CN115062381A - Design method for optimal size and classified storage of multi-lane stereoscopic warehouse - Google Patents

Design method for optimal size and classified storage of multi-lane stereoscopic warehouse Download PDF

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CN115062381A
CN115062381A CN202210654815.6A CN202210654815A CN115062381A CN 115062381 A CN115062381 A CN 115062381A CN 202210654815 A CN202210654815 A CN 202210654815A CN 115062381 A CN115062381 A CN 115062381A
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余玉刚
刘雨雨
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University of Science and Technology of China USTC
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Abstract

The invention discloses a design method for optimal size and classified storage of a multi-lane stereoscopic warehouse, which comprises the following steps: s1: dividing storage areas of all goods shelves of the multi-lane stereoscopic warehouse; s2: establishing an expected travel time model for classified storage of a multi-lane stereoscopic warehouse; s3: optimizing system dimensions in a randomly stored expected travel time model; s4: optimizing a classification boundary by adopting a dichotomy under the optimal system size; in the S1, one stacker in the multi-lane stereoscopic warehouse serves multiple lanes, the system entrance and exit are located at the entrance and exit of the first lane, the storage area is divided into two areas, and the goods with higher turnover rate are closer to the entrance and exit. The invention optimizes the two types of storage boundaries through an algorithm based on the dichotomy, can obtain the optimal classification boundary within a few seconds under the condition of determining the system size, has different shapes of the optimal boundary on each row of shelves, and has an improved range of 50 percent compared with a random storage strategy.

Description

Design method for optimal size and classified storage of multi-lane stereoscopic warehouse
Technical Field
The invention relates to the technical field of warehousing systems, in particular to a design method for optimal size and classified storage of a multi-lane stereoscopic warehouse.
Background
The automatic stereoscopic warehouse has the advantages of small occupied area, labor saving, fast goods taking time and low error rate, can save the warehouse cost and improve the operation efficiency of the warehouse, and is widely applied to logistics systems in the production, retail and logistics industries. The main hardware components of the automatic stereoscopic warehouse are a storage shelf and a stacker. The goods shelves are positioned at both sides of the tunnel, and the stacker finishes the goods storage and taking operation in the tunnel. Due to the high cost of stackers, the cost of stackers in a single lane stereoscopic warehouse (one dedicated stacker serves only one lane) accounts for 40% of the total stereoscopic warehouse. In a warehouse with a low goods turnover rate, a multi-lane stereoscopic warehouse (one stacker serves a plurality of lanes) has the advantage of saving construction cost, and meanwhile, when one stacker breaks down, other stackers can be used for completing operation instead, so that the warehouse is widely applied. Fig. 1 shows the structure of a multi-lane automated stereoscopic warehouse.
The operation efficiency of the multi-lane stereoscopic warehouse is related to the size of the system and the adopted storage strategy; the size and the storage strategy of the system are optimized, so that the picking time can be shortened, the operation efficiency of the system is improved, and the cost of the system is reduced; for the existing storage strategy, the multi-lane automatic stereoscopic warehouse has a problem of long running time, and the operating efficiency of the system needs to be further improved.
Disclosure of Invention
Based on the technical problems in the background art, the invention provides a design method for the optimal size and the classified storage of the multi-lane stereoscopic warehouse, so that the floor area of the multi-lane stereoscopic warehouse is reduced, and the operating efficiency of a warehouse system is improved.
The invention provides a design method for optimal size and classified storage of a multi-lane stereoscopic warehouse, which comprises the following steps:
s1: dividing storage areas of all goods shelves of the multi-lane stereoscopic warehouse;
s2: establishing an expected travel time model for classified storage of a multi-lane stereoscopic warehouse;
s3: optimizing system size in a randomly stored expected travel time model;
s4: and optimizing the classification boundary by adopting a dichotomy under the optimal system size.
Preferably, the entrance and exit of the multi-lane stereoscopic warehouse in S1 are located at the entrance and exit of the first lane, and the storage area is divided into two, and the goods with higher turnover rate are closer to the entrance and exit.
Preferably, the desired travel time model in S2 is:
E(t)＝G 1 (t)E 1 (t)+(1-G 1 (t))E 2 (t)
where t is the classification boundary of the first and second regions in the time dimension, E (t) is the expected travel time of the system, E 1 (t) expected travel time of the first memory area, E 2 (t) is the expected travel time of the second memory area, G 1 (t) a cumulative demand percentage for the first area to store goods.
