The allocation issues of the location of the cargo have affected the operational efficiency of retail e-commerce warehouses tremendously. Adjusting the cargo location with the change of the order and the operation of the warehouse is a significant research area. A novel approach employing the FP-Tree and the Artificial Fish Swarm Algorithms is proposed. Firstly, energy consumption and shelf stability are employed for the location-allocation. Secondly, the association rules among product items are obtained by the FP-Tree Algorithm to mine frequent list of items. Furthermore, the frequency and the weight of product items are taken into account to ensure the local stability of the shelf during data mining. Thirdly, another method of the location-allocation is obtained with the objectives of the energy consumption and the overall shelf stability along with the frequent items stored nearby that is conducted by the Artificial Fish Swarm Algorithm. Finally, the picking order distance is obtained through two methods of the location-allocation above. The performance and efficiency of the novel introduced method have been confirmed by running the experiment. The outcomes of the simulation suggest that the introduced method has a higher performance concerning criterion called the picking order distance.
Based on the newly introduced retail model, buyers have much higher demands for the timely manner of the distribution of online shopping based on the widespread use of it. The directors at the e-commerce warehouse deal with finding the better economical means that try to minimize the costs that are composed of some components, which are called the energy consumption, the distance, and/or time. One of the subsystems of the logistics system, called the sorting, has a key functionality in picking the orders satisfying the expectations of accuracy and being in timely manner. It has been reported that the time of picking the order has accounted for nearly 50% on the average [
The allocation issue of the cargo location has received higher attention concerning some criteria such as the turnover efficiency of the cargo, the shelf stability, the picking routes, and the storage strategy of the warehouse. Xie et al. [
Besides, many types of research employing distinct algorithms in this discipline have been utilized to reduce logistics cost and to increase the efficacy of order picking. Homsi et al. [
A rule mining has been successfully implemented on several problems in business and engineering such as agriculture, medicine, and computer network. However, a relatively small amount of research on picking a route and the order distance based on data mining can be found in the literature. Zhou et al. [
Several researchers primarily studied the assignment of the cargo location using the turnover efficiency of the cargo, the shelf stability, and the strategy of the warehouse storage to minimize the total distance. The manuscript has suggested implementing the data mining method to the space issue of the warehouse. Hence, the contributions of it can be articulated as follows: A new approach employing both the FP-Tree Algorithm and the Artificial Fish Swarm Algorithm was proposed whose objective is to find the best location of cargo in a shelf represented in three dimensions. Association rule between product items was obtained by the FP-Tree Algorithm to minimize the picking order distance. Specifically, the weight difference of items was taken into account to ensure the local stability of the shelf during data mining.
Then, the manuscript is organized as follows. Section
Suppose that a retail e-commerce warehouse using a shelf represented in a space composed of three dimensions is depicted in Figure
The stereogram of a shelf.
Hence, a multiobjective model to improve shelf stability and to minimize both energy consumption and the distance of frequent items due to warehouse operation is constructed, which aims at choosing an optimal method for allocation of cargo location to minimize the distance of order picking when the local stability of the shelf is satisfied.
To simplify the model, the following assumptions are assumed: Only one cargo location exists and each item is stored in one cargo location. Full boxes are used to store items. The front row is the inbound and outbound points. The zero (0) floor and column of the shelf are located at the bottom left corner in the warehouse zone. Each cargo location is the same. The volume of each product item cannot outnumber the storage capacity. One transaction order corresponds to the product items bought during the visit to the one store. All order data are acknowledged earlier. All items are placed into the system.
The variables of the model are as follows.
The notations of
The optimization of the cargo location is a readjustment process of the cargo location to lower the energy consumption and the labor cost for items and the warehouse, respectively. The model for energy consumption expands the general formulation of the cargo location-allocation issues by adding
The consumption of the energy used for a unit mass of an item from the location to the input/output point is as follows:
By optimizing the cargo location, it is essential to ensure the stability of the shelves by storing items with a large span of the weight reasonably. In other words, the distance from the center of the gravity point of the shelves to the ground in the
The optimization of the cargo location means that items are reasonably distributed to the corresponding cargo locations. By doing so, it improves the efficiency of the cargo delivery by reducing the picking distance of the test order.
