CN109677830B - Resource allocation optimization method for four-way shuttle type dense warehousing system - Google Patents

Resource allocation optimization method for four-way shuttle type dense warehousing system Download PDF

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CN109677830B
CN109677830B CN201910149788.5A CN201910149788A CN109677830B CN 109677830 B CN109677830 B CN 109677830B CN 201910149788 A CN201910149788 A CN 201910149788A CN 109677830 B CN109677830 B CN 109677830B
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shuttle
warehousing system
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CN109677830A (en
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杨玮
王婷
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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
    • B65G1/0492—Storage devices mechanical with cars adapted to travel in storage aisles
    • 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

Abstract

The invention discloses a resource allocation optimization method for a four-way shuttle type intensive warehousing system, which comprises the following steps of firstly, determining a plurality of optimization targets and decision variables related to allocation optimization of the warehousing system; then, establishing a mathematical model of each optimization target according to a warehousing operation mode and a decision variable; finally, according to the established mathematical models of the optimization targets, establishing a resource configuration multi-target optimization model, solving the decision variables by using a multi-target optimization method, and optimizing the configuration of the warehousing system by combining the solution results; according to the invention, a multi-objective optimization model is established by analyzing the related design variables influencing the investment cost and the operation cost of the warehousing system and the throughput of the warehousing system, so that the resource allocation in the warehousing system is optimized, a powerful basis is provided for the design of an enterprise when planning a warehouse at the initial stage, the investment cost and the logistics cost of the enterprise are reduced, the operation efficiency of the intensive warehousing system is improved, and the economic benefit of the enterprise is improved.

Description

Resource allocation optimization method for four-way shuttle type dense warehousing system
Technical Field
The invention belongs to the field of dense warehousing system configuration optimization, and particularly relates to a four-way shuttle type dense warehousing system resource configuration optimization method.
Background
With the rapid development of domestic economy and the increasing shortage of land resources for construction, how to store the largest amount of articles in a limited space is considered, the stock capacity rate is improved, and the warehousing system is more automated, intensive and intelligent, more and more enterprises begin to use an automated warehouse combining novel logistics equipment, and Shuttle-based compact storage and retrieval system (SB-CS/RS) is in due charge and widely applied to the enterprises.
At present, shuttle type warehousing systems at home and abroad only stay at a single-layer operation level, namely one shuttle vehicle is kept in each layer of each roadway, and most shuttle vehicles are in an idle state under the condition of small order or task amount, so that the investment cost of enterprises is increased undoubtedly, and unreasonable waste of materials is caused; due to the fact that the reconstruction cost of the warehousing system after the warehousing system is built is too high, enterprises strive to pre-estimate and make decisions on reasonable layout of the warehousing system and physical parameters of equipment in the initial construction stage.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a four-way shuttle type intensive warehousing system resource allocation optimization method, which establishes a multi-objective optimization model by analyzing decision variables influencing the system performance, optimizes the resource allocation in the warehousing system, provides a powerful basis for the design of an enterprise during planning a warehouse at the initial stage, reduces the investment cost and logistics cost of the enterprise, improves the operation efficiency of the intensive warehousing system, and further improves the economic benefit of the enterprise.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a resource allocation optimization method for a four-way shuttle type dense warehousing system comprises the following steps:
step 1, determining a plurality of optimization targets and decision variables related to warehousing system resource allocation optimization;
step 2, establishing mathematical models of optimization targets related to the resource allocation optimization of the warehousing system according to the decision variables determined in the step 1;
step 3, establishing a multi-objective optimization model for resource allocation of the warehousing system according to the mathematical models of the optimization objectives established in the step 2, and solving the multi-objective optimization model to obtain a solution result; optimizing the configuration of the warehousing system according to the solving result;
the storage system resource allocation multi-objective optimization model comprises the following mathematical expressions:
min{f1(X),f2(X)}；
Figure GDA0002962454210000021
wherein f is1(X) mean throughput time of warehousing System, f2(X) total warehouse system cost; q (X) is warehouse capacity, QminMinimum capacity for warehouse; x is a decision parameter, XlAnd XuThe upper and lower bounds of the decision parameter X are respectively; l is the number of layers of the unit shelf, C is the number of rows of the shelf, R is the number of rows of the shelf, and N is the number of the unit shelf; s is the number of shuttle vehicles; v. ofAAt the maximum running speed of the cargo lift, aAIs the acceleration of the cargo lift; v. ofBIs the maximum operating speed of the shuttle car elevator, aBIs the acceleration of the shuttle car elevator; v. ofyMaximum running speed, a, for the main passage running direction of the shuttle caryThe acceleration of the main channel running direction of the shuttle vehicle is obtained; v. ofxFor maximum running of shuttle vehicle goods tunnel running directionSpeed, axThe acceleration of the shuttle vehicle in the running direction of the goods roadway is obtained.
Further, the decision variables of the warehousing system resource allocation in the step 1 comprise three-dimensional size specifications of the goods shelves, the number of the shuttles capable of operating in a cross-layer mode and equipment motion parameters.
Further, the optimization objective in step 1 includes that the throughput capacity of the warehousing system is maximum and the cost of the system is minimum, and the throughput capacity of the system is the reciprocal of the average throughput time of the warehousing system.
Further, the storage system throughput capacity maximum model is a storage system average throughput time minimization model, and the mathematical expression of the storage system average throughput time minimization model is as follows:
minf1(X)＝minTSB-CS/RS(L,C,R,N,S,vA,aA,vB,aB,vx,ax,vy,ay)
Figure GDA0002962454210000022
wherein, TSB-CS/RSIs the average throughput time, lambda, of the warehousing systemSB-CS/RSOne hour throughput for warehousing systems, E (DCC)single-SB-CS/RSAnd k is the average throughput time of the unit storage shelf system, k is the task transaction times in a single operation period, and N is the number of unit shelves.