Preferably, the classification boundaries of the first region and the second region in the time dimension are:
t(i,x,y)＝a(i)+max(x,y)；
wherein, a (i) ═ (i-1) w is the time from the system entrance and exit to the ith tunnel entrance in the cross aisle when the system accesses goods; w is the distance between two adjacent roadways in the time dimension; max (x, y) is the maximum value of the operating time of the stacker to the cargo storage location (x, y) along the x-axis and the y-axis.
Preferably, the expected travel time of the first storage area and the expected travel time of the second storage area are respectively:
Figure BDA0003688986520000021
Figure BDA0003688986520000022
wherein, the total travel time V of all storage goods positions in the region j j (i,t)＝∫∫ (x,y)∈zonei(t) tdxdy, (j ═ 1, 2); total area S of region j j (i,t)＝∫∫ (x,y)∈zonei(t) 1dxdy，(j＝1,2)。
Preferably, the cumulative percentage demand for goods stored in the first area is:
Figure BDA0003688986520000023
wherein the content of the first and second substances,
Figure BDA0003688986520000024
is the area of the first storage region; n is the number of the lanes; b is the height of the shelf in the time dimension; c is the length of the shelf in the time dimension; and s is the shape parameter of the ABC curve.
Preferably, the shape parameter s of the ABC curve is calculated in the following manner:
G(i)＝i s ；
wherein G (i) is the accumulated demand ratio of the front i types of goods.
Preferably, the optimized system size in S3 includes the number of lanes, the height and the length of the rack in the time dimension.
Preferably, the number of lanes, the height of the shelf in the time dimension and the length after optimization are respectively:
Figure BDA0003688986520000031
Figure BDA0003688986520000032
wherein the content of the first and second substances,
Figure BDA0003688986520000033
pair of representations
Figure BDA0003688986520000034
Rounding is performed to get the whole.
Preferably, the optimal expected travel time is determined by taking the optimized number of lanes, the height and the length of the shelf in the time dimension as parameters, and the optimal classification boundary is determined by adopting a dichotomy method.
The invention has the beneficial technical effects that:
(1) by optimizing the number of the roadways of the system and the height and the length of the goods shelf, the floor area of the system can be reduced under the condition of the same system volume, and the early investment cost of the warehouse is reduced.
(2) The invention optimizes the two types of storage boundaries through an algorithm based on dichotomy, can obtain the optimal classification boundary within a few seconds under the condition of system size determination, has different shapes of the optimal boundary of the system on each row of shelves, and has an improved effect of 50 percent compared with a random storage strategy.
Drawings
Fig. 1 is a schematic structural diagram of a multi-lane stereoscopic warehouse according to the present invention.
Fig. 2 is a flowchart of a design method for optimal size and classified storage of a multi-lane stereoscopic warehouse according to the present invention.
Fig. 3 is a schematic diagram of a storage method according to the present invention.
FIG. 4 is a schematic diagram of the present invention for comparison by column sorted storage.
Fig. 5 is a schematic diagram of storage by lane classification for comparison according to the present invention.
Detailed Description
Referring to fig. 1, in the multi-lane stereoscopic warehouse according to the present invention, the stacker can freely operate in the picking lane, and the stacker can simultaneously operate in the x-axis direction and the y-axis direction when storing and taking goods, wherein the x-axis is in the horizontal direction along the length of the shelf, and the y-axis is in the vertical direction along the height of the shelf (see fig. 3); when the stacker needs to switch lanes, the stacker firstly runs to an entrance and an exit of a current lane, a transfer rail car is used as a transfer medium in a cross aisle to convey the stacker from the current lane to a target lane, and the stacker enters the target lane to complete lane switching; the railcars only operate within the cross aisle.
Examples
Referring to fig. 2, the method for designing the optimal size and the classified storage of the multi-lane stereoscopic warehouse provided by the invention comprises the following steps:
s1: dividing storage areas of all goods shelves of multi-lane stereoscopic warehouse
The gateway of the multi-lane stereoscopic warehouse system related by the invention is positioned at the gateway of the first lane, and all shelf storage areas of the system are divided into two areas, wherein the first area is shorter in distance from the gateway of the system, and the second area is longer in distance from the gateway of the system. The goods stored in the warehouse are also divided into two types according to the turnover rate of the goods, the two areas respectively and correspondingly store the goods with higher turnover rate and lower turnover rate, and the goods are randomly stored in each area, so that the purpose of storing the goods in two types is realized, and the storage and taking time of the goods is saved. The boundaries of the two regions are the decision for subsequent process optimization.
