CN110399629A - A kind of tower crane type selecting and layout optimization modeling method based on mixing shaping planning - Google Patents
A kind of tower crane type selecting and layout optimization modeling method based on mixing shaping planning Download PDFInfo
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Abstract
The invention discloses a kind of tower crane type selectings and layout optimization modeling method based on mixing shaping planning, belong to management of engineering construction field.This method is directed to construction site tower crane type selecting and Layout Problem, construction site tower crane type selecting and layout optimization modeling method are proposed based on mixed integer linear programming theory, guarantee the conevying efficiency of tower crane, by the lifting task of reasonable distribution tower crane working range overlapping region to provide reference for construction organization Planning Work.The present invention is based on mixing shaping programming theories, under conditions of there is influence to tower crane transport capacity utilization rate in the reasonable distribution for considering that tower crane interferes lifting task in region, it proposes construction site tower crane type selecting and layout optimization modeling method, and passes through the effect of optimization of case contrast verification model.
Description
Technical field
The present invention relates to the methods of a kind of Optimizing construction place tower crane type selecting and arrangement, belong to management of engineering construction neck
Domain.
Background technique
Important industry of the construction industry as support China's economic development, average growth rate per annum of the gross output value in nearly 5 years is about
It is 10.85%, but the profit margin of building enterprise only rises to 3.61% from 3.48%.Ground arrangement is ground according to manufacturing industry
Study carefully, Ground arrangement appropriate can reduce by 20%~60% transport of materials expense.Since tower crane type selecting and arrangement are construction fields
Important content in ground level arrangement optimizes tower crane type selecting and arrangement and makees to reduction building cost with very strong promotion
With.
Tower crane is mechanical as the core in the vertical transport scheme of construction site, be establish material stockyard and operation side it
Between efficient transport of materials network key link.Tower crane type selecting and Layout Problem belong to the quadratic assignment problem of operational research
(Quadratic Assignment Problem, QAP) mainly solves to meet construction speed requirement in guarantee transport of materials efficiency
Under the premise of, material vertical transport network in construction site is established with minimum cost.Transport of materials efficiency is by tower crane, material supply
The combined influence of relative positional relationship between point and demand point, and tower crane use cost is mainly influenced by tower crane model with quantity.
It is past to guarantee engineering construction progress since project investment is huge and construction period is stringent for large-scale and complex engineering project
Toward needing to be simutaneously arranged more tower cranes in certain region, so that it is guaranteed that lot of materials can transport in time in place.Tower crane number
Increasing for amount, although accelerating transport of materials rate, also increases the risk that tower crane boom mutually collides simultaneously.According to statistics,
The incidence of the mutual collision accident of construction site tower crane be only second to tower crane topple over, collision high-pressure electric wire and weight decoupling accident[10]。
Therefore when planning tower crane arrangement, need to comprehensively consider the equilibrium relation of tower crane operational efficiency and safety.Conventional method according to
By the practical experience of engineering staff, by adjusting tower crane model and position repeatedly, can just obtain relatively reasonable tower crane type selecting with
Arrangement, decision process and solution quality are influenced very big by peopleware and resource input.And tower big for place scale
The engineering project more than quantity is hung, conventional method is more difficult to take into account the balance of the efficiency of decision-making and solution quality, it is therefore necessary to visit
Rope is more efficient and accurately tower crane type selecting and method for arranging.
Aiming at the problem that conventional method, related researcher based on different optimization algorithms establish a series of tower crane type selectings with
Layout optimization model.The preferred arrangement of single tower crane completes the total time of lifting task to minimize tower crane mostly as optimization mesh
Mark.For the runing time for calculating tower crane, the characteristics of Zhang et al. is according to the tower crane method of operation, according to tower crane, demand point and supply
The triangular linear distance of point, establishes the computation model of tower crane runing time.On the basis of this model, Tam et al. utilizes something lost
Propagation algorithm minimizes the time that tower crane completes all lifting tasks by optimizing the position in tower crane and supply centre simultaneously.
Trevino and Raheem is using ant group algorithm (Ant Colony Optimization) optimization tower crane arrangement.Huang et al. needle
To separate unit tower crane arrangement and scheduling problem, using mixing shaping linear programming (Mixed Integer Linear
Programming, MILP) Method Modeling, and obtain the optimal solution of the optimization problem.