Further, when the system adopts a double-command cycle operation mode, the task transaction number k in a single operation cycle is 2.
Further, average throughput time of unit storage shelf system E (DCC)single-SB-CS/RSThe mathematical expression of (a) is:
Figure GDA0002962454210000031
wherein E (DCC)lift-AAverage throughput time of the cargo lift; wherein E (DCC)SBThe average throughput time in DCC mode is performed once for the shuttle.
Further, the shuttle vehicle executes the average throughput time E (DCC) under the DCC mode onceSBThe mathematical expression of (a) is:
Figure GDA0002962454210000032
wherein, P (DCC)1)、P(DCC2)、P(DCC3)、P(DCC4) DCC respectively for executing shuttle1Mode, DCC2Mode, DCC3Mode, DCC4Probability of pattern, E (DCC)1)SB、E(DCC2)SB、E(DCC3)SB、E(DCC4)SBDCC respectively for executing shuttle1Mode, DCC2Mode, DCC3Mode, DCC4Average operating time of pattern, wcellIs the width of the unit cell, /)cellIs the length of the unit cell, hcellIs the cell height, tp/s-BShuttle car loading/unloading time, t, for shuttle car elevatorp/sTime of loading/unloading the shuttle, tcAnd changing the driving direction time for the shuttle vehicle.
Further, the mean travel time of the cargo lift in DCC mode E (DCC)lift-AThe mathematical expression of (a) is:
E(DCC)lift-A＝2·E(TS)lift-A+E(TB)lift-A+4·tp/s-A
wherein, E (TS)lift-AExpected travel time for one-way journey of cargo lift, E (TB)lift-AFor the expected travel time, t, of the journey between two targets of the goods liftp/s-ALoading/unloading time for the cargo lift.
Further, minf2(X) the mathematical expression for the enterprise total cost minimization model is:
minf2(X)＝minCSB-CS/RS(L,C,R,N,S,vA,aA,vB,aB,vx,ax,vy,ay)
CSB-CS/RS＝CI-SB+CEC-SB
wherein, CI-SBFor initial investment cost of the system, CEC-SBAnd energy consumption cost for system operation.
Further, in the step 3, an NSGA-II algorithm is adopted to carry out optimization solution on the multi-objective optimization model, and a Pareto optimal solution set is obtained.
Compared with the prior art, the invention has the beneficial effects that:
according to the resource allocation optimization method for the four-way shuttle type intensive warehousing system, on the premise that the warehousing system meets the minimum requirement of an enterprise on the storage quantity of goods, a multi-objective optimization model is established by analyzing relevant design variables influencing the investment cost and the operation cost of the warehousing system and the throughput of the warehousing system, and resource allocation in the warehousing system is optimized, so that a powerful basis can be provided for the design of the enterprise when planning a warehouse in the initial stage, the investment cost and the logistics cost of the enterprise are reduced, the operation efficiency of the intensive warehousing system is improved, and the economic benefit of the enterprise is improved;
according to the resource allocation optimization method for the four-way shuttle type intensive warehousing system, an optimal warehousing system allocation scheme set is solved and found, an early decision basis is provided for enterprise personnel to plan the warehousing system, various operations in warehousing activities are guaranteed to be performed efficiently and coordinately, meanwhile, risks caused by improper planning and design of the shuttle type intensive warehousing system are reduced, and the method has great practical application significance.
Drawings
FIG. 1 is a DCC mode work flow diagram of a cargo lift;
figure 2 is a DCC of a shuttle1A mode work flow chart, wherein goods to be delivered to and delivered from the warehouse are positioned on the same side of the main channel of the shelf;
figure 3 is a DCC of a shuttle1A mode work flow diagram, wherein goods to be delivered to and from the warehouse are positioned on the opposite side of the main channel of the shelf;
FIG. 4 is a flow chart of a shuttle layer change operation;
figure 5 is a DCC of a shuttle3Flow chart of mode operation in which warehouse entry and exit are performedThe goods are positioned on the same side of the main channel of the goods shelf;
figure 6 is a DCC of a shuttle3A mode operation flow chart, wherein goods to be delivered into and out of the warehouse are positioned on the opposite sides of the main channel of the shelf;
FIG. 7 is a flow chart of the NSGA-II algorithm;
FIG. 8 is a Pareto frontier chart for solving the SB-CS/RS resource allocation optimization problem by the NSGA-II algorithm;
figure 9 is a flow chart of a shuttle DCC mode of operation instruction.
Detailed Description
The invention will be further explained with reference to the accompanying fig. 1-9 and the detailed description.
