CN105858043B - The warehousing system Optimization Scheduling that a kind of lift is combined with shuttle - Google Patents

The warehousing system Optimization Scheduling that a kind of lift is combined with shuttle Download PDF

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CN105858043B
CN105858043B CN201610364804.9A CN201610364804A CN105858043B CN 105858043 B CN105858043 B CN 105858043B CN 201610364804 A CN201610364804 A CN 201610364804A CN 105858043 B CN105858043 B CN 105858043B
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CN105858043A (en
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杨玮
岳婷
杜雨潇
罗洋洋
刘江
杨甜
王婷
王晓雅
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SHANGHAI JINGXING LOGISTICS EQUIPMENT ENG Co.,Ltd.
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Shaanxi University of Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
    • B65G—TRANSPORT OR STORAGE DEVICES, e.g. CONVEYORS FOR LOADING OR TIPPING, SHOP CONVEYOR SYSTEMS OR PNEUMATIC TUBE CONVEYORS
    • B65G1/00—Storing articles, individually or in orderly arrangement, in warehouses or magazines
    • B65G1/02—Storage devices
    • B65G1/04—Storage devices mechanical
    • B65G1/137—Storage devices mechanical with arrangements or automatic control means for selecting which articles are to be removed
    • B65G1/1373—Storage devices mechanical with arrangements or automatic control means for selecting which articles are to be removed for fulfilling orders in warehouses

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Abstract

The invention discloses the warehousing system Optimization Scheduling that a kind of lift is combined with shuttle, target is minimised as to dispatch journey time, using genetic algorithm going out to be put in storage model and optimize to scheduling, greatly shorten access journey time, time cost can substantially be saved, save the energy, and, same order two, which wears time of the journey time of shuttle main-auxiliary vehicle also than a set of shuttle main-auxiliary vehicle, shortening, make the high efficiency in shuttle main-auxiliary vehicle fully automatic stereo warehouse, high density, and the advantages that high usage, is not fully exerted, realize that automatic stereowarehouse is real-time, online Optimized Operation, with larger practical application meaning.

Description

The warehousing system Optimization Scheduling that a kind of lift is combined with shuttle
Technical field
The invention belongs to intensive storage inbound/outbound process dispatching technique field, and in particular to a kind of lift and shuttle main-auxiliary vehicle (1:2 types) hybrid optimization dispatching method.
Background technology
With scientific and technical and industrial fast development, the another rise for being based on " intensive storage " concept, modern enterprise For producing, storing in a warehouse and dispensing desired continuous improvement, promote storage mode from initially by the simple heap of manpower handwork Product is improved to use high position forklift, unmanned guide trolleys AGV at present, shuttled to the warehouse-type storage by simple devices such as fork trucks The tiered warehouse facility storage of the automation equipments such as car.Rail mounted shuttle (RGV) is even more so that its speed is fast, cost is low and stability is good The characteristics of more and more important role is play in the industries such as modern manufacturing industry, logistics.
More inbound/outbound process scheduling that goods is realized using piler in conventional stereo warehouse, it is to realize storehouse the advantages of piler The mechanization and automation of storehouse operation, greatly improve operating efficiency, meanwhile, it is controlled and is managed using computer, operation Journey and information processing are rapid, accurate, timely, goods and materials can be accelerated to have enough to meet the need, reduce carrying cost.However, piler need to take accordingly Tunnel carries out operation, and tiered warehouse facility effectively stores area and can not made full use of, also, the vertical and horizontal operation of separate unit piler It can not carry out simultaneously, goods inbound/outbound process is less efficient.
There are a small number of tiered warehouse facilities to be combined using shuttle with piler both at home and abroad at present and carry out operation, take full advantage of warehouse Effective area and storage area, make cargo storage centralization, three-dimensional, reduce floor space, reduce Land Purchase expense.So And research of the domestic and foreign scholars to shuttle is mostly based on static scheduling, seldom it is related to dynamic mixed scheduling, meanwhile, enterprise is fixed Inhibition and generation service is deepened continuously, and small lot, the order of multiple batches of, high timeliness feature are on the increase, conventional palletizer formula tiered warehouse facility It can not meet the nowadays market demand with shuttle vehicle type shelf imperfect at present.
The content of the invention
It is an object of the invention to provide the warehousing system Optimization Scheduling that a kind of lift is combined with shuttle.