(group's tower) preferred arrangement of more tower cranes is increasingly complex compared to separate unit tower crane preferred arrangement problem, and reasonably selects tower
Hanging model is to optimize one of the important link of group's tower arrangement.Sawhney and Mund utilizes neural network algorithm (Neural
Networks), according to the factors such as construction period, building height, place scale, orographic condition, tower crane type and type are reasonably selected
Number.Shapira and Goldenberg considers tower crane operational safety, duration progress, operating efficiency and the convenient four indices of management, benefit
The construction machinery including tower crane is reasonably selected with analytic hierarchy process (AHP) (Analytic Hierarchy Process, AHP).
Marzouk et al. also chooses suitable tower crane type, such as flat roof type, amplitude variation type using analytic hierarchy process (AHP).Sohn et al. is being examined
Under conditions of considering tower crane attachment and basic engineering situation, tower crane stability is analyzed, so that it is determined that tower crane model selection scheme.Due to
Tower crane layout completes lifting task to it and has a great impact, therefore is difficult fundamentally to improve by adjusting tower crane model merely
Group's tower operational efficiency and safe condition.
For this purpose, researcher comprehensively considers group tower number and layout, group's tower arrangement is carried out using optimization algorithm excellent
Change.Zhang et al. introduces the parametric variable for indicating lifting task quantity, to balance each tower in group's tower preferred arrangement model
The workload allocations situation hung.Based on the research contents of Zhang, Alkriz et al. improves optimization by genetic algorithm again
As a result quality.Briskorn and Dienstknecht is planned using mixing shaping, in the feelings for considering that barrier influences tower crane
Under condition, group's tower cost of use is minimized.Layout of the Moussavi et al. by adjusting group's tower and material supply point, optimization tower crane behaviour
Make expense and rent.Abdelmegid et al.[38]It is arranged using GA algorithm optimization group's tower.Yeoh and Chua is run empty using tower crane
Between set relation, the tower crane handling time is shortened by the type selecting and arrangement that optimize group's tower, so that reducing tower crane makes
Use expense.Younes and Marzouk, by Tower for Simulation handling row activity, optimizes tower in the case where considering tower crane operation interference
Arrangement is hung to reduce tower crane expense or operating time.In conclusion lifting the document of task reasonable distribution relatively for tower crane
It is few, consider that the tower crane type selecting of the lifting task reasonable distribution problem in the overlapping region of tower crane working range and layout optimization model
Enough attention and research is not yet received in method.
Summary of the invention
This method is directed to construction site tower crane type selecting and Layout Problem, it is contemplated that the lifting of tower crane working range overlapping region is appointed
The reasonable distribution of business proposes that a kind of construction site tower crane type selecting is modeled with layout optimization based on mixing shaping programming theory
Method, to provide reference for construction organization Planning Work.
Mixing shaping programming theory is an important branch in programming theory, and in air route route selection, investment is determined
Plan, the fields such as Schedule Optimization are widely applied.Such algorithm is usually NP-hard (Non-deterministic
Polynomial), i.e., analytic solutions can not be obtained by the derivation of equation, optimal solution or the office of problem can only be searched for by optimization algorithm
Portion's optimal solution, while algorithm complexity exponentially increases (index exploding) with the increase of variable.Therefore, for different excellent
Change problem needs the Influencing Mechanism abstract constraint conditional relationship according to correlative factor, establishes different Optimized models.Mix shaping
The core concept of linear programming is: position and the model relationship of tower crane are selected using 0-1 variable as decision variable；Pass through influence
Linear restriction collection corresponding to factor forms feasible zone；It can finally by branch and bound method (Branch and Bound) acquisition
Optimal solution within the scope of row domain.According to mixing shaping programming theory, the basic structure of Optimized model is mainly by comprising continuous
The Linear Constraints and linear optimization target of type and integer variable composition.The groundwork of Optimization Modeling is to propose that simulation is asked
The logical relation of topic, and be linear restriction relationship by the nonlinear restriction transformation in logical relation, to form model
Basic framework.
Min f (x)=cTx+dTy (1)
S.t.Ax+By=b, x ∈ N, y ∈ R (2)
In formula, f indicates objective function；X is integer type variable, indicates decision and judging result in operating process；Y is to connect
Ideotype variable indicates parameter and index in operating process；C indicates the coefficient matrix of integer type variable in objective function；D is indicated
The coefficient matrix of continuous variable in objective function；Subscript T indicates transposition symbol；A indicates integer type variable in constraint condition
Coefficient matrix；B indicates the coefficient matrix of continuous variable in constraint condition；B indicates right end value matrix.
