A double-layer optimization method for warehouse picking operation considering dynamic order constraints

Abstract

This invention discloses a two-layer optimization method for warehouse picking operations considering dynamic order constraints, belonging to the field of logistics and warehousing. The optimization method includes the following steps: Step 1: Digitalization of warehouse layout; Step 2: Establishing an order batch optimization model with the minimum number of picking aisles and the highest level of service counter fairness as the upper-level optimization objectives; Step 3: Establishing an employee picking operation optimization model with the shortest total picking time as the lower-level optimization objective; The next step is to optimize the models in Steps 2 and 3. Addressing the operational requirements of a logistics company, this invention studies the order allocation and picking path problems, constructing a two-layer optimization model with the minimum total number of shelves and the maximum service counter fairness as the upper-level optimization objectives, and the shortest total picking time as the lower-level optimization objective. It comprehensively considers practical operational constraints, including warehouse physical layout, personnel and auxiliary tool capabilities, etc. Compared with traditional models, the model constructed in this paper has stronger practicality.

Description

Technical Field

[0001] This invention belongs to the field of logistics and warehousing, and more specifically relates to a two-layer optimization method for warehouse picking operations that takes into account dynamic order constraints. Background Technology

[0002] In the warehousing operation problem, a large number of studies have been conducted on the joint research of order allocation and picking route optimization [3-4]. Among them, Sun Junyan et al. established a joint optimization model based on nested genetic algorithm. By continuously optimizing the order batching results in the outer layer and continuously optimizing the picking route in the inner layer, the picking efficiency was effectively improved, providing a valid basis for solving the difficult problems in warehousing operations [5]. Chen-Yang Cheng et al. designed a hybrid algorithm to solve the problem of joint batch picking and picking route [6]. In addition, some scholars have studied the impact of warehouse layout on picking time. Among them, Liu Jiansheng et al. studied the picking problem under the Flying-V type warehouse layout and designed an order allocation and path optimization model for the characteristics of warehouse layout. They further used the ant colony algorithm to solve the model. The simulation comparison results showed that the model has strong practicality [7]. Reference [8] established an optimization model for the shortest picking time for the layout characteristics of dual-zone warehouses and designed a dynamic picking strategy of dynamic goods adjustment and manual picking collaborative operation. They designed a hybrid genetic algorithm to solve the model. The simulation results showed that the strategy can significantly improve picking efficiency when there are large-scale orders. However, it did not consider the impact of the physical limitations of picking auxiliary tools on picking operations. Sun Hui et al. introduced actual constraints such as picking cart capacity constraints into the picking optimization model and verified through simulation results that the designed model has strong practical application value [9]. The above studies have all achieved certain results, but they have not involved warehouse modes such as multi-service desks. Therefore, this paper constructs an order allocation and picking route optimization model involving multiple service desks based on the warehouse layout of a certain enterprise, and attempts to solve the corresponding problems. Summary of the Invention

[0003] This paper focuses on the warehouse layout characteristics of a logistics company, comprehensively considering actual constraints such as warehouse physical limitations, picking personnel and auxiliary tool capabilities, and then constructs a two-layer optimization model involving multiple types of goods, multiple orders and multiple service stations, including order allocation and picking route optimization. By comparing the optimization results of GA, MOV, WOA, CSV and improved CSV, the improved swarm intelligence algorithm is selected for order batch optimization and picking operation route optimization.

[0004] To achieve the above objectives, the present invention employs the following technical solution: the optimization method includes the following steps, step one: digitizing warehouse layout;

[0005] Step 2: Finally, establish an order batch optimization model with the goal of minimizing picking aisles and ensuring fairness at the highest service counter.

[0006] Step 3: An employee picking operation optimization model was established with the shortest total picking time as the lower-level optimization objective.

[0007] Step 4: Optimize the models from Steps 2 and 3.

[0008] Preferably, step one: digitizing the warehouse layout; the location of each storage location is determined by the number of aisles, the number of storage locations within that aisle, the left and right sides of the aisle, and the depth of the storage location (r i ,s i ,p i ,l i ,d i ), where r i s is the number of aisles where storage location i is located; i p is the distance from the entrance to the aisle where storage location i is located; i The location i is located on the left or right side of the aisle; i d represents the number of storage levels; i The depth of storage location i;

[0009]

[0010] The distance between any two storage locations in a rectangular warehouse layout is represented as follows:

[0011]

[0012] The distance from any service counter to any storage location is:

[0013]

[0014] Where O∈{o1,o2,...,O} represents an order; B∈{b1,b2,...,B} represents a batch; M∈{m1,m2,...,M} represents a type of goods; and C... o Total order capacity, o m The order includes the types of goods. The required capacity of the goods in the order, W r The width of the alley, W c The width of the storage space, D c The depth of the storage location, H c The height of the storage location, D R Service desk number, V p Picker movement speed, V d Elevator speed, T b Packaging time.