The invention discloses a resource allocation optimization method for a four-way shuttle type dense warehousing system, which comprises the following steps of:
step 1, converting a shuttle type intensive warehousing system resource allocation system into a model under an OXYZ coordinate system;
taking a warehousing system I/O platform as a coordinate origin O; the running direction of the goods storage roadway of the shuttle car is taken as an X axis, and different shelf rows can be achieved when the shuttle car runs on the X axis; the running direction of the main channel of the shuttle vehicle is taken as the Y axis, and the shuttle vehicle can reach different shelf rows when running on the Y axis; the vertical running direction of the lifter is taken as a Z axis, and the lifter can reach different shelf layers when vertically running on the Z axis;
step 2, determining a plurality of optimization targets and decision variables related to configuration optimization of the warehousing system;
the optimization target comprises the maximum throughput capacity of the warehousing system and the minimum cost of the warehousing system; the throughput capacity of the warehousing system is the reciprocal of the average throughput time of the warehousing system, and if the throughput capacity of the warehousing system is maximum, the average throughput time of the warehousing system is minimum; therefore, the optimization objective of the present invention is the warehousing system average throughput time TSB-CS/RSMinimum and warehouse System cost CSB-CS/RSMinimum;
warehousing system cost CSB-CS/RSThe method comprises the initial investment cost of the investment construction initial stage of the warehousing system, the energy consumption cost of the operation process of the warehousing system equipment and the energy consumption cost of the operation process of the equipmentMainly the industrial electricity cost;
the decision variables are three-dimensional size specifications of a storage rack of the storage system, the number of cross-layer operation shuttle vehicles and equipment motion parameters; the shelf specifications of the warehousing system comprise L, C, R and N, wherein L is the number of the unit shelf layers, C is the number of the shelf rows, and R is the number of the shelf rows; s is the number of shuttle vehicles; v. ofAAt the maximum running speed of the cargo lift, aAIs the acceleration of the cargo lift; v. ofBIs the maximum operating speed of the shuttle car elevator, aBIs the acceleration of the shuttle car elevator; v. ofyMaximum running speed, a, for the main passage running direction of the shuttle caryThe acceleration of the main channel running direction of the shuttle vehicle is obtained; v. ofxIs the maximum running speed of the shuttle car in the running direction of the goods tunnel, axAcceleration in the running direction of the goods roadway of the shuttle car;
step 3, establishing a storage system average throughput time minimum model
Establishing a minimum model of the average throughput time of the warehousing system according to a cross-layer operation flow under a Double Command Cycle (DCC) mode of the warehousing system;
minimum average throughput time model minf of four-way shuttle type intensive warehousing system1(X) is:
minf1(X)＝minTSB-CS/RS(L,C,R,N,S,vA,aA,vB,aB,vx,ax,vy,ay)，
Figure GDA0002962454210000051
wherein f is1(X) is the average throughput time of the warehousing system, TSB-CS/RSThe average throughput time, lambda, of the four-way shuttle type dense warehousing systemSB-CS/RSOne hour throughput for warehousing systems, E (DCC)single-SB-CS/RSThe average throughput time of a storage system unit shelf system is shown, k is the task transaction times in a single operation period, and when the system adopts a double-command period operation mode, the task transaction times in the single operation periodThe number k is 2;
further, when the model with the minimum average throughput time of the four-way shuttle type intensive storage system is established, the method comprises the following steps:
(1) establishing an average throughput time model of a cargo lift
Referring to fig. 1, a cargo lift performs a DCC mode with a complete job task through the following three processes: 1) one-way stroke of the cargo elevator is as follows: the goods elevator carries goods to be warehoused and conveys the goods to be warehoused from the I/O station to the I/O point of the warehousing layer, and the warehoused goods are placed in the cache area; 2) stroke two targets of the cargo elevator is two: the lifting platform of the goods lifter is released from the I/O point of the warehousing layer and driven to the I/O point of the ex-warehousing layer; 3) one-way stroke of the cargo elevator (c): the lifting platform of the goods lifter carries goods to be delivered from the delivery layer to return to the I/O platform from the I/O point; wherein, when the goods lift executes DCC mode, the one-time complete operation task comprises three position points: I/O station (0, 0, 0), warehousing layer I/O point (0, z)i0) and Exit layer I/O Point (0, z)j，0)；
Mean travel time of cargo lift in DCC mode E (DCC)lift-AThe mathematical expression of (a) is:
E(DCC)lift-A＝2·E(TS)lift-A+E(TB)lift-A+4·tp/s-A，
wherein, E (TS)lift-AThe expected running time of one-way stroke (i) or (iii) of the goods elevator,
E(TB)lift-Athe expected travel time for the second trip between the two targets of the cargo lift,
tp/s-Aloading/unloading time for the cargo lift;
expected travel time of one-way trip of cargo lift (c) (E (TS))lift-AThe mathematical expression of (a) is:
Figure GDA0002962454210000061
Figure GDA0002962454210000062
wherein t (dz) is the travel time of the cargo lift, dz is the travel distance of the cargo lift, ω is the displacement variable, fTS(ω) is the probability density function from the origin to the random point;
expected travel time of cargo lift between two targets-lift-AThe mathematical expression of (a) is:
Figure GDA0002962454210000063
wherein f isTB(ω) is the probability density function of the cargo lift for a random inter-target travel;
when the farthest travel distance of the goods lifter is dz ═ HSR＝L·hcellMean travel time of the cargo lift in DCC mode E (DCC)lift-AThe mathematical expression of (a) is:
Figure GDA0002962454210000071
wherein HSRIs the height of the shelf hcellIs the height of the goods grid;
(2) establishing average throughput time model of shuttle vehicle
Referring to fig. 2-6 and 9, the DCC mode of the shuttle vehicle is executed according to whether the shuttle vehicle is operated across layers or not, which includes the following four modes: DCC1Mode, DCC2Mode, DCC3Mode and DCC4A mode; DCC1The mode is that the goods are stored and taken on the same layer and the layer is provided with a shuttle car; DCC2The mode is that the goods are stored and taken on the same layer and the layer is not provided with a shuttle car; DCC3The mode is that the goods are stored and taken on different layers and the goods storage layer is provided with a shuttle car; DCC4The mode is that the goods are stored and taken on different layers and the goods storage layer is not provided with a shuttle car.
DCC (dynamic channel control) of shuttle vehicle in execution1The operation flow in the mode is as follows:
referring to fig. 2 and 3, the shuttle vehicle executes DCC1During the mode task, according to whether the warehouse entry goods position is positioned on the same side of the main roadway, the mode task is divided into two different situations that goods to be warehoused and warehoused are positioned on the same side of the main rack channel and goods to be warehoused and warehoused are positioned on the different side of the main rack channel; the expected travel time under the two different conditions is the same and comprises the travel time of a shuttle vehicle main channel direction one-way travel I, the travel time of a cargo storage channel direction one-way travel II, the travel time of a cargo storage channel direction one-way travel III, the travel time of a shuttle vehicle main channel direction two-target travel IV, the travel time of a cargo storage channel direction one-way travel III, the travel time of a cargo storage channel direction one-way travel IV and the travel time of a shuttle vehicle main channel direction one-way travel III; in addition, the time for loading or unloading the goods by the shuttle and the time for switching the direction of the shuttle are four times.