Tower crane type selecting and the establishment process of layout optimization model are as follows:
1) guarantee that safety of tower crane operation is the basic guarantee of tower crane type selecting and arrangement.For larger construction site,
Tower crane quantity is more and density is larger, and adjacent tower crane, which is difficult to avoid that, to be interfered and influence.The threat of tower crane operational safety, very greatly
In degree between the tower crane and the risk of collision of tower crane and neighbouring facility (such as high-tension bus-bar).For example, in strong wind weather,
To avoid the excessive torque as caused by wind load, tower crane boom should remain able to the state being freely rotated with the wind.At this point, if
Distance or tower crane and neighbouring facility distance are unsatisfactory for minimum safe distance requirement between tower crane, and tower crane will be caused to collide or even collapse
Risk.
In formula (3a)~(3c), the number of k and k ' expression tower crane optional position；The set of K expression tower crane optional position；
N indicates the number of optional tower crane model；N indicates the set of optional tower crane model；0-1 variable αk,nIndicate that N-shaped tower crane is set up
In tower crane optional position k；0-1 variable αk′,n′It is interior to indicate that n ' model tower crane is erected at tower crane optional position k '；0-1 variable
χk,n,k′,n′It is interior to indicate that two tower cranes of n and n ' model are set up in tower crane optional position k and k ' simultaneously respectively.Formula (3a)~
(3c) is by limiting variable αk,nWith χk,n,k′,n′The constraint relationship constitute and judge two simultaneous conditions of tower crane.
Formula (4a)~(4b) limits the distance between any two tower crane (k and k ') Dk,k′With wherein any tower crane brachium
(RnAnd Rn′) difference, not less than minimum safe distance ▽ between tower crane.
Formula (5a) and (5b) limit the tower crane positioned at tower crane optional position k to the distance D of neighbouring facility ww,kWith N-shaped
Number tower crane length of boom RnDifference, not less than the minimum safe distance υ of tower crane and neighbouring facility.In formula, w indicates neighbouring facility
Number；W indicates the set of neighbouring facility.
2) guarantee that tower crane can satisfy the material requirement of operation side under conditions of avoiding secondary transhipment, be that tower crane is complete
Guarantee at the feasibility of construction site vertical transport operation.Tower crane is held as one of vertical transport tool main in construction site
Main body construction stage most material vertical transport task is carried on a shoulder pole.Tower crane transport capacity, which meets real material lifting task, to be needed
It asks, is the major criterion for guaranteeing tower crane type selecting and arrangement feasibility.The transport capacity of tower crane is divided into three levels: 1) tower crane
Meet the lifting weight demands of supply centre and demand point；2) tower crane can set up the material supply and demand between supply centre and demand point
Relationship；3) tower crane can be timely completed all lifting tasks.
(1) tower crane complete the primary of a certain lifting operation on condition that, the elevating capacity of tower crane lifts weight not less than material.
Joint effect of the tower crane elevating capacity by tower crane performance and trolley amplitude.On the one hand, the elevating capacity of different model tower crane is different；
On the other hand, when tower crane trolley is in different amplitudes, maximum hoisting weight is also different.Therefore, counting of carriers amplitude is determining
The basis of tower crane elevating capacity.Formula (6a) and (6b) utilize coordinate relationship, calculate between material supply (demand) point and tower crane
Horizontal distance, i.e. trolley amplitude.In formula, i indicates the number of material supply point；The set of I expression material supply point；XiAnd Yi
Indicate the transverse and longitudinal coordinate of material supply point i, Di,kIndicate material supply point i to the water between the tower crane of tower crane optional position k
Flat distance；The number of j expression materials demand point；The set of J expression materials demand point；XjAnd YjIndicate material supply (demand) point
The transverse and longitudinal coordinate of j, Dj,kIndicate materials demand point j to the horizontal distance between the tower crane of tower crane optional position k.Formula
In (6c) and (6d), fnIndicate the maximum hoisting weight of N-shaped tower crane and the non-linear relation of trolley work range；Ci,k,nIt indicates
Positioned at maximum crane capacity of the N-shaped tower crane at material supply (demand) point i of tower crane feasible location k；Cj,k,nExpression is located at
Maximum crane capacity of the N-shaped tower crane of tower crane feasible location k at materials demand point j.