The strategy of the association storage becomes an essential way to improve the operational efficiency of warehousing and customer satisfaction. The relationships between product items from customer orders can be extracted by employing the association rule mining. The product items with higher support have higher relations. Hence, with higher support they are potentially required to be stored nearby, decreasing the distance and reducing the error probability of the picking process. Higher efficacy can be achieved by employing storing frequent items nearby.
Besides, it needs to be ensured that weight difference of frequent items is less than the minimum weight of the two items:
To deal with all at the same time, this manuscript constructs an evaluation function by using the ideal point method that allows the different targets to be employed. The transformation of the target functions is defined by
Besides,
In 2000, the proposed FP-Tree Algorithm was called a classic association mining method that was an effective tool to mine the frequent list of items employing an extended prefix-tree structure that helps store the important information about patterns observed frequently titled the frequent-pattern tree (FP-Tree) [
Employing the divide-and-conquer mechanism is the key step of the implementation of the FP-Tree composed of three stages. The first stage is the construction of an FP tree using two gradients that are called the entries and the F-Table. The second stage performs the mining recursively on the FP-Tree and generates a frequent list of items. The third stage filters the frequent list of items meeting a given condition. Searching and constructing trees determine the frequent keywords recursively.
The fundamentals of the FP-Tree are as follows: The input is the database of transaction and the mini-support The output is the frequent pattern set How to run the FP-Tree method is summarized as follows: Step 1: to construct the FP-Tree composed of the following: (1) define the FP-Tree consisting of a root node, the item prefix son tree of the item, and its header table; (2) each node of the item prefix son tree consists of its name, its node count, and its node chain where the node count refers to the nodes numbers and node chain points to the next node with the same item name in the tree; (3) every entry of the item head table includes its name, node chain, and the header pointing to the first node in the tree Step 2: to mine the FP-Tree that gets the 1-length frequent pattern, to generate its conditional pattern base (a subdatabase), and then to establish its conditional FP-Tree and recursively mine the tree; employing the suffix mode and the frequent pattern from the conditional FP-Tree, a connection could be achieved for pattern growth Step 3: to judge the condition and to discover the frequent 2-itemset satisfying the conditions of the local stability
Artificial Fish Swarm Algorithm (AFSA) is an effective method to resolve optimization problems employed for facility location-allocation, traveling salesman problem, and sorting of activities [ Step 1: to set Step 2: to initialize Fish Swarm utilizing Step 3: to calculate the fitness value for each initial Fish Swarm called Step 4: to record the optimal initial Artificial Fish information. Step 5: to use preying, swarming, following, and random behavior. Step 6: to update the Artificial Fish optimal fitness, Step 7: to update global optimal Artificial Fish called Step 8: to determine whether the termination condition for the condition is met. Then, stop. Otherwise, return to the fifth step.
In this subsection, we expect to obtain the features of the items of the data including the weights, the amount of goods, and the original locations of each type of goods in the warehouse. Moreover, the warehouse attributes are necessary including the dimensions, the layout, and the distance between the adjacent shelf passages. Lastly, the AFSA is set as follows.
The initial information of the items in the warehouse is shown in Table
Data of the items.