DCC (dynamic channel control) of shuttle vehicle in execution1In mode, a complete job task needs to go through the following seven processes:
1) one-way stroke in main channel direction of shuttle car: the shuttle vehicle is loaded with goods to be warehoused and runs from the layer I/O point to the goods to be warehoused row port along the main channel; 2) one-way stroke in the direction of the cargo storage channel is two: the shuttle vehicle changes the driving direction at the crossroad, and the goods carried by the shuttle vehicle are driven to the goods position to be warehoused from the goods train opening to be warehoused along the goods shelf channel; 3) one-way stroke in the direction of the goods storage channel (c): unloading goods to a goods position and returning to the goods shelf row port along the original path; 4) a shuttle vehicle main channel direction two-target stroke four: the shuttle car changes the driving direction at the crossroad, and drives to the goods row opening to be delivered along the main channel; 5) one-way stroke of the direction of the goods storage channel (c): converting the driving direction, and driving to a goods position to be exported along the goods shelf channel; 6) the one-way stroke of the direction of the goods storage channel is as follows: goods to be delivered from the warehouse are loaded on the shuttle car and return to the goods shelf array port along the original path; 7) one-way stroke of main channel direction of shuttle vehicle (c): the driving direction is switched, the full-load shuttle vehicle drives to the layer I/O point along the main channel of the goods shelf, the goods are placed in the cache region, and the shuttle vehicle executes DCC1In the mode, a complete job task is completed. Wherein, the shuttle executes DCC1One-time complete job task packet in modeContains five position points: I/O point (0, 0, z) of the input/output layer located at the n-th layern) And warehousing goods row port (0, y)i，zn) Warehousing site (x)i，yi，zn) And a delivery port (0, y)j，zn) And shipment site (x)j，yj，zn)；
The shuttle is on DCC1Mean time of flight E (DCC) under mode1)SBThe mathematical expression of (a) is:
E(DCC1)SB＝2·E(TS)y+E(TB)y+4·E(TS)x+4·tp/s+4·tc，
wherein, E (TS)yOne-way expected travel time for main aisle direction of shuttle cars, E (TB)yExpected travel time for a trip between two targets, E (TS)xOne-way expected travel time for the cargo storage aisle direction; wherein, shuttle car main channel direction one-way expected running time E (TS)yThe mathematical expression of (a) is:
Figure GDA0002962454210000081
Figure GDA0002962454210000082
wherein t (dy) is the travel time in the main channel direction (Y-axis direction) of the shuttle vehicle, and dy is the travel displacement in the main channel direction of the shuttle vehicle;
shuttle vehicle main channel direction two target expected travel time E (TB)yThe mathematical expression of (a) is:
Figure GDA0002962454210000083
shuttle car cargo storage aisle (X-axis direction) one-way expected travel time E (TS)xComprises the following steps:
Figure GDA0002962454210000084
Figure GDA0002962454210000085
wherein t (dx) is the running time of the shuttle goods storage channel direction (X-axis direction), and dx is the running displacement of the shuttle goods storage channel direction;
when the goods elevator is located at the middle position of the goods shelf, the farthest distance traveled in one way in the direction of the goods storage channel is 1/2 of the width of the goods shelf, when dx is WSR/2＝R·wcellAnd 2, the farthest travel distance dy in the main channel direction of the shuttle car is equal to LSR＝C·lcellIn time, the shuttle executes DCC once1Mean time of flight E (DCC) under mode1)SCComprises the following steps:
Figure GDA0002962454210000091
wherein L isSRIs the length of the shelf, WSRIs the width of the goods shelf;
DCC (dynamic channel control) of shuttle vehicle in execution2The operation flow in the mode is as follows:
referring to fig. 4, the shuttle is performing DCC2When the task is in a mode, the goods are stored and taken at the same layer, and the layer is not provided with a shuttle, and one complete operation task needs to be carried out on the DCC1And carrying out layer changing operation of the shuttle car in advance on the basis of operation in the mode.
