# Two-Stage Metaheuristic Algorithms for Order-Batching and Routing Problems
## 2 Literature Review  
In the literature, most studies on warehouse order picking have focused only on picker routing or order batching. Articles that only consider order picking can be classified into certain [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] and uncertain cases [18; 19]. Picker routing can be considered a traditional traveling-salesman problem (TSP). Through the distance between storage spaces, pickers plan how to visit each storage space through the shortest path before returning to the starting point. However, when the number of storage spaces increases, the computation time required to obtain an optimal solution is long [20]. Among the certain cases, many studies have considered the operating environment of AS/RS [4; 5; 10; 11; 12; 13; 14; 17]. Storage systems, capacity, and strategies were introduced in [14; 17]. Zone picking was used as the picking method in [8; 15; 16]. [PERSON] [21] evaluated the returning characteristic in routing policies to ensure that pickers enter an aisle to collect the required items, exit through the path they entered, and then, travel to subsequent aisles in succession. Regarding algorithm design, the genetic algorithm (GA) can be seen in [9; 15]. In the area of order batching, most of the papers are certain cases [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. Uncertain issues can only be seen in [35; 36]. [PERSON] and [PERSON] [25] developed an order-batching algorithm that is based on cluster analysis by considering three outing policies, namely traversal, return, and midpoint routing. Moreover, [PERSON] et al. [37] applied the midpoint method in which pickers enter from one end of an aisle to pick goods, and then, turn to another aisle in succession as each aisle is completed. [PERSON] and [PERSON] [38] resolved the question of how to combine customer orders to shorten the total picking distance. They suggested two metaheuristic algorithms, namely a classic tabu search (TS) algorithm and an attribute-based hill-climbing approach, and both approaches were superior to existing methods. [PERSON] et al. [39] solved batch order processing as a clustering problem. They defined items as attribute vectors and used three similarity measures to develop six cluster classification algorithms. The experimental results proved that merging orders with higher degrees of similarity improved the picking efficiency. The heterogeneous pick devices [34] and multiple pickers [36] were extended to the batching problem. Regarding the algorithm design, GA [28; 31; 33] and VNS [29; 34; 36] were widely introduced. Among the integration issues considered together with order picking and order batching, we can see that most of them are certain issues [3; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50] and uncertain issues can be found in [51; 52]. The concept of storage systems, capacity, and strategy was introduced in [45; 51]. [PERSON] and [PERSON] [52] used AS/RS as the operating environment. Regarding the algorithm design, [PERSON] and [PERSON] [40] solved the order-batching and picking-sequence problem by using hybrid heuristic algorithms. The first heuristic determines order batching, and the second heuristic identifies the picking sequence. [PERSON] et al. al. [3] and [PERSON] [44] used TS to deal with the problem of order batching, while on the issue of picking, [PERSON] et al. [3] adopted a 2-opt method, and [PERSON] [44] proposed a picking strategy. [PERSON] et al. [53] employed a two-stage GA to solve an order-batching and picking-sequence problem. The objective was to minimize the total traveling time. The first stage of the GA involved determining the order batches, and the second stage entailed determining the shortest picking paths for these batches. [PERSON] et al. [48] considered a picking route based on the Manhattan distance and used particle swarm optimization (PSO) to solve the joint order-batching and picking-route problem. [PERSON] et al. [47] used PSO to deal with order batching and used ACO to find the most efficient route for each batch.