To reach above-mentioned purpose, present invention employs following technical scheme：
1) established according to a lift in fully automatic stereo warehouse with two dispatch situations for wearing shuttle main-auxiliary vehicle based on Calculate the mathematical modeling of scheduling journey time；
2) target is minimised as to dispatch journey time, using the mathematical modeling that step 1) is established to each in scheduler task The dispatching sequence of individual goods to be dispatched optimizes, and determines that the scheduler task is wearing shuttle main-auxiliary vehicle using a lift with two Complete the optimal scheduling order under dispatch situation.
The scheduler task includes simple stock operation, simple unstaffing and access goods multiple working.
Under the simple stock handling situations, the mathematical modeling for calculating the scheduling journey time of single stock is expressed as：
Wherein, x, y and z are that goods corresponds to goods yard coordinate under OXYZ coordinate systems, in the OXYZ coordinate systems, origin O The I/O positions in corresponding fully automatic stereo warehouse, X-axis correspond to female car moving direction, and Y-axis corresponds to sub- car moving direction, and Z axis is corresponding to be risen Drop machine moving direction；tzFor sub- car picking or unloading time；tmSub- car is taken for female car under no-load condition or is unloaded the time of sub- car；tm' Sub- car is taken for female car under full load conditions or is unloaded the time of sub- car；tsFor lift under no-load condition take female Che Huo unload female car when Between；ts' it is that lift takes female Che Huo to unload time of female car under full load conditions；vsFor elevator speed；vmFor female car no-load speed, vm' it is female car full-load speed；vzFor sub- car no-load speed, vz' it is sub- car full-load speed；I represents the last stock point, and j is represented The last last time stock point.
In the case of the simple unstaffing, the mathematical modeling for calculating the scheduling journey time of single picking is expressed as：
Wherein, x, y and z are that goods corresponds to goods yard coordinate under OXYZ coordinate systems, in the OXYZ coordinate systems, origin O The I/O positions in corresponding fully automatic stereo warehouse, X-axis correspond to female car moving direction, and Y-axis corresponds to sub- car moving direction, and Z axis is corresponding to be risen Drop machine moving direction；tzFor sub- car picking or unloading time；tmSub- car is taken for female car under no-load condition or is unloaded the time of sub- car；tm' Sub- car is taken for female car under full load conditions or is unloaded the time of sub- car；tsFor lift under no-load condition take female Che Huo unload female car when Between；ts' it is that lift takes female Che Huo to unload time of female car under full load conditions；vsFor elevator speed；vmFor female car no-load speed, vm' it is female car full-load speed；vzFor sub- car no-load speed, vz' it is sub- car full-load speed；I represents the last picking point, and j is represented The last last time picking point.
In the case of goods multiple working is accessed, the mathematical modeling for calculating the scheduling journey time of single access pair is expressed as：
If i, j, k point is not in same layer：
If i, k points are in same layer：
If j, k points are in same layer：
Wherein, x, y and z are that goods corresponds to goods yard coordinate under OXYZ coordinate systems, in the OXYZ coordinate systems, origin O The I/O positions in corresponding fully automatic stereo warehouse, X-axis correspond to female car moving direction, and Y-axis corresponds to sub- car moving direction, and Z axis is corresponding to be risen Drop machine moving direction；tzFor sub- car picking or unloading time；tmSub- car is taken for female car under no-load condition or is unloaded the time of sub- car；tm' Sub- car is taken for female car under full load conditions or is unloaded the time of sub- car；tsFor lift under no-load condition take female Che Huo unload female car when Between；ts' it is that lift takes female Che Huo to unload time of female car under full load conditions；vsFor elevator speed；vmFor female car no-load speed, vm' it is female car full-load speed；vzFor sub- car no-load speed, vz' it is sub- car full-load speed；Access to expression first deposit take afterwards it is continuous Goods is dispatched twice；I represents a shuttle main-auxiliary vehicle position, and j represents another shuttle main-auxiliary vehicle position, and k is represented New picking point.
The method of the optimization is genetic algorithm.
Crossover probability P in the genetic algorithmcFor 0.7~0.9, mutation probability PmFor 0.1~0.2.