S2: establishing expected travel time model for classified storage of multi-lane stereoscopic warehouse
The invention uses the running time of the system to measure the operation efficiency of the system, and the size and the classification boundary are measured by time. Let a (i) ═ 1) w be the time from the system entrance and exit to the ith roadway entrance in the crossing aisle when the system accesses goods, w be the distance (time dimension) between two adjacent roadways, and set the system to have N roadways in total, then the farthest distance of the rail transfer car running in the crossing aisle is a (N) ═ 1 w, and the length of the crossing aisle is Nw; b is the height of the shelf in the time dimension; c is the length of the shelf in the time dimension.
The expected travel time models in two categories are:
E(t)＝G 1 (t)E 1 (t)+(1-G 1 (t))E 2 (t)
where t is the classification boundary of the first and second regions in the time dimension, E (t) is the expected travel time of the system, E 1 (t) expected travel time of the first memory area, E 2 (t) is the expected travel time of the second memory area, G 1 (t) a cumulative demand percentage for the first area to store goods.
The classification boundary t can be expressed as a one-way time for one-time stock or pickup in the multi-lane stereoscopic warehouse, and the one-way access time from the entrance and exit of the system to the storage position (x, y) of the rack on one side in the ith lane is as follows:
t(i,x,y)＝a(i)+max(x,y)
where max (x, y) is the maximum of the operating times of the stacker to the cargo storage location (x, y) along the x-axis and the y-axis.
The expected travel time of the first storage area and the expected travel time of the second storage area are respectively as follows:
Figure BDA0003688986520000051
Figure BDA0003688986520000052
wherein, the total travel time V of all storage goods positions in the region j j (i,t)＝∫∫ (x,y)∈zonei(t) tdxdy, (j ═ 1, 2); total area S of region j j (i,t)＝∫∫ (x,y)∈zonei(t) 1dxdy，(j＝1,2)。
In addition, the cumulative percentage demand for the first area to store goods is:
Figure BDA0003688986520000053
therein, sigma i:(i,x,y)∈zone1(t) S 1 (i, t) is the area of the first storage region; n is the number of the lanes; b is the height of the shelf in the time dimension; c is the length of the shelf in the time dimension; s is the shape parameter of the ABC curve; the shape parameter s of the ABC curve is calculated in the following way: g (i) ═ i s G (i) is the cumulative demand ratio of the top i types of goods, and for example, when the cumulative demand of the top 20% of the goods is 80%, s is 0.139.
S3: the system size is optimized in the expected travel time of the random storage strategy (special case of classified storage of expected travel time models).
The invention obtains the size of the system by using an expected travel time model under a random storage strategy: the height and length of the rack in the time dimension, and the number of lanes of the system. When the classification boundary t is 0, there is only one storage region, and the expected travel time model classified in two categories as in S2 is the expected time ER (N, b, c) under the random storage policy, where:
Figure BDA0003688986520000054
the volume of the system is normalized to 1, i.e., Nwbc equals 1. By proving that the second derivative of the expected time ER (N, b, c) under the random storage strategy is larger than 0, and utilizing a first derivative expression, the optimal size N of the system is obtained * 、b * 、c * ：
Figure BDA0003688986520000061
Figure BDA0003688986520000062
Wherein the content of the first and second substances,
Figure BDA0003688986520000063
presentation pair
Figure BDA0003688986520000064
Rounding is performed to get the whole.
S4: and optimizing the classification boundary by adopting a dichotomy under the optimal system size.
Obtaining the optimal size N of the system * 、b * 、c * Substituting the expected travel time expressions divided into two types to further obtain the optimal classification boundary.
Aiming at the optimal classification boundary, the invention provides an algorithm based on a dichotomy to search the optimal classification boundary, the size of a system and the distance w between two adjacent roadways in a fixed parameter time dimension are input, the optimal expected travel time and the optimal classification boundary can be obtained, and the algorithm is as follows:
Figure BDA0003688986520000065
Figure BDA0003688986520000071
the invention considers the condition that the speed of the rail transfer vehicle is inconsistent with the speed of the stacker, and the speed ratio of the stacker to the rail transfer vehicle is 1: alpha.
Table 1 shows the improvement of the system at different railcar speeds and roadway lengths, where I γ The improvement range of the strategy of the invention compared with the random access strategy is shown, and the improvement effect is as high as 50% under the condition of adopting a 20%/80% ABC curve; i is α The improvement range of the method compared with the operation time of the storage method classified according to columns is shown, and the improvement effect can reach 30% under the condition of adopting a 20%/80% ABC curve; i is w The improvement effect of the method of the invention is more than 10% compared with the operation time of the storage method classified by the laneway. Fig. 3-5 illustrate the storage method, the storage method by column classification, and the storage method by lane classification of the present invention, in which the boundaries by column classification and by lane classification are obtained by a one-dimensional search method.