[0015] Preferably, in step two: the final order batch optimization model is established with the optimization objectives of minimizing picking aisles and ensuring fairness at the highest service counter. The optimization model is shown below:

[0016]

[0017]

[0018]

[0019] in,

[0020]

[0021]

[0022]

[0023]

[0024] Formula (4) represents the number of picking aisles required; Formula (5) represents the fairness of the service counters within the warehouse; Formula (6) is the objective function for the upper-level optimization, where λ1 and λ2 represent weights, satisfying λ1 + λ2 = 1; Formula (7) represents the number of service counter batches; Formula (8) is a 0-1 variable, where Y... i b When = 1, it means that batch b needs shelf i, otherwise; formula (9) is a 0-1 variable, when When, it means that order o belongs to batch b, otherwise; formula (10) is a 0-1 variable, when When, it means that batch b has been assigned to the Service Desk DR, and vice versa;

[0025] Constraints:

[0026]

[0027]

[0028]

[0029]

[0030] Constraint (11) indicates that each batch is handled by one service desk; constraint (12) indicates that each order can only be assigned to one batch; constraint (13) indicates that the shelf can meet the item requirements of the order in that batch; constraint (14) indicates that it does not exceed the maximum supply capacity of the warehouse.

[0031] Preferably, in step three, an employee picking operation optimization model with the shortest total picking time as the lower-level optimization objective is established. The total picking operation time consists of three parts: employee walking time, working time of the lifting tool, and goods counting and settlement time. The formula for calculating the walking time of the picking operation personnel is shown in formula (15), and the formula for calculating the working time of the lifting tool during the picking operation is shown in formula (16).

[0032]

[0033]

[0034] In summary, the objective function of the lower-level employee picking operation optimization model is shown in formula (17):

[0035]

[0036] in,

[0037]

[0038]

[0039]

[0040] Formula (18) is a 0-1 variable, when When, it means that the picker completes picking at location i in a batch b and then goes to pick at location j, and vice versa; formula (19) is a 0-1 variable, when When, it means that the picking staff is responsible for order o in batch b, and vice versa; formula (20) is a 0-1 variable, when When, it indicates that the picking staff starts from the service desk (DR), and vice versa; T b For packaging time,

[0041] Constraints:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] WT+LT+T b ≤T pmax (26)

[0048]

[0049] Constraint (21) indicates that the picking operation does not exceed the maximum number of people; constraint (22) indicates that each person is responsible for one batch; constraints (23) and (24) indicate that the shelf can only be picked once in a batch; constraint (25) indicates that the order capacity does not exceed the picking tool limit; constraint (26) indicates that the working time of an order does not exceed the maximum continuous work of the picking personnel; constraint (27) indicates that the picking personnel return to the service desk at the departure point after completing the picking.

[0050] Preferably, in step four: the models from steps two and three are optimized using matrix index numbers to represent order numbers, and the values ​​in the matrix represent batches. For example, assuming 10 orders are batched, the batching result is represented by "[1,1,2,3,4,4,2,3,5,2]", where orders 1 and 2 are in batch 1, orders 3, 7, and 10 are in batch 2, orders 4 and 8 are in batch 3, orders 5 and 6 are in batch 4, and order 9 is in batch 10. The capacity and volume limits of the picking equipment, as well as the number of crows, the maximum number of iterations (maxGen1), the matrix dimension (dim), the perception probability (AP), and the flight distance are determined. Beneficial effects of this invention:

[0051] This paper focuses on the warehouse layout characteristics of a logistics company, comprehensively considering actual constraints such as warehouse physical limitations, picking personnel and auxiliary tool capabilities, and then constructs a two-layer optimization model involving multiple types of goods, multiple orders and multiple service stations, including order allocation and picking route optimization. By comparing the optimization results of GA, MOV, WOA, CSV and improved CSV, the improved swarm intelligence algorithm is selected for order batch optimization and picking operation route optimization. Attached Figure Description

[0052] Figure 1 Algorithm flow;

[0053] Figure 2 Types of route congestion;

[0054] Figure 3 Path adjustment design approach;

[0055] Figure 4 Floor plan of the picking area. Detailed Implementation

[0056] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0057] The optimization method includes the following steps: Step 1: Digitalization of warehouse layout;

[0058] Step 2: Finally, establish an order batch optimization model with the goal of minimizing picking aisles and ensuring fairness at the highest service counter.

