CN106651309A - Project schedule tracking adjustment method and system based on PERT - Google Patents

Project schedule tracking adjustment method and system based on PERT Download PDF

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CN106651309A
CN106651309A CN201611205023.1A CN201611205023A CN106651309A CN 106651309 A CN106651309 A CN 106651309A CN 201611205023 A CN201611205023 A CN 201611205023A CN 106651309 A CN106651309 A CN 106651309A
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time
duration
probability
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CN106651309B (en
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刘志清
高浩瀚
张永武
张映晖
刘家远
张学凯
方敬韬
刘佳
刘效真
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State Grid Shandong Electric Power Co Ltd
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Abstract

The invention discloses a project schedule tracking adjustment method and a system based on a PERT. With the planned project duration complying with beta distribution as a basis, a scale principle estimated to be followed by time parameters is demonstrated, a method of replacing the most optimistic time by the minimum time for resource allocation consideration is brought forward, and an estimation basis for time parameters is cleared; a fitting method is adopted to solve the beta distribution corresponding to the time parameters; and finally, a cost-projection duration linear model is further built, according to the beta distribution probability constraints and given project duration float requirements, a schedule plan is solved, and more reasonable schedule plan making is realized. Problems that schedule plan deviation is likely to happen as the time parameter estimation scale is inaccurately mastered and project resource constraints are not considered in the network PERT can be solved, and the method and the system are applicable to scheme plan making and tracking adjustment for a large construction project.

Description

Project process tracking adjustment method and system based on PERT
Technical field
The present invention relates to be based on the project process tracking adjustment method and system of PERT.
Background technology
As project owner now requires project construction side more and more higher, project construction side is in order to ensure project on request Complete, it is necessary to formulate rational project schedule plan, the actual progress of real-time tracking project and in time correction adjustment in addition.Project Plan and adjustment it is indivisible, but in existing method or technology, concentrate on the formulation to project preliminary plan, and adjust Whole plan mostly is experience that is heuristic and depending on construction party, lacks the linked system with plan.
In the method that project schedule plan is formulated, PERT (programme evaluation and review technique) extensive application.PERT is to consider Duration, probabilistic network planning was formulated and assessment technique.It is applied to the basic procedure of project under construction schedule formulation To plot network according to logical relation between project under construction each operation；After the project duration of clear and definite owner is expected, to each operation Duration is estimated, and generally assumes that the duration obeys β distributions, and using triple-time estimate method the distribution is obtained；Finally, with network Expect that the path of the maximum path of duration sum or inter process TF equal to 0, as critical path, draws schedule.Enter one Step can calculate the time kept in reserve of each operation in critical path, deviate for tackling progress in subsequently carrying out in project.PERT is present Yardstick is estimated to time parameter to hold inaccurate and cause schedule formulation larger with actual progress deviation, and does not consider resource Constrain the technical problem affected on three time values.
Additionally, the method for adjustment of project process is mainly the utilization to the inter process time difference or time kept in reserve.In Large Construction In project, due to the complexity of construction network graph structure, in the tracking adjustment of progress, schedule method mostly takes inspiration Formula method adjusts the time kept in reserve, and inefficiency, reasonability is poor, lacks to the overall consideration of project.
The content of the invention
For classical PERT above shortcomings, the present invention propose the project process tracking adjustment method based on PERT and System；Estimate under the hypothesis that the duration obeys β distributions retaining, the meaning and practical situation based on time parameter, to time parameter Selection yardstick carried out clearly；And resource constraint is attached to into the most optimistic time as duration corresponding probability level is estimated In value, the restriction to assignment of due dates is embodied；Finally, with reference to the lax resource constraint of bounding theory thought and consider that quality will Element, sets up expense --- duration linear model, define and meet prescription, complete in advance, realize network minimal simultaneously as far as possible The PERT schedules estimated based on improvement time parameter with higher Completion Probability are formulated.