The layer changing operation of the shuttle car needs to go through three processes:
1) the shuttle car main channel direction whole journey is firstly: determining to execute the DCC2The operating shuttle car on the mth layer runs through the main tunnel from the front end of the main tunnel to the tail end of the main tunnel, and meanwhile, the shuttle car lifting platform runs from the previous task stop position to the tail end of the main tunnel on the mth layer; 2) layer changing stroke of the shuttle car is two: the shuttle car lifter conveys the shuttle car to the tail of the target layer/nth layer roadway; 3) shuttle car main channel direction whole journey stroke (c): shuttle vehicle slave nth layer main laneThe tail end of the lane runs to an I/O point at the front end of the nth layer of main roadway to complete the layer changing operation; then, the shuttle vehicle completing the layer changing operation is according to DCC1Mode for warehouse-in and warehouse-out operation, single DCC2Completing the task; wherein, the shuttle contains four position points in the operation process of changing the layer: I/O point (0, 0, z) at front end of main roadway of initial layer/mth layer of shuttle carm) Main tunnel end point (0, y)C，zm) And a main roadway front end I/O point (0, 0, z) located at the nth layern) And main roadway end point (0, y)C，zn)；
Average travel time E of shuttle layer changing operationSB-changeThe mathematical expression of (a) is:
ESB-change＝2·E(TF)y+E(TB)lift-B+2·tp/s-B
wherein, E (TF)yFor shuttle Y-axis full travel time, E (TB)lift-BIs the expected travel time between two targets of the shuttle car elevator; t is tp/s-BShuttle car loading/unloading time for the shuttle car elevator;
when the shuttle vehicle moves by dyn equal to LSR＝C·lcellThe mathematical expression of the time t (dy) required by the shuttle vehicle is as follows:
Figure GDA0002962454210000092
shuttle Y-axis whole-course expected running time E (TF)yComprises the following steps:
Figure GDA0002962454210000093
the mathematical expression of the required time t (dz') for the shuttle car elevator is:
Figure GDA0002962454210000101
wherein dz' is the running displacement of the shuttle car lifter;
expected travel time between two targets of shuttle car elevator E (TB)lift-BThe mathematical expression of (a) is:
Figure GDA0002962454210000102
when the shuttle car carries out layer changing operation and the running distance of the shuttle car lifter is farthest, dz ═ hcellL/S, mean travel time E of shuttle layer Change operationSB-changeThe mathematical expression of (a) is:
Figure GDA0002962454210000103
DCC (dynamic channel control) of shuttle vehicle in execution2In the mode, the average travel time of the complete job task is the average travel time of the shuttle layer changing and the average travel time of the shuttle layer changing in DCC1Sum of average travel times in mode; performing DCC once2Mean time of flight E (DCC) under mode2)SBThe mathematical expression of (a) is:
Figure GDA0002962454210000104
DCC (dynamic channel control) of shuttle vehicle in execution3The operation flow in the mode is as follows:
referring to fig. 5 and 6, the shuttle vehicle performs DCC3During the task, according to whether goods to be delivered into and delivered out of the warehouse are positioned on the same side of the main roadway, the goods to be delivered into and delivered out of the warehouse are positioned on the same side of the main channel of the goods shelf and on the different side of the main channel of the goods shelf, but the expected travel time under the two conditions is the same and comprises the travel time of a unidirectional travel (I) in the Y direction of the shuttle car, the travel time of a one-way travel (II) in the X direction of the shuttle car, the travel time of a one-way travel (III) in the Y direction of the shuttle car, the travel time of a stroke (III) between two targets of the shuttle car lifter, the travel time of a one-way travel (III) in the Y direction of the shuttle car, the travel time of a one-way travelThe travel time of the shuttle car and the travel time of the unidirectional travel ninthly in the Y direction of the shuttle car;
DCC (dynamic channel control) of shuttle vehicle in execution3In the mode, the goods are stored and taken in different layers, and the goods storage layer is provided with a shuttle car; a complete job task needs to go through nine processes: 1) one-way stroke of the shuttle car in the Y direction is as follows: the shuttle vehicle carries goods and drives to a goods row port to be warehoused from an I/O point of a storage layer; 2) one-way stroke of the shuttle car in the X direction is II: the shuttle vehicle changes the driving direction at the crossroad, and the goods carried by the shuttle vehicle are driven to the goods position to be warehoused from the goods train opening to be warehoused along the goods shelf channel; 3) the shuttle car X direction one-way stroke (c): unloading the goods to a goods position and then returning the goods to the goods shelf row port along the original path; 4) and C, unidirectional travel of the shuttle vehicle in the Y direction: the shuttle car changes the driving direction and drives to the tail end of a main roadway of the layer where the warehoused goods are located along the main channel; 5) the stroke between two targets of the shuttle car lifter is fifth: when the shuttle car carries out inventory operation, the shuttle car lifting platform is lifted/lowered to the tail end of the main roadway of the layer where the warehousing goods position is located; the shuttle vehicle carries an upper elevator, and the shuttle vehicle elevator conveys the shuttle vehicle to the tail end of a main roadway of a layer where the warehouse-out goods location is located; 6) the Y-direction one-way stroke of the shuttle vehicle: the shuttle car runs from the tail end of the roadway to a goods row port to be delivered out of the warehouse; 7) one-way stroke of shuttle car in X direction (c): the shuttle car changes the driving direction at the crossroad, and drives to the goods position to be exported along the goods shelf storage channel; 8) one-way stroke of the shuttle car in the X direction is (b): goods to be delivered from the warehouse are loaded on the shuttle car and return to the goods shelf array port along the original path; 9) y-direction one-way stroke ninthly of the shuttle vehicle: the shuttle vehicle converts the driving direction again, the goods to be delivered are driven to the layer I/O point along the main tunnel of the goods shelf, the goods are placed in the buffer area, and the single DCC3Completing the task; wherein, the shuttle executes DCC3In the mode, a complete job task comprises eight position points: I/O point (0, 0, z) of warehousing goods space layer at mth layerm) And warehousing goods row port (0, y)i，zm) Warehousing site (x)i，yi，zm) End point (0, y) of main roadway on layer of warehouse-in goods locationC，zm) And a main roadway end point (0, y) located at the layer where the nth layer warehouse-out goods location is locatedC，zn) And a delivery port (0, y)j，zn) And go out of the warehouseCargo site (x)j，yj，zn) And an export cargo space level I/O point (0, 0, z)n)；