[0059] Step 3: An employee picking operation optimization model was established with the shortest total picking time as the lower-level optimization objective.

[0060] Step 4: Optimize the models from Steps 2 and 3.

[0061] Preferably, step one: digitizing the warehouse layout; the location of each storage location is determined by the number of aisles, the number of storage locations within that aisle, the left and right sides of the aisle, and the depth of the storage location (r i ,s i ,p i ,l i ,d i ), where r i s is the number of aisles where storage location i is located; i p is the distance from the entrance to the aisle where storage location i is located; i The location i is located on the left or right side of the aisle; i d represents the number of storage levels; i The depth of storage location i;

[0062]

[0063] The distance between any two storage locations in a rectangular warehouse layout is represented as follows:

[0064]

[0065] The distance from any service counter to any storage location is:

[0066]

[0067] Where O∈{o1,o2,...,O} represents an order; B∈{b1,b2,...,B} represents a batch; M∈{m1,m2,...,M} represents a type of goods; and C... o Total order capacity, o m The order includes the types of goods. The required capacity of the goods in the order, W r The width of the alley, W c The width of the storage space, D c The depth of the storage location, H c The height of the storage location, D R Service desk number, V p Picker movement speed, V d Elevator speed, T b Packaging time.

[0068] Preferably, in step two: the final order batch optimization model is established with the optimization objectives of minimizing picking aisles and ensuring fairness at the highest service counter. The optimization model is shown below:

[0069]

[0070]

[0071]

[0072] in,

[0073]

[0074]

[0075]

[0076]

[0077] Formula (4) represents the number of picking aisles required; Formula (5) represents the fairness of the service counters within the warehouse; Formula (6) is the objective function for the upper-level optimization, where λ1 and λ2 represent weights, satisfying λ1 + λ2 = 1; Formula (7) represents the number of service counter batches; Formula (8) is a 0-1 variable, where Y... i b When = 1, it means that batch b needs shelf i, otherwise; formula (9) is a 0-1 variable, when When, it means that order o belongs to batch b, otherwise; formula (10) is a 0-1 variable, when When, it means that batch b has been assigned to the Service Desk DR, and vice versa;

[0078] Constraints:

[0079]

[0080]

[0081]

[0082]

[0083] Constraint (11) indicates that each batch is handled by one service desk; constraint (12) indicates that each order can only be assigned to one batch; constraint (13) indicates that the shelf can meet the item requirements of the order in that batch; constraint (14) indicates that it does not exceed the maximum supply capacity of the warehouse.

[0084] Preferably, in step three, an employee picking operation optimization model with the shortest total picking time as the lower-level optimization objective is established. The total picking operation time consists of three parts: employee walking time, working time of the lifting tool, and goods counting and settlement time. The formula for calculating the walking time of the picking operation personnel is shown in formula (15), and the formula for calculating the working time of the lifting tool during the picking operation is shown in formula (16).

[0085]

[0086]

[0087] In summary, the objective function of the lower-level employee picking operation optimization model is shown in formula (17):

[0088]

[0089] in,

[0090]

[0091]

[0092]

[0093] Formula (18) is a 0-1 variable, when When, it means that the picker completes picking at location i in a batch b and then goes to pick at location j, and vice versa; formula (19) is a 0-1 variable, when When, it means that the picking staff is responsible for order o in batch b, and vice versa; formula (20) is a 0-1 variable, when When, it indicates that the picking staff starts from the service desk (DR), and vice versa; T b For packaging time,

[0094] Constraints:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] WT+LT+T b ≤T pmax (26)

[0101]

[0102] Constraint (21) indicates that the picking operation does not exceed the maximum number of people; constraint (22) indicates that each person is responsible for one batch; constraints (23) and (24) indicate that the shelf can only be picked once in a batch; constraint (25) indicates that the order capacity does not exceed the picking tool limit; constraint (26) indicates that the working time of an order does not exceed the maximum continuous work of the picking personnel; constraint (27) indicates that the picking personnel return to the service desk at the departure point after completing the picking.