Based on the project process tracking adjustment method of PERT, methods described has been come by computer program control computer equipment Into the computer that the computer equipment includes memorizer, processor and storage on a memory and can run on a processor Program；Following steps are realized described in the computing device during computer program：
Data input step, typing project essential information, project essential information includes：Prescription conversion to project is general Rate is required, operation divides three temporal informations estimated with activity's precedence relationships, project material information, triple-time estimate method；
Pre-treatment step, process the time parameter estimated obtain correspondence β accumulated probability distributed constants, will be right in data inputting The prescription transition probability of project requires, forms project process using β accumulated probabilities distribution function and require that is, each duration is about Beam, forms construction network scheme and obtains critical path using process information in data；
Project process formulates step, and according to the solving result of Period of Construction Cost model schedule is arranged；
Tracking adjustment step, to project actual progress monitor in real time is carried out, and the actual progress to occurring to deviate is carried out in time Adjustment.
Based on the project process tracking adjustment method of PERT, methods described has been come by computer program control computer equipment Into the computer that the computer equipment includes memorizer, processor and storage on a memory and can run on a processor Program；Following steps are realized described in the computing device during computer program：
Step (1)：The essential information of typing project under construction；Improved PERT is adopted to project under construction each operation time parameter In triple-time estimate method three times are estimated, and typing estimation results；It is corresponding in improved PERT triple-time estimate methods Three times refer to：Consider most optimistic time a, the most pessimistic time b and most likely time m of resource allocation；Data inputting is finished After perform pretreatment operation, choose a maximum construction path of the total lever factor calculated by most pessimistic time b as critical path； The essential information includes that operation is divided and activity's precedence relationships；
Step (2)：Three times estimated using step (1) and three time fixation probability fitting β accumulated probabilities point Cloth function：According to each operation fixation probability P=[P (a), P (m), P (b)] and its it is corresponding estimate duration t=[a, m, b], intend Close out β accumulated probabilities distribution function and make its fitting variance Δ ε minimum, and then the β accumulated probability distributed constant r for obtaining fitting And s；
Step (3)：According to most pessimistic and restriction P (a of the most optimistic time to Completion Probabilityi)≤Pi≤P(bi), to project Ensure that the Completion Probability under quality condition requires Pi≥PQi, by P (ai)、P(bi) andThe β accumulated probabilities of step (2) are substituted into respectively Correspond in distribution function and solve t (ai)、t(bi) andFormed the duration constraint, and integration project administration section to it is motor-driven when Between N requirement build expense-duration linear optimization model, solve on the most pessimistic time the compressible duration；
Step (4)：The most pessimistic time upper compressible duration x obtained by step (3)iAfterwards, target advance is calculated；Engineering item Mesh presses the target advance guiding construction；
Step (5)：Into tracking adjustment module, actual progress is monitored；
Step (6)：Judge actual progress with target advance deviation whether more than setting value；If it is not, then return to step (5)； If just record changes and locates operation serial number K；
Step (7)：According to variation amendment P (a) value of practice of construction resource, according to amendment posterior probability P=[P (a), P (m), P (b)], the value of a, m, b is estimated again；
Step (8)：Judge the number n of total operation whether more than K；If being put into step (9)；Represent that project is in if not Final acceptance process stages, are limited to the deviation occurred on operation final acceptance process stages and only once adjust：Amendment is motor-driven Time N value, again advance estimate modification operation n unit interval compression expense CnValue；Obtain optimization schedule value, tracking adjustment operation Terminate；
Step (9)：Judge that whether compressible duration summation is less than N in critical path, if just amendment N values, and it is again pre- Estimate amendment ciValue, return to step (2)；If it is not, direct return to step (2).
Triple-time estimate method in the step (1) in improved PERT is estimated to three times, and i-th operation is most Optimistic time aiTo consider the minimum time of resource allocation, according to Completion Probability P (ai) estimated.
Oi：The number of resources of i-th operation occupancy, resource refers to working sources, such as specialized team of different work posts；R：Work Journey project total resources number；P(ai)∈(0,1)；Most likely time, m was estimated according to Completion Probability P (m)=0.5；When most pessimistic Between b estimated according to Completion Probability P (b)=0.95.