Elevating capacity of the tower crane in supply centre and demand point must not drop below material lifting weight.Formula (7a) passes through comparison
Positioned at maximum crane capacity C of the N-shaped tower crane at material supply point i of tower crane feasible location ki,k,nWith the material supply point
Maximum lifting weight WiRelationship, judge whether tower crane elevating capacity meets the maximum lifting weight at this.Formula (7b) passes through
Comparison is located at maximum crane capacity C of the N-shaped tower crane of tower crane feasible location k at materials demand point jj,k,nWith the material supply
The maximum lifting weight W of pointjRelationship, judge whether tower crane elevating capacity meets the maximum lifting weight at this.Formula (7c)
(7d) then ensure that the maximum lifting weight of all feed points or demand point can be met.In formula, 0-1 variable δi,k,nTable
Show that the N-shaped tower crane positioned at tower crane optional position k can satisfy the maximum lifting weight demands at material supply point i；0-1 variable
δj,k,nIndicate that the N-shaped tower crane positioned at tower crane optional position k can satisfy the maximum lifting weight demands at materials demand point j.
(2) material that the foundation of material relation between supply and demand does not require nothing more than supply centre offer must be kept with demand point material requested
Type is consistent, and tower crane elevating capacity is required to meet the requirement that material lifts weight.
Formula (8a)~(8b), which limits supply centre, can provide demand point material requested type, to ensure that supply centre
The material of offer and the consistency of demand point material requested type.In formula, m indicates the number of material category；M indicates material category
Set；0-1 variable λi,mIndicate that material supply point i can provide material m；0-1 variableIndicate that materials demand point j needs
Material m；0-1 variable φi,j,mIndicate that material supply point i can provide material m for demand point j.
Formula (9a)~(9d) has judged whether tower crane performance meets the lifting weight demands of supply centre and demand point.Formula
In, 0-1 variable εi,j,k,nIndicate that the N-shaped tower crane positioned at tower crane feasible location k meets material supply point i and demand point j simultaneously
Lifting weight.
Formula (10a)~(10c) has judged that tower crane completes the feasible of this transport of materials task by integrating above-mentioned condition
Property.In formula, 0-1 variable γi,j,k,m,nIndicating the N-shaped tower crane positioned at tower crane feasible location k can hang material m from supply centre i
Transport to demand point j.
Formula (11) ensure that tower crane can satisfy the materials demand of each demand point.
3) it is influenced by tower crane performance and layout, transport capacity of the tower crane within the unit time is limited.Work as separate unit
When tower crane is unable to complete whole lifting tasks in its service range, it is necessary to which more tower cranes are assisted within the scope of respective transport capacity
Same operation, to complete lifting mission requirements jointly.In order to lift task amount in reasonable distribution tower crane overlapping region, this model exists
On the basis of analysis lifting operation runing time, tower crane transport capacity is rationally assessed, to establish group constraint of tower collaboration transport
Condition.
(1) tower crane lifting operating process is the basic integral link that tower crane completes transport of materials flow of task, and assessment
The basic research object of tower crane transport capacity.The runing time calculation method of tower crane lifting operation is referring to Zhang et al.[28]'s
Model.The process of tower crane lifting operation, can be decomposed into horizontal direction operational process and vertical direction operational process, wherein horizontal
Direction operation can be analyzed to the radial operational process along boom direction and the tangential operational process that rotates around tower body again.
Formula (12) describes the process that tower crane trolley does radial motion along boom.In formula, TRi,j,k,nIt indicates to be located at tower crane
N type tower crane at feasible location k runs to the radial runing time of demand point j from material supply point i；Di,kAnd Dj,kIt indicates to supply
To point i and demand point j to the horizontal distance for being located at tower crane at tower crane feasible location k；| | indicate the arithmetic operation to take absolute value；
SRk,nIndicate the carriage amplitude varying speed of N-shaped tower crane.
Formula (13) describes the process that tower crane boom does tangential motion around swing mechanism.In formula, TTi,j,k,nExpression is located at
N type tower crane at tower crane feasible location k runs to the tangential runing time of demand point j from material feed point i；Di,jIndicate material
Expect the distance of feed point i to demand point j；STk,nIndicate N-shaped tower crane boom velocity of rotation.
Formula (14) describes the tangential influence relationship with tangential operational efficiency of tower crane.In formula, THi,j,k,nIt indicates to be located at tower
Hang the horizontal direction runing time that the n type tower crane at feasible location k runs to demand point j from material feed point i；Max and min
Respectively indicate the arithmetic operation for taking the larger value and smaller value；σ indicates tower crane in the coordination degree radially and tangentially run, with tower
The technical level for hanging driver is related, value 0.25.
The vertical direction operational process that formula (15) statement crane hook is carried out with hawser folding and unfolding.In formula, TVi,j,k,n
When indicating that the N-shaped tower crane being located at tower crane feasible location k is run from the vertical direction that material feed point i runs to demand point j
Between；ZiAnd ZjIndicate the height of material feed point i and demand point j；It is high that τ is expressed as the minimum lifting for guaranteeing Hoisting Security and being arranged
Degree；SVk,nIndicate the promotion speed of N-shaped tower crane.