[0103] Order batching and picking route optimization are crucial components of picking operation optimization. Order batching aims to minimize the total number of shelves required, ensuring that the weight and volume of goods in each batch do not exceed the maximum volume and load capacity of the picking cart. After order batching, picking routes are planned based on the batching results to obtain the optimal picking route for each batch. In actual production activities, most warehouses have more than one picking person; therefore, after obtaining the optimal picking route for each batch, it is necessary to check for conflict points during the picking process. The overall framework is as follows: Figure 1 As shown

[0104] Step 4: Optimize the models from Steps 2 and 3. Use matrix index numbers to represent order numbers, and the values ​​in the matrix to represent batches. For example, assuming 10 orders are batched, the batching result is represented by "[1,1,2,3,4,4,2,3,5,2]", where orders 1 and 2 are in batch 1, orders 3, 7, and 10 are in batch 2, orders 4 and 8 are in batch 3, orders 5 and 6 are in batch 4, and order 9 is in batch 10. Determine the capacity and volume limits of the picking equipment, as well as the number of crows, the maximum number of iterations (maxGen1), the matrix dimension (dim), the perception probability (AP), and the flight distance.

[0105] In the picking route optimization problem, a matrix index is used to represent the order in which pickers pass through corresponding picking locations, and the integers in the matrix represent the picking location information that a batch needs to pass through. For example, "[1,2,3,8,23,45,32,34,12]" indicates that picking locations 1,2,3,8,23,45,32,34,12 are passed in sequence. After determining the encoding of the independent variables, the whale population size (SearchAgent), variable dimension (dim), maximum number of iterations (maxGen2), coefficient vectors A and c are initialized, and the variable dimension is equal to the number of picking locations that need to be passed through.

[0106] Example 1:

[0107] When the number of picking personnel is greater than 1, due to the width limitation of the picking aisle, blockage is very likely to occur. Combining the literature

[11] with the actual situation of the enterprise, the types of blockage can be divided into the following three categories, such as Figure 3 As shown:

[0108] (1) One picker needs to pass through this picking aisle to reach the destination picking location to pick items, while another picker has picking tasks in this picking aisle, such as... Figure 2 'a' in 'a';

[0109] (2) When both pickers have tasks in the picking lane, there are three situations. The target picking positions of the two pickers are located on both sides of the picking lane, and both need to pass through the other's target picking position as shown in b(1) in the figure below; the target picking positions of the two pickers are located in adjacent positions on both sides of the same lane as shown in b(2) in the figure below; the two pickers pick goods in the same lane as shown in b(3).

[0110] (3) Neither of the two pickers has a picking task in the picking channel, but they need to go through the same picking channel to reach the destination picking position, as shown in c in the figure below.

[0111] When encountering the situations listed above, to avoid congestion, path adjustments are necessary. This paper, based on dynamic programming, uses the time it takes for pickers to reach two adjacent storage locations as a unit to check for conflict points. When the employee picking speed is 1.39 m / s, logistics pickers need a 6-minute rest after working an average of 48 minutes. Therefore, whenever a picker completes a task, it is necessary to check if the employee's cumulative working time has reached 48 minutes. If it has, the employee needs to rest. The specific process is as follows... Figure 3 As shown.

[0112] Warehouse layout as follows Figure 4 As shown, the picking area consists of 5 picking aisles, 4 lanes, and 160 picking positions. Each picking position is numbered; in the diagram, D1 represents the width of the picking aisle, D2 represents the width of the picking position, D3 represents the length of the picking position, and D4 represents the width of the lane. The entrances and exits are located near picking positions 1, 40, 41, 80, 81, 120, and 121.

[0113] Twenty randomly generated orders were handled by four pickers. After the 20 orders were divided into batches (see Appendix for batching results), path planning was performed on the batching results. The optimized picking distance and picking time for each batch are shown in Table 1.

[0114] Table 1 Path Adjustment Results

[0115]

[0116]

[0117] A preliminary study was conducted on the optimized paths in the table above. The picking tasks were assigned to four pickers. The picking process was checked for picking conflicts based on the time it takes to pass through one picking location. If conflicts were found, the paths were adjusted according to priority. The adjustment results are shown in Table 2.