The β accumulated probability distribution functions of the step (2)：
R and s：Accumulated probability distributed model unknown shape parameter；
Fitting variance Δ ε：
Completion Probability requirement lower limit project ensured under quality condition of the step (3)：
Wherein, PQiEnsure project that the Completion Probability under quality condition requires lower limit for owner；Qi：Construction quality will Ask, multiscale can be divided into, as prescription is high, Q is seti=0.95, the high Q of prescriptioni=0.85, prescription is general Qi=0.75；ωi：Conversion coefficient between quality Completion Probability；
Expense-duration linear optimization model：
Constraints includes that the compressible duration under the constraint of operation duration compressible level, guarantee quality constrains and motor-driven Time-constrain：
xi≤t(bi)-t(ai)；
Wherein, C：The total cost that project is produced because of the compression duration；Ci：The operation i unit interval compresses expense, by estimating Arrive；xi：The compressible duration on the most pessimistic time；t(ai)：Duration probability P (a at most optimistic timei) correspond to β accumulated probabilities Duration under distribution；t(bi)：The duration probability of most pessimistic time is corresponding to the duration under the distribution of β accumulated probabilities；tQi：Owner couple Completion Probability requires lower limit P in the case that project ensures qualityQiDuration under correspondence β accumulated probability distributions；N：When engineering is motor-driven Between, to the situation for tackling burst or deviation plan, adjusted according to actual progress.
The computing formula of the target advance of the step (4) is：
Hi=bi-xi
By calculated HiValue is used as target advance.
In the step (8) and step (9), the amendment of time kept in reserve N value is adjusted according to actual progress, but must be fulfilled for Lower two conditions：
Meet owner's construction period T, i.e.,
To ensure mobility, time kept in reserve N value is less than or equal to 80% of maximum compressible duration sum in critical path, i.e.,
Based on the project process tracking adjustment system of PERT, including：Memorizer, processor and storage are on a memory and can The computer program for running on a processor；The processor includes：
Data input module, for typing project essential information, project essential information includes：The prescription of project is turned Change probability demands, operation and divide three temporal informations estimated with activity's precedence relationships, project material information, triple-time estimate method；
Pretreatment module, obtains correspondence β accumulated probability distributed constants, by data inputting for processing the time parameter estimated In the prescription transition probability of project is required, form project process using β accumulated probabilities distribution function and require, i.e., each duration Constraint, forms construction network scheme and obtains critical path using process information in data；
Project process formulates module, for arranging schedule according to the solving result of Period of Construction Cost model；
Tracking adjustment module, for carrying out monitor in real time to project actual progress, the actual progress to occurring to deviate is carried out Adjustment in time.
Beneficial effects of the present invention：
1 present invention is capable of achieving to estimate the science of three time parameters of operation the rational with project schedule plan；
2 present invention are capable of achieving the real-time tracking adjustment of the project process that linkage is formed with plan；
Schedule formulation and tracking adjustment are not affected by the complexity of construction network graph structure in 3 present invention.
Description of the drawings
Fig. 1 is present system structure chart
Fig. 2 is the overview flow chart of the present invention；
Fig. 3 is that example flow chart is formulated in schedule；
Fig. 4 is that classics PERT and improved method progress measurement index probability comparison diagram under example are formulated in schedule.
Specific embodiment
Below in conjunction with the accompanying drawings the invention will be further described with embodiment.
Present system structure is as shown in Figure 1.Structure is divided into data input module, pretreatment module, schedule module And tracking adjustment module.