Beneficial effects of the present invention are embodied in：
The present invention, with the two dispatch situation founding mathematical models for wearing shuttle main-auxiliary vehicle, then establishes corresponding to a lift Go out to be put in storage model, using genetic algorithm to going out to be put in storage model optimization after, so that it is determined that goods optimal scheduling order, scheduling is gone The journey time greatly shortens, and can substantially save time cost, saves the energy, makes the efficient of shuttle main-auxiliary vehicle fully automatic stereo warehouse Rate, high density, and be not fully exerted the advantages that high usage, realize that the optimization that automatic stereowarehouse is real-time, online is adjusted Degree, has larger practical application meaning.
Brief description of the drawings
Fig. 1 is shuttle main-auxiliary vehicle fully automatic stereo warehouse schematic diagram；
Fig. 2 is shuttle main-auxiliary vehicle fully automatic stereo storehouse model figure；
Fig. 3 is 1:Simple stock operation running schematic diagram in the case of 2；
Fig. 4 is 1:Simple unstaffing running schematic diagram in the case of 2；
Fig. 5 is 1:Goods multiple working running schematic diagram is accessed in the case of 2；
Fig. 6 is 30 equal goods yard coordinate diagrams of access goods quantity；Wherein, fork and rhombus represent stock goods yard and taken respectively Goods goods yard；
In figure：1 is female track road, and 2 be sub- track road, and 3 be rail of lifter.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
The present invention provides one kind 1:2 type lifts and shuttle main-auxiliary vehicle hybrid optimization dispatching method, specifically according to following step It is rapid to implement：
Step 1 wears shuttle main-auxiliary vehicle (1 to a lift with two:2) situation establishes rational mathematical modeling；
1.1 pairs of shuttle main-auxiliary vehicle fully automatic stereo warehouses are analyzed and researched, and formulate goods access rule
Referring to Fig. 1, shuttle main-auxiliary vehicle fully automatic stereo warehouse includes：Shuttle main-auxiliary vehicle (being made up of sub- car and female car), wear Shuttle-type shelf, female garage walk track (tunnel), track (shelf row) is walked by sub- garage, pallet vertical lifting system (lift), support Disk induction system, CMS apparatus control systems, WMS warehouse management systems.By the shuttle main-auxiliary vehicle fully automatic stereo storehouse shown in Fig. 1 Storehouse material object is converted into the model under OXYZ coordinate systems, as shown in Fig. 2 including rail of lifter 3, female track road 1 and sub- track road 2.Wherein, lift carries out goods, main-auxiliary vehicle the transport of Z-direction, and female car carries out goods, sub- car the transport of X-direction, Sub- car carries out goods the transport of Y direction.Single goods yard coordinate is [x, y, z], and this coordinate refers to the centrical coordinate of goods.With I/O points (going out inbound station) are above-mentioned coordinate origin O.
The present invention also sets following goods access rule：
During (1) two set of main-auxiliary vehicle (A, B car), when a set of main-auxiliary vehicle (setting A cars) stock, the another set of main-auxiliary vehicle of elevator scheduling When (setting B cars), A car stocks terminate the position that rear sub- car returns to female car, and female car is rested at the goods row port where goods, this When sub- car return interval disregard.Once transport and be only capable of carrying a goods.
(2) initial position of lift and shuttle main-auxiliary vehicle is going out inbound station.
During two sets of main-auxiliary vehicles of (3) elevator schedulings, adjacent operation twice is not in same layer.
Go out and be put in storage order placement, warehouse management system (WMS) is analyzed order, according to simple stock operation, merely Unstaffing, access goods three kinds of situations of multiple working, apparatus control system (CMS) regulate and control lift by main-auxiliary vehicle lifting to accordingly Layer, female car rested at the goods row where goods, female car discharges sub- car, and sub- car is completed stock or taken in tunnel movement Returned after goods operation.
1.2 establish a lift wears shuttle main-auxiliary vehicle (1 with two:2) goods mathematical modeling is accessed
Each situation of the lift with two sets of main-auxiliary vehicles is mainly studied scheduling of the lift to two sets of main-auxiliary vehicles and selected.It is fixed Justice：Elevator speed is vs；Female car no-load speed is vm, full-load speed vm'；Sub- car no-load speed is vz, full-load speed vz'； The sub- car loading, unloading goods time is tz, female car loading, unloading unloaded sub- car time is tm, it is t that the sub- car time is fully loaded with female car loading, unloadingm', rise Drop machine loading, unloading unloaded female car time is ts, it is t that female car time is fully loaded with lift loading, unloadings', the loading and unloading time is the same.