The shuttle is on DCC3Mean time of flight E (DCC) under mode3)SBThe mathematical expression of (a) is:
Figure GDA0002962454210000111
wherein, E (TS)yOne-way expected travel time for main aisle direction (Y-axis direction) of shuttle cars, E (TS)xOne-way expected travel time for shuttle cargo storage aisle direction (X-axis direction), E (TB)lift-BIs the expected travel time between two targets of the shuttle car elevator;
further, the shuttle vehicle executes DCC once3Mean time of flight E (DCC) under mode3)SBThe mathematical expression of (a) is:
Figure GDA0002962454210000121
DCC (dynamic channel control) of shuttle vehicle in execution4The operation flow in the mode is as follows:
on DCC4Under the mode, one complete job task needs to be on DCC3The layer changing operation of the shuttle car is carried out in advance on the basis of the operation under the mode, the layer of the shuttle car is changed to the layer where the goods position to be stored is located, and then the goods position is changed according to DCC3The mode is only required to carry out goods storing and taking operation;
DCC for shuttle to execute once4Mean time of flight E (DCC) under mode4)SBComprises the following steps:
Figure GDA0002962454210000122
the probabilities of the shuttle vehicle performing the warehouse entry and exit operations in the four different modes under DCC are respectively recorded as: p (DCC)1)、P(DCC2)、P(DCC3) And P (DCC)4)，P(DCC1)、P(DCC2)、P(DCC3) And P (DCC)4) Are respectively
Figure GDA0002962454210000123
Figure GDA0002962454210000124
Figure GDA0002962454210000125
Figure GDA0002962454210000126
Wherein, P1Probability of access to the same layer, P2The probability that the shuttle car exists in the warehousing operation layer is shown;
in conclusion, the shuttle car executes the average travel time E (DCC) in the DCC mode onceSBThe mathematical expression of (a) is:
Figure GDA0002962454210000131
average throughput time of Unit shelf System E (DCC)single-SB-CS/RSThe maximum value of the average throughput time of the elevator and the S-set shuttle, therefore, the average throughput time of the unit shelf system E (DCC)single-SB-CS/RSThe mathematical expression of (a) is:
Figure GDA0002962454210000132
average throughput time T of whole four-way shuttle type intensive warehousing systemSB-CS/RSThe mathematical expression of (a) is:
Figure GDA0002962454210000133
wherein λ isSB-CS/RSFor a one hour throughput capability of the warehousing system,
k is the task transaction frequency in a single operation period, and when the system adopts a double-command period operation mode, the task transaction frequency k in the single operation period is 2;
step 4, establishing a warehousing system cost model;
the cost of the four-way shuttle type intensive warehousing system comprises the initial investment cost of the warehousing system at the initial investment construction stage and the operation cost of the warehousing system in the aspect of equipment energy consumption in the operation process;
the mathematical expression for minimizing the cost of the four-way shuttle type dense warehousing system is as follows:
minf2(X)＝minCSB-CS/RS(L,C,R,N,S,vA,aA,vB,aB,vx,ax,vy,ay)
wherein, CSB-CS/RSThe total cost model of the four-way shuttle type dense warehousing system;
the initial investment cost of the warehousing system in the initial construction stage comprises the cost C of purchasing automatic logistics equipmentECost of constructing a shelf CSRAnd shelf floor area lease cost CA(ii) a Initial investment cost C of shuttle type intensive warehousing systemI-SBThe mathematical expression of (a) is:
CI-SB＝CE+CSR+CA
CE＝(Clift-A+Clift-B+S·Cshuttle)·N
CSR＝Ccell·L·C·R·N
CA＝CSA·LSR·WSR·N·TP＝CSA·(lcell·C)·(wcell·R)·N·TP
wherein, Clift-ACost per cargo lift, Clift-BCost for a single shuttle car lift, CshuttleCost for a single shuttle, CcellFor the cost of construction of the unit cells, CSAAnnual lease cost per unit area;
the operation cost in the aspect of equipment energy consumption of the shuttle type intensive warehousing system comprises the energy consumption cost of elevator movement and the energy consumption cost of shuttle vehicle movement;
the average power of the engine required during the movement of the goods elevator and the shuttle elevator is respectively
Figure GDA0002962454210000141
Figure GDA0002962454210000142
Wherein, PAa、PAvAnd PAbThe engine power P required by the acceleration, uniform speed and deceleration of the cargo liftBa、PBvAnd PBbThe power t of the engine required by the shuttle car lifter during acceleration, uniform speed and deceleration respectivelyAa、tAvAnd tAbRespectively the time required for the acceleration, uniform speed and deceleration of the goods lift, tBa、tBvAnd tBbRespectively the time required by the acceleration, uniform speed and deceleration of the shuttle car lifter;
the average power of the engine required during the motion of the shuttle is:
Figure GDA0002962454210000143
Figure GDA0002962454210000144
wherein, Pya、PyvAnd PybThe engine power P required by the main channel direction of the shuttle vehicle during acceleration, uniform speed and deceleration motionxa、PxvAnd PxbThe engine power t required by the shuttle vehicle during acceleration, uniform speed and deceleration movement in the direction of the goods storage channelya、tyvAnd tybThe time t respectively needed by the main channel direction of the shuttle bus to accelerate, uniform and deceleratexa、txvAnd txbRespectively providing time required by the direction acceleration, uniform speed and deceleration of the goods storage channel of the shuttle vehicle;
the overall operation cost of the four-way shuttle type dense warehousing system is as follows:
CEC-SB＝P·N·Tday·nw-days·nweeks·TP·ηSB-CS/RS·CSE，
P＝(Px+Py)·S+PA+PB，
wherein P is the total operating power of the unit shelf system, CSEThe cost (yuan/kw.h) of each degree of industrial electricity;
in summary, the total cost model of the four-way shuttle type dense warehousing system is as follows:
CSB-CS/RS＝CI-SB+CEC-SB；
step 5, converting each target model established in the step 4 into a Pareto multi-target optimization problem;
the mathematical expression of the resource allocation multi-objective optimization model minf (X) of the four-way shuttle type dense warehousing system is as follows:
min{f1(X),f2(X)}；
Figure GDA0002962454210000151
wherein f is1(X) mean throughput time of warehousing System, f2(X) total warehouse system cost; q (X) is warehouse capacity, QminMinimum capacity for warehouse; x is a decision parameter, XlAnd XuThe upper and lower bounds of the decision parameter X are respectively;
step 6, solving the optimization model to determine the optimal configuration of the warehousing system; and (3) optimizing and solving the model by adopting an NSGA-II algorithm to obtain a Pareto optimal solution set, wherein the Pareto optimal solutions have no difference between advantages and disadvantages, and a decision-maker determines a proper solution according to requirements.