Fig. 2 is the overview flow chart of the present invention, and Fig. 3 is that example flow chart is formulated in schedule, as shown in the figure.Realization is based on Improve comprising the following steps that for the PERT schedule formulating methods that time parameter is estimated：
1) each operation duration of certain project single label network planning figure is estimated by most pessimistic duration b, chooses chief engineer The critical path for obtaining is expressed as 1 → 2 → 3 → 4 → 5, critical process by one construction path of phase maximum as critical path Flow chart is as shown in figure 3, the activity description that the nodal scheme in path is represented is constituted；
2) it is i.e. most happy to two other time value of 5 procedure-nodes in the schedule formulation example flow chart of Fig. 3 Seeing a, most likely time m also needs to be estimated；
3) β Cumulative Distribution Functions are fitted using three time fixation probabilities, i.e., according to each operation fixation probability P=[P (a), P (m), P (b)] and its it is corresponding estimate duration t=[a, m, b], (t is respectively in example of the present invention1,P1)、(t2,P2)、 (t3,P3)、(t4,P4)、(t5,P5) fit the β distributions of each operation respectively and make its fitting variance Δ ε1、Δε2、Δε3、Δε4、 Δε5Minimum, and then the β distributed constants for obtaining fitting.
Example evaluation time, probability parameter：
The time estimation parameter list of table 1 three
Node serial number P(a) ta P(m) tm P(b) tb
1 0.75 33 0.5 25 0.95 40
2 0.375 8 0.5 10 0.95 18
3 0.625 14 0.5 12 0.95 20
4 0.625 21 0.5 18 0.95 30
5 0 3 0.5 5 0.95 9
The β cumulative distribution parameters that fitting draws：
The β cumulative distribution parameter lists of table 2
Node serial number r s
1 1.7311 1.3114
2 1.4574 1.4319
3 1.8128 1.5582
4 1.8128 1.5582
5 10.2629 5.1974e+06
Wherein, r, s：Accumulated probability distributed model unknown shape parameter
4) estimate three times and the β distributed datas expense of bringing into for obtaining-duration linear model are solved most happy The sight time upper compressible duration：
Constraints includes that the probability constraintses of operation duration compressible level, quality constraint, administration section are required in advance Completion
Duration constraint：
xi≤t(bi)-t(ai)
xi≤t(bi)-tQi
Wherein, Ci：The operation i unit interval compresses expense, estimates and obtains；xi：In P (bi) corresponding time biOn the basis of work The compressible duration of sequence i；t(ai)：Duration probability P (a at most optimistic timei) corresponding to the duration under the distribution of β accumulated probabilities；t (bi)：The duration probability of most pessimistic time is corresponding to the duration under the distribution of β accumulated probabilities；Owner ensures project the feelings of quality Completion Probability requires P under conditionQiDuration under correspondence β accumulated probability distributions；Qi：Prescription；ωi：Turn between quality Completion Probability Change coefficient；N：Time kept in reserve.
To expense-duration linear optimization Model Parameter setting：
3 expenses of table-duration linear optimization Model Parameter table
5) 5 operations all solve compression duration x in exampleiAfterwards, using xiSolve schedule Hi, schedule asks Solution formula：
Hi=bi-xi
Schedule result：
The schedule result of table 4
6) present invention in inventive method schedule Comparative result classics PERT schedule results：
The schedule effect comparison table of table 5
The progress that the Completion Probability of the schedule that inventive method is obtained is obtained with classics PERT schedules in the present invention The comparison of scheduled completion probability such as Fig. 4.
Shown by example comparative result：In the inventive method each operation H and for 92, each operation m in classical PERT With for 70, ∑ H is significantly greater than ∑ m, and relief area N has been left while schedule requirement is met for tackling emergency case；And H Probability in correspondence β probability distribution probability in most cases more than μ, more meets the completion to critical process and is expected；Probability is 0 Corresponding calculated term of works, slightly larger than the value of calculation in the inventive method in classical PERT, but all presses close to 0；Probability is 1 corresponding Calculated term of works, the value of calculation being significantly greater than in classical PERT in improved method, and it is more beyond b, and in the inventive method Value of calculation is closer to b, and the inventive method more meets duration estimation practical situation；The calculating variance of the inventive method is much smaller than classics Calculating variance in PERT.
Although the above-mentioned accompanying drawing that combines is described to the specific embodiment of the present invention, not to present invention protection model The restriction enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not Need the various modifications made by paying creative work or deformation still within protection scope of the present invention.

