According to the above results and Figure 10, the following results can be obtained with the Chevron layout: (1) Compared with the Return-type picking path strategy, the Mixed-type path strategy has better results. Compared with the S-type picking path strategy, the resulting advantage of the Mixed-type path strategy gradually decreases with the increase of the number of locations to be picked in the order.

2.4. Mixed-Type Picking Path Model

2.3. S-Type Picking Path Model

2.2. Return-Type Picking Path Model

its goal is to minimize the total walking distance of the picking operation.

D=min(d01x01+∑i=1n∑j=1ndijxij+dn0xn0),

Pansart et al. [7] and Hong et al. [11] respectively proposed the application of mixed integer programming to optimize order batching to realize the optimization of order picking path. Dijkstra et al. [12] and Liu et al. [13] comprehensively considered the impact of location allocation on picking paths. Lu et al. [14] studied the warehouse picking strategy based on the dynamic picking path optimization algorithm. Through simulation, it was found that the algorithm is better than the static and heuristic picking path optimization algorithm under certain conditions. Bódis et al. [15] used Bacterial Memory algorithm and Simulated Annealing algorithm to solve the order picking problem in the unit picking warehouse. The simulation results show that the former has a more obvious optimization effect on the picking walking path problem than the latter. Zhou et al. [16] applied the intelligent algorithm to the picking path optimization of Fishbone layout, and simulated the model through data mining. Masae et al. [17] proposed four heuristic paths based on Euclidean distance and dynamic programming process under Leaf warehouse layout.Žulj et al. [18] proposed a picking path strategy combined with priority constraints based on practical cases and analyzed the sensitivity of the parameters to propose the best priority constraints. Scholz et al. [19] proposed a variable neighborhood descent algorithm for various neighborhood structures of batch processing and sorting problems. Moons et al. [20] used a single optimization framework to solve the order picking problem and the vehicle routing problem with a time window and release date at the same time. Pferschy et al. [21], from the perspective of commodity similarity in orders, through the example verification under four different order scale scenarios, found that the average walking distance of picking in batches is saved by 34.7% compared to that in no-batches. Weidinger et al. [22] increased the distribution range of goods in the warehouse, thus shortening the walking distance of the picking operation. Liu et al. [23] aimed at the path optimization problem in the traditional two zone warehouse, and found that the Ant Colony algorithm can effectively reduce the walking distance and time. Based on the Fishbone layout, they proposed a multi-population genetic algorithm with an evolutionary reversal operator and proved the superiority of the algorithm results by comparing them with other traditional algorithms [24]. Giannikas et al. [25] proposed an intervention picking strategy considering new orders and operation interruption to improve the response-ability of the picking system. Moons et al. [26] proposed a memory travel algorithm to solve the comprehensive picking vehicle routing problem. Liu et al. [27] studied the order picking path optimization problem based on Flying-V layout, and found that the use of Ant Colony algorithm can greatly reduce the picking time and improve the picking efficiency. Öztürkoğlu [28] proposed a double objective mathematical model which can better shorten the picking walking distance than other models. Chae et al. [29] proposed a double row layout model and compared the existing literature with the proposed model. The results show that the new model has better performance and a shorter picking time. Masae et al. [30] proposed an optimal order picker routing strategy for conventional warehouses with double partitions and arbitrary starting and ending points. Masae et al. [31] and Çelik et al. [32] proposed the best order picking strategy by using dynamic programming and the heuristic algorithm respectively based on the concept of graph theory. Alipour et al. [33] proposed a new heuristic algorithm for multi-picking vehicles to solve the online order batch processing problem. Shavaki et al. [34] comprehensively considered the constraints such as warehouse storage, online order batching, robot scheduling, and route selection, and proposed a rule-based heuristic path algorithm.

the Chevron warehouse layout

Order picking is the part with the highest proportion of operation cost and time in the warehouse.

Our research has two differences with real systems. First, our analytic model is based on Whitt approximations, which will lead to relative errors. Second, we have not considered battery management in the RMFS. Future research might evaluate battery charging and swapping strategies in the RMFS.

Verification of Analytic Results Via Simulation

Numerical Experiments

congestion near picker workstations can be serious, since the space in front of each picker station is limited.

barcode stickers on the warehouse floor

f(x)={1W,0,0≤x≤W

served by one order picker

The RMFS can reduce order fulfillment time in warehouses, allowing them to meet customer expectations for speedy delivery.

One of the research topics relevant to the RMFS is routing design [30], and the objective of routing research is to minimize the throughput time of a warehouse.