Formula (16) describes the influence relationship of tower crane both horizontally and vertically operational efficiency.In formula, Ti,j,k,nIndicate position
N type tower crane at tower crane feasible location k runs to the actual run time of demand point j from material feed point i；ρ indicates tower
The coordination degree both horizontally and vertically run is hung, value 1.00 related to the technical level of tower crane driver.
(2) transport capacity of tower crane can simply be equivalent to the limit that can be completed in unit time lifting number, i.e. tower
Theory is hung to hang time.Model is by calculating the average operating time that all potential liftings operate in tower crane working range, in conjunction with tower crane
Every working hour estimates tower crane theory lifting number.
Formula (17a)~(17b) has judged whether material feed point i and demand point j are located at feasible location k respectively
N type tower crane working range in.In formula, 0-1 variable βi,k,nIndicate that material feed point i is located in tower crane feasible location k
In the working range of the n type tower crane at place；βj,k,nIndicate that demand point j is located in the n type tower at tower crane feasible location k
In the working range hung.
Formula (18a)~(18c) judged material feed point i or demand point j whether simultaneously place at tower crane feasible location k
N type tower crane working range in.In formula, 0-1 variable ωi,j,k,nIndicate that material feed point i and demand point j is in tower simultaneously
In the working range hung.
Formula (19) calculates all potential liftings in the n type tower crane working range at tower crane feasible location k
The average operating time MT of operationk,n。
Formula (20) calculates the daily theory of the n type tower crane at tower crane feasible location k and hangs time Fk,n.In formula, number
The actual motion state of the expression tower crane reciprocating working of word 2.
(3) cooperation between tower crane provides greater flexibility with being combined into tower crane management, also makes each tower crane transport capacity
It is given full play to.Formula (21a)~(21b) is by establishing 0-1 variable γi,j,k,m,nWith integer variable Si,j,k,m,nConstraint close
System, forms distribution mechanism of the tower crane lifting task between tower crane, and in formula, N indicates a very big positive number；Si,j,k,m,nIt indicates
Positioned at number of the N-shaped tower crane by material m from material supply point i to demand point j of tower crane feasible location k.
Formula (22) guarantees that all lifting tasks can obtain and is efficiently accomplished, in formula, Qj,mIndicate materials demand point j institute
Need the weight of material m；RmIndicate the weight of the average material m of lifting every time of tower crane；Expression rounds up.
In order to guarantee tower crane operational efficiency, formula (23) ensure that the practical lifting frequency of tower crane is no more than it in the unit time
Theory is hung secondary.If the transport capacity of group's tower can satisfy the lifting mission requirements of construction speed most tonic phase, can illustrate
The type selecting and arrangement in other any stages be all it is feasible, in formula, Fk,nIndicate the N-shaped number for being located at tower crane feasible location k
Tower crane odd-numbered day maximum lifts number.
4) in the case where the background for saving building cost is constantly sought by construction enterprises, tower crane cost is to measure tower crane type selecting and arrangement
The key index of scheme superiority and inferiority, therefore tower crane use cost is the primary optimization aim of tower crane type selecting Yu layout optimization model.Tower
Hanging cost both includes the cost relevant to construction period such as tower crane depreciation cost (rent), price for repairing, fuel cost and labour cost, is also wrapped
It is disposably put into containing basic production costs, traffic expense and assembling and disassembling expense etc..Formula (24) summarizes general expenses and forms tower crane cost
Assess formula.In formula, ΦnIndicate the running cost of N-shaped tower crane；ΨnIndicate the constant expense of N-shaped tower crane；D indicates tower crane
Service life.
Detailed description of the invention
The construction site Fig. 1 plan view.
Fig. 2 optimization front and back tower crane type selecting and arrangement compare.
Fig. 3 is this method implementation flow chart.
Specific embodiment
Below in conjunction with drawings and examples, the present invention is described in detail.
Model is applied as follows with compliance test result process:
By taking group's tower option of certain engineering project and arrangement as an example, used by group's tower of comparison initial scheme and prioritization scheme
Expense demonstrates the effect of optimization of this Optimized model.Project profile 39276.5 square metres of single story building area as shown in Figure 1:；
Include 77 Work sectors；Each Work sectors choose a materials demand point；Tower crane service life 12 months.Alternate column bull ladle
4 kinds of models are included, specific performance index and cost parameters are as shown in table 1.