Claims (10)

1. the project process tracking adjustment method based on PERT, is characterized in that, methods described is by computer program control computer Completing, the computer equipment includes memorizer, processor and storage on a memory and can run on a processor equipment Computer program；Following steps are realized described in the computing device during computer program：
Data input step, typing project essential information, project essential information includes：Will to the prescription transition probability of project Ask, operation divides three temporal informations estimated with activity's precedence relationships, project material information, triple-time estimate method；
Pre-treatment step, process the time parameter estimated obtain correspondence β accumulated probability distributed constants, by data inputting to project Prescription transition probability require, form project process using β accumulated probabilities distribution function and require, i.e. each duration constraint, profit Construction network scheme is formed with process information in data and obtain critical path；
Project process formulates step, and according to the solving result of Period of Construction Cost model schedule is arranged；
Tracking adjustment step, to project actual progress monitor in real time is carried out, and the actual progress to occurring to deviate is adjusted in time.
2. the project process tracking adjustment method based on PERT as claimed in claim 1, is characterized in that, methods described is by calculating Completing, the computer equipment includes memorizer, processor and storage on a memory simultaneously to machine programmed computer apparatus The computer program that can be run on a processor；Following steps are realized described in the computing device during computer program：
Step (1)：The essential information of typing project under construction；To project under construction each operation time parameter using in improved PERT Triple-time estimate method is estimated to three times, and typing estimation results；Corresponding three in improved PERT triple-time estimate methods Time refers to：Consider most optimistic time a, the most pessimistic time b and most likely time m of resource allocation；Data inputting is held after finishing Row pretreatment operation, chooses a construction path of the total lever factor maximum calculated by most pessimistic time b as critical path；It is described Essential information includes that operation is divided and activity's precedence relationships；
Step (2)：Three times estimated using step (1) and three time fixation probability fitting β accumulated probability distribution letters Number：According to each operation fixation probability P=[P (a), P (m), P (b)] and its it is corresponding estimate duration t=[a, m, b], fit β accumulated probabilities distribution function and make its fitting variance Δ ε minimum, and then β accumulated probability the distributed constant r and s for obtaining fitting；
Step (3)：According to most pessimistic and restriction P (a of the most optimistic time to Completion Probabilityi)≤Pi≤P(bi), project is ensured Completion Probability under quality condition requires Pi≥PQi, by P (ai)、P(bi) andThe β accumulated probabilities distribution of step (2) is substituted into respectively Correspond in function and solve t (ai)、t(bi) andDuration constraint is formed, and integration project administration section is to time kept in reserve N's Structure expense-duration linear optimization model is required, the compressible duration on the most pessimistic time is solved；
Step (4)：The most pessimistic time upper compressible duration x obtained by step (3)iAfterwards, target advance is calculated；Engineering project is pressed The target advance guiding construction；
Step (5)：Into tracking adjustment module, actual progress is monitored；
Step (6)：Judge actual progress with target advance deviation whether more than setting value；If it is not, then return to step (5)；If Just record changes and locates operation serial number K；
Step (7)：According to variation amendment P (a) value of practice of construction resource, according to amendment posterior probability P=[P (a), P (m), P (b)], the value of a, m, b is estimated again；
Step (8)：Judge the number n of total operation whether more than K；If being put into step (9)；Represent project in last if not Process stages are checked and accepted, the deviation occurred on operation final acceptance process stages is limited to and is only once adjusted：Amendment time kept in reserve N Value, again advance estimate modification operation n unit interval compression expense CnValue；Obtain optimization schedule value, tracking adjustment end of run；
Step (9)：Judge that whether compressible duration summation is less than N in critical path, if repairing with regard to correcting N values, and estimating again Positive ciValue, return to step (2)；If it is not, direct return to step (2).