Referring to fig. 7, the resource allocation optimization model is solved by using the NSGA-II algorithm, and the method comprises the following specific steps:
step 1, encoding and population initialization; the chromosome coding adopts a real number coding mode and is coded as (L, C, R, N, S, v)A,aA,vB,aB,vx,ax,vy,ay) (ii) a The initial population adopts a random generation mode, so that the diversity of the initial population can be fully ensured. Setting an initial population P0The population number of (1) is N (N ═ 100);
step 2, generating a first generation subgroup; for initial population P0Selection and crossing (crossing probability P)c0.9) and mutation (probability of mutation is Pm0.1) operation to obtain a new first generation subgroup Q0；
Step 3, an elite reservation strategy; fusing the offspring and parent population into a synthetic population Q with the population number of 2N, and selecting a new generation parent population P with the population number of N from the synthetic population Q according to Pareto level sorting and crowding degree sorting principlest+1。
Step 3.1 non-dominated sorting; and (4) firstly carrying out non-dominant grade distribution on the new synthetic population Q, wherein a quick sequencing method is mostly adopted for grade distribution. Sequence numbers are distributed to non-dominated sorting levels, the highest level sequence number is zero level, the second level sequence number is first level, the third level sequence number is second level, and so on.
Step 3.2, the crowding distances are sorted; and then arranging the individuals in the same level from large to small according to the crowding degree, and selecting the individuals with larger crowding distance to join the new generation of population in order to keep the individuals evenly distributed and prevent local accumulation.
Step 4, optimizing a new population; for new generation parent population Pt+1Selecting, crossing and mutating to obtain new generation subgroup Qt+1；
Step 5, terminating conditions; if the iteration number is equal to the maximum iteration number Gen (Gen is 200), outputting the result, otherwise, returning to the step 3.
Simulation example
The invention carries out example verification and numerical analysis based on four-way shuttle type intensive storage system equipment operation parameters provided by a certain storage equipment supplier and storage shelf actual data parameters provided by a certain e-commerce distribution center, and predicts the minimum storage capacity Q of a warehousemin20000, and the weight m of each box is 100 kg. The data parameters and equipment parameters of the storage shelf of the four-way shuttle type dense storage system are shown in a table 1;
the number of layers, the number of columns, the number of rows and the number of shelves of the shuttle type dense warehousing system are limited within a certain value range, so that the optimization constraint of the minimum warehousing capacity of the warehouse is met. The equipment operating parameters satisfy the value ranges that can be reached by the current technical conditions, and the decision variable parameter range values are shown in table 2.
The multi-objective optimization problem of the four-way shuttle type dense warehousing system is solved by using NSGA-II, the number of initial populations is 100, the cross probability is 0.9, the variation probability is 0.1, the number of iterations is 200, 100 different configuration combination schemes are obtained, and an optimization result Pareto frontier chart is shown in figure 8. The Pareto front edge of the resource allocation optimization problem of the shuttle type intensive warehousing system capable of performing cross-layer operation obtained through the NSGA-II algorithm accords with the evaluation standard for solving a Pareto solution set of the multi-objective optimization problem, the Pareto non-dominated solution set obtained by solving is approximate to a smooth curve, the Pareto solution set is uniformly distributed, and the distribution range is wide; in fig. 6, each Pareto non-dominated solution can be used as an optimal solution for resource allocation of the four-way shuttle-type dense warehousing system.
According to the invention, a Pareto solution set of two problems, namely the system performance and the investment and operation cost, which need to be considered when enterprises invest and construct a four-way shuttle type dense warehousing system is obtained through an NSGA-II algorithm. Each non-dominated solution ensures that the average throughput time of the shuttle type intensive warehousing system, the warehousing investment cost and the operation cost are different; in order to facilitate the decision maker to know the difference between the quality and the disadvantage of each scheme in more detail, a proper configuration scheme is selected according to the self needs of the enterprise,the invention sorts the two objective function values according to the optimal principle and makes specific analysis and comparison, and only partial data is given here because the data amount is too much and cannot be listed one by one. When the average throughput time T of the warehousing system is respectively usedSB-CS/RSAnd total cost CSB-CS/RSWhen the objective function values are sorted in an ascending order, the obtained resource allocation planning scheme of the four-way shuttle type intensive storage system is shown in tables 3 and 4.
Table 3 is that after 200 iterations, the 100 non-dominated solutions of the resource allocation of the four-way shuttle-type dense warehousing system are sorted according to the average throughput time, the average throughput time can reach 2.30s at least, at this time, the overall allocation scheme is that 5 shelves are 4 layers, 48 columns and 22 rows of unit shelves, and each unit shelf is allocated with 4 sets of primary and secondary shuttles, that is, one set of each layer. The floor area of the dense storage system is 2534.4m2Therefore, the stereoscopic warehouse under the scheme is of a flat structure, occupies a large area on a plane, and is suitable for a traditional single-story warehouse with a lower stereoscopic space. The average throughput time is 27.14s at most and is about 12 times of the minimum time, and the scheme is the scheme with the minimum total storage cost in the table 4, the total cost of the stereoscopic warehouse is 1051.26 ten thousand yuan at this time, which is 1/2 which is less than the total cost of the scheme with the minimum time, and 1180.7 ten thousand yuan is saved.
The equipment configuration of the four-way shuttle type intensive warehousing system during high-efficiency operation brings high-cost investment to enterprises. Therefore, the enterprise needs to combine the self requirements in the initial planning and select the warehousing equipment meeting the enterprise throughput requirement, and the warehousing system does not need to be pursued as fast as possible. The cost saved for the enterprise by the reasonable warehousing system resource allocation planning scheme becomes invisible income.