The number of items | The frequency of items | The weight of items (kg) | The original coordinates of items |
---|---|---|---|
1 | 1 | 2.8 | (3,6,4) |
2 | 8 | 8.6 | (5,6,6) |
3 | 6 | 4.91 | (1,5,1) |
4 | 2 | 3.52 | (1,6,1) |
5 | 5 | 2.81 | (2,6,1) |
6 | 5 | 3.16 | (6,2,1) |
7 | 1 | 4.25 | (1,5,2) |
8 | 5 | 5.13 | (3,5,2) |
9 | 10 | 1.3 | (3,1,4) |
10 | 8 | 2.16 | (2,4,1) |
11 | 1 | 2.5 | (2,4,2) |
12 | 4 | 5 | (1,3,5) |
13 | 8 | 2.48 | (5,6,1) |
14 | 3 | 8.65 | (1,2,2) |
15 | 9 | 1.62 | (3,4,4) |
16 | 9 | 3.45 | (6,6,2) |
17 | 9 | 2.45 | (1,1,5) |
18 | 5 | 2.31 | (4,1,6) |
19 | 1 | 1.98 | (3,1,6) |
20 | 4 | 2.23 | (2,3,1) |
21 | 6 | 5.06 | (5,2,2) |
22 | 9 | 2.96 | (4,1,1) |
23 | 8 | 4.48 | (4,3,2) |
24 | 2 | 1.12 | (3,3,3) |
25 | 6 | 6.54 | (3,5,2) |
26 | 6 | 3.79 | (1,6,5) |
27 | 5 | 5.04 | (4,3,6) |
28 | 3 | 4.7 | (5,5,4) |
29 | 4 | 12.57 | (5,3,5) |
30 | 2 | 3.1 | (1,6,6) |
31 | 5 | 6.97 | (5,6,5) |
32 | 3 | 2.5 | (4,6,3) |
33 | 2 | 10.41 | (1,2,6) |
34 | 4 | 8.12 | (6,1,3) |
35 | 6 | 6.28 | (2,4,4) |
36 | 4 | 6.31 | (4,3,3) |
37 | 9 | 8.85 | (4,4,2) |
38 | 4 | 4.27 | (4,5,4) |
39 | 5 | 4.62 | (5,5,4) |
40 | 4 | 8.19 | (4,6,3) |
41 | 2 | 3.51 | (6,6,5) |
42 | 11 | 4.74 | (1,2,4) |
43 | 4 | 5.77 | (6,6,1) |
44 | 3 | 8.13 | (1,3,2) |
45 | 5 | 7.83 | (4,4,6) |
46 | 1 | 4.38 | (3,5,5) |
47 | 4 | 8.92 | (6,1,2) |
48 | 2 | 3.51 | (1,2,5) |
49 | 5 | 9.16 | (5,6,5) |
50 | 1 | 10.53 | (5,4,2) |
The parameters called the population size
Two concepts can be stated for the convenience as follows: many orders are randomly selected from the data of the order of a certain month of the warehouse using the “rand” function to take the samples for data mining, which are called sample orders. Additionally, many orders are randomly selected from the order data of the warehouse in the next month to test the picking distance of ways of cargo location-allocation, which are called test orders.
An illustrative example shown in a python program presents an order database including 60 orders of 50 different items. To obtain the frequencies of items and frequent list of items of the 50 items, we conducted several experiments of data mining for 60 sample orders. Firstly, the information including the data of 60 sample orders and the weight of 50 items are imported into the FP-Tree Algorithm program. Secondly, the “FOR” loop statement is used to accumulate the number of items in the sample order. Hence, the number of items is obtained as the corresponding frequencies of items in and out of the storage. The threshold value (
It is a fact that the parameter values have a great impact on the performance of the algorithm, which is a principal challenge for the algorithm affected by the design details. Hence, adjusting parameters for AFSA needs to be done. Two performance measures for parameters are employed, which are called the total objective optimized value and the algorithm convergence rate in general. The total target value refers to the weighted optimal value of objective 1 and objective 2 in the comparative experiment. The parameters of the AFSA are called Fish Swarm size
Adjustment of the parameter
Adjustment of the parameter
Adjustment of the parameter
Adjustment of the parameter det
The Fish Swarm size
The maximum heuristic times denoted by
Similarly, Figures
In this subsection, the simulation experiment first obtains a new allocation way for the optimization targets of energy consumption and the overall shelf stability. Afterward, the present optimization targets extend the general targets by adding the association rules mining, which obtains another allocation way. The performances of these two approaches of the cargo location-allocation are primarily compared based on the travel distance of test orders. Lastly, a statistical test was employed to verify the outcomes of the analysis and the validity of the model and the method in this manuscript.