3. method as claimed in claim 2, is characterized in that, the triple-time estimate method pair in the step (1) in improved PERT Three times are estimated, the most optimistic time a of i-th operationiTo consider the minimum time of resource allocation, according to Completion Probability P(ai) estimated；
P ( a i ) = O i R + 1
Oi：The number of resources of i-th operation occupancy, resource refers to working sources, such as specialized team of different work posts；R：Engineering item Mesh total resources number；P(ai)∈(0,1)；Most likely time, m was estimated according to Completion Probability P (m)=0.5；Most pessimistic time b Estimated according to Completion Probability P (b)=0.95.
4. method as claimed in claim 2, is characterized in that, the β accumulated probability distribution functions of the step (2)：
P = F ( x | r , s ) = 1 B ( r , s ) ∫ 0 x t r - 1 ( 1 - t ) s - 1 d t
R and s：Accumulated probability distributed model unknown shape parameter；
Fitting variance Δ ε：
Δ ϵ = 1 n Σ i = 1 n [ β ( t i ) - P i ] 2 .
5. method as claimed in claim 2, is characterized in that, the completion ensured project under quality condition of the step (3) Probability demands lower limit：
P Q i = 1 - Q i ω i
Wherein, PQiEnsure project that the Completion Probability under quality condition requires lower limit for owner；Qi：The requirement of construction quality, can Multiscale is divided into, as prescription is high, Q is seti=0.95, the high Q of prescriptioni=0.85, the general Q of prescriptioni= 0.75；ωi：Conversion coefficient between quality Completion Probability.
6. method as claimed in claim 5, is characterized in that,
Expense-duration linear optimization model：
min C = Σ i = 1 n C i x i ;
When constraints includes that the compressible duration under the constraint of operation duration compressible level, guarantee quality constrains and be motor-driven Between constrain：
xi≤t(bi)-t(ai)；
x i ≤ t ( b i ) - t Q i ;
Σ i = 1 n x i ≥ N ;
Wherein, C：The total cost that project is produced because of the compression duration；Ci：The operation i unit interval compresses expense, is obtained by estimating； xi：The compressible duration on the most pessimistic time；t(ai)：Duration probability P (a at most optimistic timei) corresponding to the distribution of β accumulated probabilities Under duration；t(bi)：The duration probability of most pessimistic time is corresponding to the duration under the distribution of β accumulated probabilities；Owner protects to project Completion Probability requires lower limit P in the case of card qualityQiDuration under correspondence β accumulated probability distributions；N：The engineering time kept in reserve, to Reply burst deviates situation about planning, and is adjusted according to actual progress.
7. method as claimed in claim 2, is characterized in that, the computing formula of the target advance of the step (4) is：
Hi=bi-xi
By calculated HiValue is used as target advance.
8. method as claimed in claim 2, is characterized in that, in the step (8) and step (9), the amendment of time kept in reserve N value Adjusted according to actual progress, but must be fulfilled for following two conditions：
Meet owner's construction period T, i.e.,
To ensure mobility, time kept in reserve N value is less than or equal to 80% of maximum compressible duration sum in critical path, i.e.,
9. the project process tracking adjustment system based on PERT, is characterized in that, including：Memorizer, processor and it is stored in storage On device and the computer program that can run on a processor；The processor includes：
Data input module, for typing project essential information；
Pretreatment module, for process the time parameter estimated obtain correspondence β accumulated probability distributed constants, will be right in data inputting The prescription transition probability of project requires, forms project process using β accumulated probabilities distribution function and require that is, each duration is about Beam, forms construction network scheme and obtains critical path using process information in data；
Project process formulates module, for arranging schedule according to the solving result of Period of Construction Cost model；
Tracking adjustment module, for carrying out monitor in real time to project actual progress, the actual progress to occurring to deviate is carried out in time Adjustment.
10. the project process tracking adjustment system based on PERT as claimed in claim 9, is characterized in that, project essential information Including：The requirement of prescription transition probability, operation to project is estimated when dividing with activity's precedence relationships, project material information, three Three temporal informations that meter method is estimated.
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CN114282827A (en) * 2021-12-27 2022-04-05 中铁建工集团有限公司 Method and system for scheduling construction period progress
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