(1) simple stock job model
Simple stock operation running is as shown in Figure 3.A, B car will be screened during stock each time, selection is carried out down Most short main-auxiliary vehicle of secondary stock time.Then single stock time Tc1For：
Wherein, i represents the last stock point, is deposited by A cars；J represents the last last time stock point, is deposited by B cars.
Then simple stock operation total stock time (scheduling journey time) TcFor：
Tc=∑ Tc1 (2)
(2) simple unstaffing model
Simple unstaffing running is as shown in Figure 4.Single picking time Tq1For：
I represents the last picking point, is taken by B cars；J represents the last last time picking point, is taken by A cars；
Then simple unstaffing total picking time (scheduling journey time) TqFor：
Tq=∑ Tq1 (4)
(3) goods multiple working model is accessed
It is as shown in Figure 5 to access the running of goods multiple working.The access of goods is matched, referred to as access pair, i.e., one deposits one It is taken as a unit.The method for taking access pair, i is made to represent B cars position, j represents A cars position, and k represents new and taken Goods point.The then scheduling journey time T of an access paird1It is as follows：
If i, j, k point is not in same layer：
If i, k points are in same layer：
If j, k points are in same layer：
What min { } was selected in formula (5) is the journey time minimum value that A cars or B cars are sent to picking at k.Then access goods The total activation journey time of multiple working is：
Td=∑ Td1 (8)
To sum up, wear shuttle main-auxiliary vehicle with two for a lift to access total model as follows：
Step 2 optimizes emulation to Access Model, determines input work optimal scheduling order and most minor degree stroke Time.
To all goods yard numberings that access goods, the coding of genetic algorithm is used as using the traversal order in goods yard.
The initial population being made up of 100 (population number n=100) random ergodic order is produced in MATLAB.Goods Specified before the compiling of position, the coordinate parameters generated at random can also be used.
The traversal order in goods yard is optimized using the selection in basic genetic algorithmic, intersection, mutation operation, selection changes Generation number c=50, crossover probability Pc=0.9, mutation probability Pm=0.2, adaptation value, which is eliminated, accelerates exponent m=2.Make in the present invention Objective function is as follows：
Fitness (i, 1)=(1- ((len (i, 1)-minlen)/(maxlen-minlen+0.0001))) ^m
Wherein, len (i, 1) represents scheduling journey time corresponding to any individual i, and maxlen and minlen are respectively colony Time used in middle scheduling journey time most long and shortest path.
Utilize fitness>Rand selection individuals, by time smaller (fitness is larger) individual choice and are remained.
For accessing goods multiple working, the present invention carries out simulation analysis based on genetic algorithm with MATLAB, for one Lift is studied in terms of two with two situations for wearing shuttle main-auxiliary vehicle, is respectively：Inventory amounts are equal to picking quantity, And inventory amounts are more than picking quantity.The situation that inventory amounts are less than picking quantity is not considered.Two are discussed in detail herein Wear access in the case of shuttle main-auxiliary vehicle goods quantity it is equal when 30 task amounts result of study, wherein parameter value is shown in Table 1.Specific step It is rapid as follows：
When inventory amounts are exactly equal to picking quantity：
30 goods correspond to goods yard coordinate and are expressed as N (x y z) and N ' (x y z), wherein, 15 are stock (square Battle array A), N represents stock goods yard numbering (N=1~15), and 15 are picking (matrix B), and N ' represents picking goods yard numbering (N '=1 ' ~15 ').For seek a paths make access goods complete time it is most short, goods yard coordinate is as follows corresponding to goods, referring to Fig. 6：
A=[1 (13 10 3)；2(7 6 4)；3(15 11 2)；4(3 5 2)；5(14 9 3)；6(8 2 1)；7(12 12 2)；8(16 3 4)；9(20 9 2)；10(2 4 3)；11(3 8 2)；12(3 10 3)；13(13 9 1)；14(5 8 2)；15(14 4 3)]；
B=[1 ' (5 7 4)；2’(16 4 1)；3’(17 6 2)；4’(4 11 2)；5’(10 11 1)；6’(9 2 3)； 7’(8 4 2)；8’(16 5 3)；9’(19 5 1)；10’(13 6 1)；11’(17 9 3)；12’(7 3 2)；13’(2 2 4)；14’(12 1 2)；15’(18 7 2)]；
Random generation 100 on the putting in order of element in A (traversal order array a), random generation 100 on (the traversal order array b), it is then determined that element (representing a traversal order) and array b in array a that puts in order of element in B The one-to-one corresponding mapping relations of middle element (representing a traversal order), by 100 mapping relations so as to formed 100 on The traversal order of the access goods multiple working of 30 car loadings.Genetic algorithm progress is utilized respectively to element in array a and array b Optimization, change the value (i.e. traversal order) of element in array, and adaptation is calculated according to the traversal order of access goods multiple working Value (it is both the adaptation value of respective element in the adaptation value of respective element in array a, and array b, so-called corresponding i.e. composition one Two elements of mapping relations).