The fitness function of AFSA is constructed by the distance between the optimal value and the actual point. The optimal values of the Target 1 and Target 2 are calculated by using AFSA and the results are 80527 and 1.1095, respectively.
Comparing two methods provides some useful insights. Firstly, optimal results are attained not utilizing the association rules in the experiment after adjusting the parameters. On the other hand, the parameters of the experiment employing association rules are consistent with those of the first experiment. Secondly, the average value of 20 runs of the experiment was selected as the final optimization value of the two methods.
When just taking into account both Target 1 and Target 2 in the above model, the results of the experimentation are obtained by AFSA shown in both Figures
(a) The optimized cargo position stereogram. (b) Algorithm comparison iteration diagram.
The final results show that the value of Target 1 is optimized from the initial value 202258.5205 to an optimized value 91807.0375, which decreased by 54.6091%. The value of Target 2 is optimized from 4.7211 to 1.5894, which decreased by 66.3341%. The new method of cargo location-allocation is obtained shown in Table
Data of items.
The number of items | Without considering association rules | Considering association rules |
---|---|---|
1 | (4,6,1) | (3,6,1) |
2 | (2,3,1) | (2,4,1) |
3 | (1,3,2) | (2,3,2) |
4 | (4,4,1) | (3,4,1) |
5 | (1,3,3) | (2,2,3) |
6 | (2,2,3) | (2,3,3) |
7 | (3,5,1) | (4,5,1) |
8 | (1,4,2) | (2,4,2) |
9 | (2,1,2) | (2,1,2) |
10 | (2,1,3) | (2,2,2) |
11 | (4,1,2) | (3,1,2) |
12 | (2,6,2) | (2,6,2) |
13 | (1,2,2) | (1,1,3) |
14 | (4,3,1) | (3,3,1) |
15 | (1,1,3) | (1,2,2) |
16 | (1,1,1) | (1,2,1) |
17 | (1,1,2) | (1,1,2) |
18 | (1,2,3) | (1,2,3) |
19 | (2,6,3) | (4,1,2) |
20 | (2,3,3) | (1,4,3) |
21 | (2,2,2) | (2,5,1) |
22 | (2,2,1) | (2,1,1) |
23 | (1,3,1) | (1,3,1) |
24 | (2,1,4) | (1,1,4) |
25 | (2,4,1) | (1,4,1) |
26 | (2,3,2) | (2,1,3) |
27 | (2,4,2) | (1,4,2) |
28 | (4,2,1) | (4,2,1) |
29 | (1,6,1) | (3,1,1) |
30 | (2,5,3) | (1,5,3) |
31 | (1,5,1) | (1,3,2) |
32 | (2,4,3) | (2,4,3) |
33 | (3,4,1) | (4,4,1) |
34 | (3,1,1) | (4,1,1) |
35 | (1,4,1) | (2,3,1) |
36 | (1,6,2) | (2,5,2) |
37 | (1,2,1) | (2,2,1) |
38 | (1,4,3) | (1,3,3) |
39 | (2,5,2) | (1,5,2) |
40 | (3,2,1) | (3,2,1) |
41 | (1,6,3) | (2,5,3) |
42 | (2,1,1) | (1,1,1) |
43 | (1,5,2) | (1,6,2) |
44 | (3,3,1) | (4,3,1) |
45 | (2,6,1) | (1,6,1) |
46 | (3,6,1) | (4,6,1) |
47 | (4,1,1) | (2,6,1) |
48 | (1,5,3) | (2,6,3) |
49 | (2,5,1) | (1,5,1) |
50 | (4,5,1) | (3,5,1) |
Based on the above experiments, the optimization targets extend the above targets by adding frequent items stored nearby in this experiment. When taking into account both Target 1 and Target 2 and the frequent items stored nearby in Target 3, the results of the experimentations also are obtained by AFSA shown in Figures
(a) The optimized cargo position stereogram. (b) The algorithm of the comparison iteration diagram.