TABLE 1 four-way shuttle type dense warehouse system goods shelf and equipment basic parameter values
Figure GDA0002962454210000171
Figure GDA0002962454210000181
TABLE 2 decision variable parameter Range values
Figure GDA0002962454210000182
TABLE 3 pareto optimal solution ordered by mean throughput time for optimization scheme of four-way shuttle type dense warehouse system
Figure GDA0002962454210000183
Figure GDA0002962454210000191
TABLE 4 pareto optimal solution for optimal ordering of optimization schemes of four-way shuttle type dense warehousing system by total cost
Figure GDA0002962454210000192

Claims (9)

1. A resource allocation optimization method for a four-way shuttle type dense warehousing system is characterized by comprising the following steps:
step 1, determining a plurality of optimization targets and decision variables related to warehousing system resource allocation optimization;
step 2, establishing mathematical models of optimization targets related to the resource allocation optimization of the warehousing system according to the decision variables determined in the step 1;
step 3, establishing a multi-objective optimization model for resource allocation of the warehousing system according to the mathematical models of the optimization objectives established in the step 2, and solving the multi-objective optimization model to obtain a solution result; optimizing the configuration of the warehousing system according to the solving result;
the storage system resource allocation multi-objective optimization model comprises the following mathematical expressions:
min{f1(X),f2(X)}；
Figure FDA0002865338080000011
wherein f is1(X) mean throughput time of warehousing System, f2(X) total warehouse system cost; q (X) is warehouse capacity, QminMinimum capacity for warehouse; x is a decision parameter, XlAnd XuThe upper and lower bounds of the decision parameter X are respectively; l is the number of layers of the unit shelf, C is the number of rows of the shelf, R is the number of rows of the shelf, and N is the number of the unit shelf; s is the number of shuttle vehicles; v. ofAAt the maximum running speed of the cargo lift, aAIs the acceleration of the cargo lift; v. ofBIs the maximum operating speed of the shuttle car elevator, aBIs the acceleration of the shuttle car elevator; v. ofyMaximum running speed, a, for the main passage running direction of the shuttle caryThe acceleration of the main channel running direction of the shuttle vehicle is obtained; v. ofxIs the maximum running speed of the shuttle car in the running direction of the goods tunnel, axAcceleration in the running direction of the goods roadway of the shuttle car;
average throughput time E (DCC) of shuttle vehicle in DCC modeSBThe mathematical expression of (a) is:
Figure FDA0002865338080000012
wherein, P (DCC)1)、P(DCC2)、P(DCC3)、P(DCC4) DCC respectively for executing shuttle1Mode, DCC2Mode, DCC3Mode, DCC4Probability of pattern, E (DCC)1)SB、E(DCC2)SB、E(DCC3)SB、E(DCC4)SBDCC respectively for executing shuttle1Mode, DCC2Mode, DCC3Mode, DCC4Average operating time of pattern, wcellIs the width of the unit cell, /)cellIs the length of the unit cell, hcellIs a unit cargo heightDegree, tp/s-BShuttle car loading/unloading time, t, for shuttle car elevatorp/sTime of loading/unloading the shuttle, tcAnd changing the driving direction time for the shuttle vehicle.
2. The method for optimizing the resource allocation of the four-way shuttle type dense warehousing system as claimed in claim 1, wherein the decision variables of the resource allocation of the warehousing system in the step 1 include three-dimensional size specification of a shelf, the number of shuttles capable of being operated across layers and equipment motion parameters.
3. The method as claimed in claim 1, wherein the optimization objectives in step 1 include maximum throughput capacity of the warehousing system and minimum system cost, and the system throughput capacity is the inverse of the average throughput time of the warehousing system.
4. The method as claimed in claim 3, wherein the maximum warehousing system throughput capacity model is a minimum warehousing system average throughput time model, and the mathematical expression of the minimum warehousing system average throughput time model is:
min f1(X)＝min TSB-CS/RS(L,C,R,N,S,vA,aA,vB,aB,vx,ax,vy,ay)
Figure FDA0002865338080000021
wherein, TSB-CS/RSIs the average throughput time, lambda, of the warehousing systemSB-CS/RSOne hour throughput for warehousing systems, E (DCC)single-SB-CS/RSAnd k is the average throughput time of the unit storage shelf system, k is the task transaction times in a single operation period, and N is the number of unit shelves.
5. The method as claimed in claim 4, wherein when the system adopts a dual-command cycle operation mode, the number of task transactions k in a single operation cycle is 2.
6. The resource allocation optimization method of the four-way shuttle type intensive storage system according to claim 4, wherein the average throughput time of the unit storage shelf system is E (DCC)single-SB-CS/RSThe mathematical expression of (a) is:
Figure FDA0002865338080000022
wherein E (DCC)lift-AAverage throughput time of the cargo lift; wherein E (DCC)SBThe average throughput time in DCC mode is performed once for the shuttle.
7. The resource allocation optimization method for the four-way shuttle type dense warehouse system according to claim 6, wherein the average travel time of the cargo lift in DCC mode is E (DCC)lift-AThe mathematical expression of (a) is:
E(DCC)lift-A＝2·E(TS)lift-A+E(TB)lift-A+4·tp/s-A
wherein, E (TS)lift-AExpected travel time for one-way journey of cargo lift, E (TB)lift-AFor the expected travel time, t, of the journey between two targets of the goods liftp/s-ALoading/unloading time for the cargo lift.
8. The method as claimed in claim 1, wherein the minf is a resource allocation optimization method for a four-way shuttle type dense warehousing system2(X) the mathematical expression for the enterprise total cost minimization model is:
minf2(X)＝minCSB-CS/RS(L,C,R,N,S,vA,aA,vB,aB,vx,ax,vy,ay)
CSB-CS/RS＝CI-SB+CEC-SB
wherein, CI-SBFor initial investment cost of the system, CEC-SBAnd energy consumption cost for system operation.
9. The resource allocation optimization method of the four-way shuttle type intensive warehousing system according to claim 1, characterized in that in the step 3, an NSGA-II algorithm is adopted to carry out optimization solution on the multi-objective optimization model to obtain a Pareto optimal solution set.
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