1 tower crane performance parameter of table
Optimization front and back tower crane type selecting and arrangement are as shown in Figure 2.Initial and prioritization scheme selects STT200-12t type
Number tower crane, illustrates that the model tower crane sexual valence is relatively high.In initial scheme, tower crane quantity is 6, cost of use total 437.16
Wan Yuan；In prioritization scheme, tower crane quantity is 5, and cost of use is 364.3 ten thousand yuan total.Group's tower type selecting is improved by Optimized model
With arrangement, tower crane cost of use 16.67% is saved.It follows that proposed tower crane type selecting is built with layout optimization
Mould method has theoretic reasonability.
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Claims (1)
1. a kind of tower crane type selecting and layout optimization modeling method based on mixing shaping planning, according to mixing shaping linear programming reason
By the basic structure of Optimized model is by the Linear Constraints comprising continuous type and integer variable and linear optimization target group
At；
Min f (x)=cTx+dTy (1)
S.t.Ax+By=b, x ∈ N, y ∈ R (2)
In formula, f indicates objective function；X is integer type variable, indicates decision and judging result in operating process；Y is continuous type
Variable indicates parameter and index in operating process；C indicates the coefficient matrix of integer type variable in objective function；D indicates target
The coefficient matrix of continuous variable in function；Subscript T indicates transposition symbol；A indicates the coefficient of integer type variable in constraint condition
Matrix；B indicates the coefficient matrix of continuous variable in constraint condition；B indicates right end value matrix；
It is characterized by: tower crane type selecting and the establishment process of layout optimization model are as follows:
1) guarantee that safety of tower crane operation is tower crane type selecting and arrangement；
In formula (3a)~(3c), the number of k and k ' expression tower crane optional position；The set of K expression tower crane optional position；N table
Show the number of optional tower crane model；N indicates the set of optional tower crane model；0-1 variable αk,nIndicate that N-shaped tower crane is erected at
In tower crane optional position k；0-1 variable αk′,n′It is interior to indicate that n ' model tower crane is erected at tower crane optional position k '；0-1 variable
χk,n,k′,n′It is interior to indicate that two tower cranes of n and n ' model are set up in tower crane optional position k and k ' simultaneously respectively；Formula (3a)~
(3c) is by limiting variable αk,nWith χk,n,k′,n′The constraint relationship constitute and judge two simultaneous conditions of tower crane；
Formula (4a)~(4b) limits the distance between any two tower cranes k and k ' Dk,k′With wherein any tower crane brachium RnAnd Rn′
Difference, not less than minimum safe distance ▽ between tower crane；
Formula (5a) and (5b) limit the tower crane positioned at tower crane optional position k to the distance D of neighbouring facility ww,kWith N-shaped tower
Hang length of boom RnDifference, not less than the minimum safe distance υ of tower crane and neighbouring facility；In formula, w indicates the volume of neighbouring facility
Number；W indicates the set of neighbouring facility；
2) transport capacity of tower crane is divided into three levels: tower crane meets the lifting weight demands of supply centre and demand point；Tower crane energy
Enough set up the material relation between supply and demand between supply centre and demand point；Tower crane can be timely completed all lifting tasks；
(1) tower crane complete the primary of a certain lifting operation on condition that, the elevating capacity of tower crane lifts weight not less than material；Tower crane
Joint effect of the elevating capacity by tower crane performance and trolley amplitude；On the one hand, the elevating capacity of different model tower crane is different；It is another
Aspect, when tower crane trolley is in different amplitudes, maximum hoisting weight is also different；Therefore, counting of carriers amplitude is determining tower crane
The basis of elevating capacity；Formula (6a) and (6b) utilize coordinate relationship, calculate the water between material supply or demand point and tower crane
Flat distance, i.e. trolley amplitude；In formula, i indicates the number of material supply point；The set of I expression material supply point；XiAnd YiIt indicates
The transverse and longitudinal coordinate of material supply point i, Di,kIndicate material supply point i arrive positioned at tower crane optional position k tower crane between level away from
From；The number of j expression materials demand point；The set of J expression materials demand point；XjAnd YjIndicate material supply or the cross of demand point j
Ordinate, Dj,kIndicate materials demand point j to the horizontal distance between the tower crane of tower crane optional position k；Formula (6c) and
In (6d), fnIndicate the maximum hoisting weight of N-shaped tower crane and the non-linear relation of trolley work range；Ci,k,nIt indicates to be located at tower
Hang maximum crane capacity of the N-shaped tower crane of feasible location k at material supply or demand point i；Cj,k,nIndicating can positioned at tower crane