It is according to one group of access goods multiple working order of the random gained of program：(10→12’)→(11→5’)→(13→ 9’)→(8→15’)→(5→14’)→(4→10’)→(2→13’)→(7→3’)→(9→6’)→(15→1’)→(1→ 8’)→(12→2’)→(14→4’)→(3→11’)→(6→7’).Journey time is：RTime=642.35 (s).
One group of access goods multiple working order of gained is after optimization：(15→6’)→(12→9’)→(3→7’)→ (13→10’)→(4→5’)→(5→11’)→(1→8’)→(6→2’)→(7→1’)→(11→15’)→(10→14’) →(2→12’)→(9→3’)→(14→4’)→(8→13’).Journey time is：RTime=589.25 (s).Optimization efficiency： η=(journey time after m- optimization during optimization front travel)/optimization front travel time=(642.35-589.25)/642.35= 8.3%.
Other situation methods are same as above, and the result finally given is summarized as follows into table 2.Wherein, when inventory amounts ＞ picking numbers During amount, (0,0, the 0) point that can introduce respective numbers is used as picking goods yard coordinate so that inventory amounts=picking quantity.Meanwhile by When two wear shuttle main-auxiliary vehicle, for simple stock or the order of simple picking, its journey time and stock or picking Order also has certain relation, can also reach the purpose that scheduling optimized using the inventive method.
The model program parameters of table 1.
The simulation analysis result of table 2.
Learnt by table 2 and optimized by the scheduling of goods after model of the invention, algorithm optimization, shuttle and liter The journey time of drop machine and it is obvious shorten, time cost can be greatlyd save, improve efficiency, further demonstrate the model, The feasibility of algorithm；It is another it can be found that two wear shuttle main-auxiliary vehicle and have shortening than a set of shuttle main-auxiliary vehicle journey time, it is seen that increase After a set of shuttle main-auxiliary vehicle, although equipment cost increased, in the long term, one shuttle main-auxiliary vehicle of increase can also drop Low significant cost, economic benefits.

Claims (4)

  1. A kind of 1. warehousing system Optimization Scheduling that lift is combined with shuttle, it is characterised in that：Comprise the following steps：
    1) established with two dispatch situations for wearing shuttle main-auxiliary vehicle according to a lift in fully automatic stereo warehouse and adjusted for calculating Spend the mathematical modeling of journey time；
    2) target is minimised as to dispatch journey time, is treated using the mathematical modeling that step 1) is established to each in scheduler task The dispatching sequence of scheduling goods optimizes, and determines that the scheduler task is wearing the completion of shuttle main-auxiliary vehicle using a lift with two Optimal scheduling order under dispatch situation；
    The scheduler task includes simple stock operation, simple unstaffing and access goods multiple working；
    Under the simple stock handling situations, the mathematical modeling for calculating the scheduling journey time of single stock is expressed as：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>z</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>+</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>{</mo> <mfrac> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>z</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>x</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>m</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>z</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>,</mo> <mfrac> <msub> <mi>x</mi> <mi>j</mi> </msub> <msub> <mi>v</mi> <mi>m</mi> </msub> </mfrac> <mo>&amp;rsqb;</mo> <mo>+</mo> <mfrac> <msub> <mi>z</mi> <mi>j</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>}</mo> </mrow>
    Wherein, x, y and z are that goods correspond to goods yard coordinate under OXYZ coordinate systems, in the OXYZ coordinate systems, origin O correspondences The I/O positions in fully automatic stereo warehouse, X-axis correspond to female car moving direction, and Y-axis corresponds to sub- car moving direction, and Z axis corresponds to lift Moving direction；tzFor sub- car picking or unloading time；tmSub- car is taken for female car under no-load condition or is unloaded the time of sub- car；tm' it is full Female car takes sub- car or unloaded the time of sub- car in the case of load；tsFemale Che Huo is taken to unload time of female car for lift under no-load condition；ts' Female Che Huo is taken to unload time of female car for lift under full load conditions；vsFor elevator speed；vmFor female car no-load speed, vm' it is mother Car full-load speed；vzFor sub- car no-load speed, vz' it is sub- car full-load speed；I represents the last stock point, and j represents nearest one Secondary last time stock point；
