditional retail warehouse can utilize this two-stage algorithm for their daily routine picking jobs. As for the picking of large objects in practice, the picking efficiency can be measured over time by increasing the picking time of some picking points. The objective can be adjusted to the minimal picking time and the concept of the whole two-stage algorithm can still be applied. In further studies, this topic could be divided into three aspects to discuss. First, some restrictions could be loosened in the problem.