[0118] Table 2 Path Adjustment

[0119]

[0120] Analysis of Tables 1 and 2 shows that the time taken for a single person to pick this batch of goods was 18.29 minutes, the total time for multiple people to pick was 24.57 minutes, and the total time to complete the picking task was 6.69 minutes. Although the picking time for some batches was longer than before the adjustment, the picking time for multiple people to complete the task was significantly shorter and more efficient. Furthermore, the multi-person picking system considered the optimal working time for each individual based on ergonomics, and reasonable rest periods were set for staff after a certain working time was reached.

[0121] The specific embodiments described above are merely illustrative or explanatory of the principles of the present invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A two-level optimization method for warehouse picking operations considering dynamic order constraints, characterized in that: The optimization method includes the following steps: Step 1: Digitize the warehouse; Step 2: Establish an order batch optimization model with the optimization objectives of minimizing picking aisles and ensuring fairness at the highest service counter; Step two: Finally, establish an order batch optimization model with the optimization objectives of minimizing picking aisles and ensuring fairness at the highest service counter. The optimization model is shown below: (4) (5) (6) in, (7) (8) (9) (10) Formula (4) represents the number of picking aisles required; Formula (5) represents the fairness of the service counters within the warehouse; Formula (6) is the objective function for the upper-level optimization. , Represents the weight, satisfying Formula (7) represents the number of service counter batches; Formula (8) is a 0-1 variable, when When, it means that batch b needs shelf i; formula (9) is a 0-1 variable, when When, it indicates that order o belongs to batch b; formula (10) is a 0-1 variable, when At that time, it indicates that batch b has been assigned to service desk D. R ; Constraints: (11) (12) (13) (14) Constraint (11) indicates that each batch is handled by one service desk; Constraint (12) indicates that each order can only be assigned to one batch; Constraint (13) indicates that the shelf can meet the item requirements of the order in that batch; Constraint (14) indicates that it does not exceed the maximum supply capacity of the warehouse; Step 3: An employee picking operation optimization model was established with the shortest total picking time as the lower-level optimization objective. Step 4: Optimize the models from Steps 2 and 3.

2. The two-level optimization method for warehouse picking operations considering dynamic order constraints according to claim 1, characterized in that: Step one: Digitalization of warehouse layout; the location of each storage location is determined by the number of aisles, the number of storage locations within that aisle, the left and right sides of the aisle, and the depth of the storage location. ,in, Let i be the number of the lane where the cargo location i is located; The distance from the entrance to the alleyway where cargo location i is located; The location i is located on the left or right side of the aisle; This refers to the number of storage layers; The depth of storage location i; (1) The distance between any two storage locations in a rectangular warehouse layout is represented as follows: (2) The distance from any service counter to any storage location is: (3) in, For orders; For batches, For the type of goods, Total order capacity The order includes the types of goods. The width of the alley, The width of the storage space, The depth of the storage space, Service desk number.

3. The two-level optimization method for warehouse picking operations considering dynamic order constraints as described in claim 1, characterized in that: Step 3: An employee picking operation optimization model was established with the shortest total picking time as the lower-level optimization objective. The total picking operation time consists of three parts: employee walking time, working time of the lifting tool, and goods counting and settlement time. The formula for calculating the walking time of the picking operation personnel is shown in formula (15), and the formula for calculating the working time of the lifting tool is shown in formula (16). (15) (16) In summary, the objective function of the lower-level employee picking operation optimization model is shown in formula (17): (17) in, (18) (19) (20) Formula (18) is a 0-1 variable, when When, it means that the picker has completed picking at location i in a batch b and then goes to pick at location j; formula (19) is a 0-1 variable, when When, it means that the picking staff is responsible for order o in batch b; formula (20) is a 0-1 variable, when At that time, it indicates that the picking staff will pick items from service desk D. R Set off; For packaging time, Constraints: (21) (22) (23) (24) (25) (26) (27) Constraint (21) indicates that the picking operation does not exceed the maximum number of people; constraint (22) indicates that each person is responsible for one batch; constraints (23) and (24) indicate that the shelf can only be picked once in a batch; constraint (25) indicates that the order capacity does not exceed the picking tool limit; constraint (26) indicates that the working time of an order does not exceed the maximum continuous work of the picking personnel; constraint (27) indicates that the picking personnel return to the service desk at the departure point after completing the picking.

4. The two-level optimization method for warehouse picking operations considering dynamic order constraints according to claim 1, characterized in that: Step 4: Optimize the models from Steps 2 and 3, using matrix index numbers to represent order numbers and numerical values ​​in the matrix to represent batches.

Images