    In the case of the simple unstaffing, the mathematical modeling for calculating the scheduling journey time of single picking is expressed as：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>q</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>z</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>+</mo> <mi>min</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <msub> <mi>x</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>m</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>z</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>z</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>+</mo> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <mi>max</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mo>|</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>|</mo> </mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>,</mo> <mfrac> <msub> <mi>x</mi> <mi>j</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>z</mi> <mi>j</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  2. 2. the warehousing system Optimization Scheduling that a kind of lift is combined with shuttle according to claim 1, its feature exist In：In the case of goods multiple working is accessed, the mathematical modeling for calculating the scheduling journey time of single access pair is expressed as：
    If i, j, k point is not in same layer：
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mrow> <mi>d</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>z</mi> <mi>k</mi> </msub> </mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>x</mi> <mi>k</mi> </msub> <msub> <mi>v</mi> <mi>m</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>k</mi> </msub> <msub> <mi>v</mi> <mi>z</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>k</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>x</mi> <mi>k</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <mn>3</mn> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>+</mo> <mn>2</mn> <msup> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mi>min</mi> <mrow> <mo>{</mo> <mrow> <mfrac> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>z</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>x</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>m</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>z</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>,</mo> <mi>max</mi> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mfrac> <mrow> <mo>|</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>,</mo> <mfrac> <msub> <mi>x</mi> <mi>j</mi> </msub> <msub> <mi>v</mi> <mi>m</mi> </msub> </mfrac> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>z</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>|</mo> </mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
    If i, k points are in same layer：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>d</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mfrac> <msub> <mi>z</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> </mrow> <mrow> <msup> <msub> <mi>v</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>y</mi> <mi>k</mi> </msub> </mrow> <mrow> <msup> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>y</mi> <mi>k</mi> </msub> </mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>|</mo> </mrow> <msub> <mi>v</mi> <mi>m</mi> </msub> </mfrac> <mo>+</mo> <mn>4</mn> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>+</mo> <mn>2</mn> <msup> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <mn>2</mn> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>+</mo> <mn>2</mn> <msup> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow>
    If j, k points are in same layer：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>d</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>z</mi> <mi>i</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>{</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>|</mo> </mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>,</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>|</mo> </mrow> <msub> <mi>v</mi> <mi>m</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>k</mi> </msub> <msub> <mi>v</mi> <mi>z</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>y</mi> <mi>k</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>x</mi> <mi>k</mi> </msub> <mrow> <msup> <msub> <mi>v</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>z</mi> <mi>k</mi> </msub> <msub> <mi>v</mi> <mi>s</mi> </msub> </mfrac> <mo>+</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <msup> <msub> <mi>t</mi> <mi>s</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <mn>2</mn> <msub> <mi>t</mi> <mi>z</mi> </msub> <mo>}</mo> </mrow>
    Wherein, access and the goods twice in succession taken afterwards scheduling is first deposited to expression；I represents a shuttle main-auxiliary vehicle position, j tables Show another shuttle main-auxiliary vehicle position, k represents new picking point.
  3. 3. the warehousing system Optimization Scheduling that a kind of lift is combined with shuttle according to claim 1, its feature exist In：The method of the optimization is genetic algorithm.
  4. 4. the warehousing system Optimization Scheduling that a kind of lift is combined with shuttle according to claim 3, its feature exist In：Crossover probability P in the genetic algorithmcFor 0.7~0.9, mutation probability PmFor 0.1~0.2.
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