The final results show that the value of Target 1 is optimized from the initial value 202258.5205 to optimized value 90787.6995 decreased by 55.1130%. The value of Target 2 is optimized from 4.7211 to 1.5870 decreased by 66.3855%. The new way of the cargo location-allocation is obtained as shown in Table
The outputs of the simulation experiments compared are shown in Table
Data of the items.
Target functions | Initial value | Not taking into account the association rules | Not taking into account the association rules (%) | Taking into account the association rules | Taking into account the association rules (%) |
---|---|---|---|---|---|
Target 1 | 202258.5205 | 91807.0375 | 54.6091 | 90787.6995 | 55.1130 |
Target 2 | 4.7211 | 1.5894 | 66.3341 | 1.587 | 66.3855 |
Picking distance | 900 | 840 | 6.6667 | 615 | 31.6667 |
We first started with assigning the weights of the algorithms in contrast experiment
The usability of the proposed association rules mining is demonstrated for the optimization of the cargo location. Hence, we conduct experiments employing 30, 70, 90, 130, and 170 items apart from 50 items, respectively. Tables
The initial and the optimal values of each single target.
Number of items | Initial value | Single target optimal value | |||
---|---|---|---|---|---|
Target 1 | Target 2 | Picking distance | Target 1 | Target 2 | |
30 | 110542.2357 | 3.7606 | 885 | 39872 | 0.8 |
50 | 202258.5205 | 4.7211 | 900 | 80527 | 1.1095 |
70 | 273865.2278 | 5.0688 | 1330 | 125190 | 1.2611 |
90 | 434942.3138 | 5.1419 | 2130 | 243120 | 1.5762 |
130 | 571449.73 | 4.7087 | 2520 | 307960 | 2.1645 |
170 | 744384.8193 | 4.724 | 3028 | 446680 | 2.7609 |
The optimization values for each single target.
Number of items | Without taking into account the association rules | Taking into account the association rules | ||||
---|---|---|---|---|---|---|
Target 1 | Target 2 | Picking distance | Target 1 | Target 2 | Picking distance | |
30 | 51229.2478 | 0.83231 | 399 | 51398.2718 | 0.83231 | 312 |
50 | 91807.0375 | 1.5894 | 840 | 90787.6995 | 1.587 | 615 |
70 | 143181.8787 | 1.5527 | 910 | 143736.6967 | 1.6078 | 647 |
90 | 277383.6008 | 1.9022 | 1890 | 284470.6593 | 1.8598 | 1410 |
130 | 343235.2265 | 2.1906 | 2347 | 365492.8285 | 2.2367 | 1851 |
170 | 471758.8858 | 2.917 | 2806 | 480056.4822 | 3.0596 | 2648 |
The optimization percentage for each target.
Number of items | Without taking into account the association rules | Taking into account the association rules | ||||
---|---|---|---|---|---|---|
Target 1 (%) | Target 2 (%) | Picking distance | Target 1 (%) | Target 2 (%) | Picking distance | |
30 | 53.66 | 77.87 | 54.92 | 53.50 | 77.87 | 64.75 |
50 | 54.61 | 66.33 | 6.67 | 55.11 | 66.39 | 31.67 |
70 | 47.72 | 69.37 | 31.58 | 47.52 | 68.28 | 51.35 |
90 | 36.23 | 63.01 | 11.27 | 34.60 | 63.83 | 33.80 |
130 | 39.94 | 53.48 | 6.87 | 36.04 | 52.50 | 26.55 |
170 | 36.62 | 38.25 | 7.33 | 35.51 | 35.23 | 12.55 |
The difference between the two optimized values.