TABLE 1 improvement of the System at different railcar speeds and cross aisle lengths
Figure BDA0003688986520000072
The present invention is not limited to the above preferred embodiments, and any modifications, equivalent substitutions, improvements, etc. within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. The design method for the optimal size and classified storage of the multi-lane stereoscopic warehouse is characterized by comprising the following steps of:
s1: dividing storage areas of all goods shelves of the multi-lane stereoscopic warehouse;
s2: establishing an expected travel time model for classified storage of a multi-lane stereoscopic warehouse;
s3: optimizing system size in a randomly stored expected travel time model;
s4: and optimizing the classification boundary by adopting a dichotomy under the optimal system size.
2. The method as claimed in claim 1, wherein one stacker in the multi-lane stereoscopic warehouse in S1 serves a plurality of lanes, the system entrance is located at the entrance of the first lane, the storage area is divided into two, and the goods with higher turnover rate are closer to the entrance.
3. The design method for optimal size and classified storage of a multi-lane stereoscopic warehouse as claimed in claim 2, wherein the expected travel time model in S2 is:
E(t)＝G 1 (t)E 1 (t)+(1-G 1 (t))E 2 (t)
where t is the classification boundary of the first and second regions in the time dimension, E (t) is the expected travel time of the system, E 1 (t) expected travel time of the first memory area, E 2 (t) is the expected travel time of the second memory area, G 1 (t) a cumulative demand percentage for the first area to store goods.
4. The design method for optimal size and classification storage of a multi-lane stereoscopic warehouse according to claim 3, wherein the classification boundaries of the first area and the second area in the time dimension are as follows:
t(i,x,y)＝a(i)+max(x,y)；
wherein, a (i) ═ (i-1) w is the time from the system entrance and exit to the ith tunnel entrance in the cross aisle when the system accesses goods; w is the distance between two adjacent roadways in the time dimension; max (x, y) is the maximum value of the operating time of the stacker to the cargo storage location (x, y) along the x-axis and the y-axis.
5. The design method for the optimal size and the classified storage of the multi-lane stereoscopic warehouse according to claim 3, wherein the expected travel time of the first storage area and the expected travel time of the second storage area are respectively:
Figure FDA0003688986510000011
Figure FDA0003688986510000021
wherein, the total travel time V of all storage goods positions in the region j j (i,t)＝∫∫ (x,y)∈zonei(t) tdxdy, (j ═ 1, 2); total area S of region j j (i,t)＝∫∫ (x,y)∈zonei(t) 1dxdy，(j＝1,2)。
6. The design method for the optimal size and the classified storage of the multi-lane stereoscopic warehouse as claimed in claim 3, wherein the cumulative percentage demand for storing goods in the first area is as follows:
Figure FDA0003688986510000022
therein, sigma i:(i,x,y)∈zone1(t) S 1 (i, t) is the area of the first storage region; n is the number of the lanes; b is the height of the shelf in the time dimension; c is the length of the shelf in the time dimension; and s is the shape parameter of the ABC curve.
7. The design method for the optimal size and classified storage of the multi-lane stereoscopic warehouse as claimed in claim 6, wherein the shape parameter s of the ABC curve is calculated in a manner that:
G(i)＝i s ；
wherein G (i) is the accumulated demand ratio of the front i types of goods.
8. The design method for the optimal size and classified storage of the multi-lane stereoscopic warehouse as claimed in claim 1, wherein the system size optimized in S3 includes the number of lanes, the height and the length of the rack in the time dimension.
9. The design method for the optimal size and the classified storage of the multi-lane stereoscopic warehouse as claimed in claim 8, wherein the number of the optimized lanes, the height of the shelf in the time dimension and the length of the shelf are respectively:
Figure FDA0003688986510000023
Figure FDA0003688986510000024
wherein the content of the first and second substances,
Figure FDA0003688986510000025
presentation pair
Figure FDA0003688986510000026
Rounding is performed to get the whole.
10. The method of claim 9, wherein the optimal expected travel time is determined using the optimized number of lanes, height and length of shelves in time dimension as parameters and the optimal classification boundary is determined by dichotomy.
CN202210654815.6A 2022-06-10 2022-06-10 Design method for optimal size and classified storage of multi-lane stereoscopic warehouse Pending CN115062381A (en)

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