Line position sets maximum crane capacity of the N-shaped tower crane of k at materials demand point j；
Elevating capacity of the tower crane in supply centre and demand point must not drop below material lifting weight；Formula (7a) is located at by comparison
Maximum crane capacity C of the N-shaped tower crane of tower crane feasible location k at material supply point ii,k,nWith the maximum of the material supply point
Lift weight WiRelationship, judge whether tower crane elevating capacity meets the maximum lifting weight at this；Formula (7b) passes through comparison
Positioned at maximum crane capacity C of the N-shaped tower crane at materials demand point j of tower crane feasible location kj,k,nWith the material supply point
Maximum lifting weight WjRelationship, judge whether tower crane elevating capacity meets the maximum lifting weight at this；Formula (7c) and
(7d) then ensure that the maximum lifting weight of all feed points or demand point can be met；In formula, 0-1 variable δi,k,nIt indicates
It can satisfy the maximum lifting weight demands at material supply point i positioned at the N-shaped tower crane of tower crane optional position k；0-1 variable
δj,k,nIndicate that the N-shaped tower crane positioned at tower crane optional position k can satisfy the maximum lifting weight demands at materials demand point j；
(2) foundation of material relation between supply and demand, which does not require nothing more than the material of supply centre offer and demand point material requested, must keep type
Unanimously, and tower crane elevating capacity is required to meet the requirement that material lifts weight；
Formula (8a)~(8b) limits supply centre and provides demand point material requested type, to ensure that the material that supply centre provides
The consistency of material and demand point material requested type；In formula, m indicates the number of material category；The set of M expression material category；
0-1 variable λi,mIndicate that material supply point i provides material m；0-1 variableIndicate that materials demand point j needs material m；0-1 becomes
Measure φi,j,mIndicate that material supply point i provides material m for demand point j；
Formula (9a)~(9d) has judged whether tower crane performance meets the lifting weight demands of supply centre and demand point；In formula, 0-1
Variable εi,j,k,nIndicate the lifting for meeting material supply point i and demand point j simultaneously positioned at the N-shaped tower crane of tower crane feasible location k
Weight；
Formula (10a)~(10c) has judged that tower crane completes the feasibility of this transport of materials task by integrating above-mentioned condition；
In formula, 0-1 variable γi,j,k,m,nIndicate that the N-shaped tower crane positioned at tower crane feasible location k can be by material m from supply centre i handling
To demand point j；
Formula (11) ensure that tower crane can satisfy the materials demand of each demand point；
3) it is influenced by tower crane performance and layout, transport capacity of the tower crane within the unit time is limited；When separate unit tower crane
When the whole lifting tasks being unable to complete in its service range, it is necessary to which more tower cranes cooperate with work within the scope of respective transport capacity
Industry, to complete lifting mission requirements jointly；In order to lift task amount in reasonable distribution tower crane overlapping region, this model is being analyzed
On the basis of lifting operation runing time, tower crane transport capacity is rationally assessed, to establish group constraint condition of tower collaboration transport；
(1) tower crane lifting operating process is the basic integral link that tower crane completes transport of materials flow of task, and assessment tower crane
The basic research object of transport capacity；The process of tower crane lifting operation, is decomposed into horizontal direction operational process and vertical direction fortune
Row process, wherein horizontal direction operation is decomposed into radial operational process and the tangential operation that rotates around tower body along boom direction again
Process；
Formula (12) describes the process that tower crane trolley does radial motion along boom；In formula, TRi,j,k,nIndicate feasible positioned at tower crane
N type tower crane at the k of position runs to the radial runing time of demand point j from material supply point i；Di,kAnd Dj,kIndicate feed point
I and demand point j to be located at tower crane feasible location k at tower crane horizontal distance；| | indicate the arithmetic operation to take absolute value；SRk,n
Indicate the carriage amplitude varying speed of N-shaped tower crane；
Formula (13) describes the process that tower crane boom does tangential motion around swing mechanism；In formula, TTi,j,k,nIt indicates to be located at tower crane
N type tower crane at feasible location k runs to the tangential runing time of demand point j from material feed point i；Di,jIndicate that material supplies
To point i to the distance of demand point j；STk,nIndicate N-shaped tower crane boom velocity of rotation；
Formula (14) describes the tangential influence relationship with tangential operational efficiency of tower crane；In formula, THi,j,k,nIndicating can positioned at tower crane