Number of items | Target 1 (%) | Target 2 (%) | Picking distance (%) |
---|---|---|---|
30 | −0.16 | 0.00 | 9.83 |
50 | 0.50 | 0.06 | 25.00 |
70 | −0.20 | −1.09 | 19.77 |
90 | −1.64 | 0.82 | 22.53 |
130 | −3.90 | −0.98 | 19.68 |
170 | −1.11 | −3.02 | 5.22 |
The optimized values of the single target corresponding to the different number of the items can be attained with the experiment either utilizing the association rules and or not utilizing the ones shown in Table
Then, several simulation experiments were conducted to assess the performance of the FP-Tree. The target values presented in both Tables
Finally, the optimized percentages of Target 1 and Target 2 and test order distance in the simulation experiment not utilizing the association rules in Table
Finally, the comparison results are presented in curves. The results of the experiments by taking into account the association rules lead to a considerable improvement compared to not taking into account the association rules. According to the comparison curves of Target 1 shown in Figure
The comparison results of the Target function 1.
The comparison results of the Target function 2.
The comparison results of the picking distance.
To judge whether the conclusion provided above is reliable or not, the statistical test, called the paired sample mean test, is conducted to determine whether there is a significant difference between the optimization effects of the association rules and experiments not utilizing association rules. The optimization effects of experiments deal with the energy consumption, the shelf stability, and the distance of the order picking. Hence, the objective is to decide whether the optimization effects of energy consumption, the shelf stability, and the distance of the order picking behave the same as the ones whose optimized effect is in the experiments not utilizing association rules. The optimized percentage of each target employs 30, 50, 70, 90, 130, and 170 products, respectively, and conditions of the two experiments are presented in Table The optimized outcomes of the energy consumption are tested after two experiments are conducted. The null hypothesis and alternative hypothesis are represented as follows: The The following result is attained by looking up the The comparison The optimized results of shelf stability after running a statistical test using the data in Table The comparison Similarly, the optimized results of shelf stability after running statistical test employing the data in Table
The comparison
It can be said that the optimization results of the distance of order picking are better in the experiments utilizing association rule. The optimization outcomes of the energy consumption and shelf stability are the same as the former when compared with the experiments not utilizing association rules.
In this manuscript, an approach based on the proposed FP-Tree Algorithm and AFSA can obtain a much better allocation way of cargo location to significantly reduce the picking order distance. The FP-Tree Algorithm, called a data mining technique, is employed to determine the relation rules implying demand structure extracted directly from the customer data. Besides, the frequent list of items generated by the FP-Tree Algorithm not only corresponds to some requirements of minimum support but also provides the local stability of the shelf. The results suggest that taking into account the association rules significantly decreases the total travel distance without increasing energy consumption and decreasing the shelf stability. The efficacy of the proposed method is confirmed by the experiment employing different quantities of items extracted from an e-commerce warehouse. Therefore, employing the FP-Tree Algorithm and AFSA looks more effective in finding the solution to the issue of cargo location-allocation than does the AFSA. The proposed method is a novel approach to deal with this kind of problem. Furthermore, it can be easily applied to retail e-commerce and has a larger potential value for the applications of the logistics industry.
The proposed method has some limitations: only the binomial frequent list of items is attained to conduct the research when extracting association rules. The problem of cargo location-allocation could become more complicated if the larger frequent list of items stored nearby is also considered. Therefore, the suggested method is more suitable for small retail enterprises having less number of product categories. Besides, test orders are drawn from a known dataset. However, unpredictability is a widely encountered situation when dealing with actual orders, which has a great effect on the distance of order picking. It would be more practical to combine the optimization of order position with the actual strategy of order picking. Future work will focus on dealing with these issues.
The data used to support the findings of this study are included within the article.
The authors declare no conflicts of interest.
This research was funded by Anhui province “excellent six, a top” outstanding talent cultivating innovation project (grant number SK2018A0064); Anhui University of Technology quality project (grant number 20184900004); and Anhui University of Technology education teaching research project (grant number 2018jy19).