Line position sets the horizontal direction runing time that the n type tower crane at k runs to demand point j from material feed point i；Max and min difference
Expression takes the arithmetic operation of the larger value and smaller value；σ indicates tower crane in the coordination degree radially and tangentially run, with tower crane department
The technical level of machine is related, value 0.25；
THi,j,k,n=max (TRi,j,k,n,TTi,j,k,n)+σ×min(TRi,j,k,n,TTi,j,k,n),
The vertical direction operational process that formula (15) statement crane hook is carried out with hawser folding and unfolding；In formula, TVi,j,k,nIndicate position
N-shaped tower crane at tower crane feasible location k runs to the vertical direction runing time of demand point j from material feed point i；ZiWith
ZjIndicate the height of material feed point i and demand point j；τ is expressed as guaranteeing Hoisting Security and the minimum sling height that is arranged；SVk,n
Indicate the promotion speed of N-shaped tower crane；
Formula (16) describes the influence relationship of tower crane both horizontally and vertically operational efficiency；In formula, Ti,j,k,nIt indicates to be located at tower crane
N type tower crane at feasible location k runs to the actual run time of demand point j from material feed point i；ρ indicates that tower crane is horizontal
With the coordination degree of vertical direction operation, value 1.00 related to the technical level of tower crane driver；
Ti,j,k,n=max (THi,j,k,n,TVi,j,k,n)+ρ×min(THi,j,k,n,TVi,j,k,n),
(2) transport capacity of tower crane is equivalent to the limit that can be completed in unit time lifting number, i.e. tower crane theory is hung secondary；Mould
Type is by calculating the average operating times of all potential lifting operations in tower crane working range, in conjunction with the every working hour of tower crane,
Estimate tower crane theory lifting number；
Formula (17a)~(17b) has judged whether material feed point i and demand point j are located in the n at feasible location k respectively
In the working range of type tower crane；In formula, 0-1 variable βi,k,nIndicate that material feed point i is located at tower crane feasible location k
In the working range of n type tower crane；βj,k,nIndicate that demand point j is located in the n type tower crane at tower crane feasible location k
In working range；
Whether simultaneously formula (18a)~(18c) judged material feed point i or demand point j n of the place at tower crane feasible location k
In the working range of type tower crane；In formula, 0-1 variable ωi,j,k,nIndicate that material feed point i and demand point j is in tower crane simultaneously
Working range in；
Formula (19) calculates all potential lifting operations in the n type tower crane working range at tower crane feasible location k
Average operating time MTk,n；
Formula (20) calculates the daily theory of the n type tower crane at tower crane feasible location k and hangs time Fk,n；In formula, number 2
Indicate the actual motion state of tower crane reciprocating working；
(3) cooperation between tower crane provides greater flexibility with being combined into tower crane management, also enables each tower crane transport capacity
It gives full play to；Formula (21a)~(21b) is by establishing 0-1 variable γi,j,k,m,nWith integer variable Si,j,k,m,nThe constraint relationship,
Form distribution mechanism of the tower crane lifting task between tower crane, in formula, N indicates a very big positive number；Si,j,k,m,nExpression is located at
Number of the N-shaped tower crane of tower crane feasible location k by material m from material supply point i to demand point j；
Formula (22) guarantees that all lifting tasks can obtain and is efficiently accomplished, in formula, Qj,mMaterial needed for indicating materials demand point j
Expect the weight of m；RmIndicate the weight of the average material m of lifting every time of tower crane；Expression rounds up；
In order to guarantee tower crane operational efficiency, formula (23) ensure that it is theoretical to be no more than it for the practical lifting frequency of tower crane in the unit time
It hangs secondary；If the transport capacity of group's tower can satisfy the lifting mission requirements of construction speed most tonic phase, it can illustrate the choosing
Type and arrangement in other any stages be all it is feasible, in formula, Fk,nIndicate the N-shaped tower crane for being located at tower crane feasible location k
Odd-numbered day maximum lifts number；
4) in the case where the background for saving building cost is constantly sought by construction enterprises, tower crane cost is to measure tower crane type selecting and arrangement
The key index of superiority and inferiority, therefore tower crane use cost is the primary optimization aim of tower crane type selecting Yu layout optimization model；Tower crane at
This both includes tower crane depreciation cost, price for repairing, fuel cost and labour cost cost relevant to construction period, also comprising basis production
Take, the disposable investment such as traffic expense and assembling and disassembling expense；Formula (24) summarizes general expenses and forms tower crane assessment of cost formula；Formula
In, ΦnIndicate the running cost of N-shaped tower crane；ΨnIndicate the constant expense of N-shaped tower crane；The service life of D expression tower crane；
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