CN112308333B - Construction progress risk control method based on random probability - Google Patents
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Abstract
The invention discloses a construction progress risk control method based on random probability, which comprises the following steps: 1) The method comprises the steps of obtaining decomposition work of a construction project plan, wherein the least work time L, the longest work time U and the general work time M of each work are obtained; 2) Setting a control standard threshold value of construction project cut-off date and failure probability; 3) Modeling the work by adopting a planning network model; 4) Sampling the working time length through three-point estimation parameters, estimating the failure probability through a sampling sample, and recording the average floating time and the average lag time of each work in the failure sample; 5) And carrying out risk prediction according to the planned failure probability calculation result. The method can quickly and effectively calculate the possibility of out-of-date failure of a given plan in a fixed delivery period, find out work which is easy to cause failure, assist project managers to carry out planning optimization, and greatly improve evaluation efficiency and optimization quality in large-scale projects.
Description
Technical Field
The invention relates to a construction engineering technology, in particular to a construction progress risk control method based on random probability.
Background
Classical project control theory assumes that work is done at a fixed time, without consideration of the possibility of advancing or pushing back in actual execution, which results in the theoretical duration of the critical path being smaller than the actual completion of the project in some special cases, which is particularly apparent when there is a large uncertainty in the project, which also results in an overly optimistic estimate of the project completion. This can present significant risk of default to the constructor in projects where delivery times are explicitly specified. To ensure smooth delivery of the schedule, typically, the manager will reserve a buffer time for the project in advance, but the rationality of the choice of the buffer time depends entirely on the manager's experience, and experience-based methods are difficult to quantify and standardize.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a construction progress risk prediction method based on random probability, by which the possibility of out-of-date failure of a given schedule in a fixed delivery period can be rapidly and effectively calculated.
The technical scheme adopted for solving the technical problems is as follows: a construction progress risk control method based on random probability comprises the following steps:
1) The method comprises the steps of obtaining decomposition work of a construction project plan, wherein the least work time L, the longest work time U and the general work time M of each work are obtained;
2) Setting a control standard threshold value of construction project cut-off date and failure probability;
3) Modeling the works by adopting a planning network model, wherein each work is regarded as a node V, the dependency relationship between the works is regarded as a directed edge E, and the two are combined into a directed graph G (V, E); each node contains all information of work, including three-point parameters (L, M, U) used, work number and work name; each edge contains work dependency information, if work A is connected to work B, then A is the immediately preceding work of B, B is the immediately following work of A, for each work, only if all the immediately preceding works are all completed, the work can be started;
4) The three-point estimation parameters model the probability of the working time length, sample the probability, solve the total time length of the sample by adopting a Digestron algorithm (Modified Dijkstra Algorithm), perform state transition by using a Markov chain Monte Carlo Method (MCMC), estimate the failure probability by using a subset simulation method (Subset Simulation), and record the average floating time and the average lag time of each point in the failure sample. The detailed steps are as follows:
step 4.1) topologically ordering the planned network using the Kahn Algorithm Algorithm (Kahn Algorithm), which steps are as follows:
step 4.1.1) calculating the degree of ingress of each node of the planning network model, wherein the degree of ingress is the number d of directed edges pointing to the node i i ：
d i ＝|N i |,N i ＝{n|(n,i)∈E}
Wherein N is i For a node set of a node i adjacent to and pointing to the node i, i·| is the cardinality of the set, representing the size of the set;
step 4.1.2) finding out a node with the degree of entry of 0, removing the node from the planning network, and putting the node into the sorting;
step 4.1.3) if all nodes are removed, the resulting ordering is the topology order of the planned network.
Step 4.2) sampling the working time of each work;
step 4.3) calculating the total duration of the planned network using the dijkstra algorithm (Modified Dijkstra Algorithm), which steps are as follows:
step 4.3.1) respectively calculating the earliest starting time and the earliest ending time of each work according to the topological positive sequence of the planned network:
for each job, if its immediately preceding job is empty, its earliest start time is 0, if not empty, its earliest start time is the earliest end time of the job that ends the latest in the immediately preceding job; the earliest end time is the earliest start time plus the sampling working time:
EF i ＝ES i +T i
the end time of the work that ends the latest among all works is the total duration of the planned network:
step 4.3.2) calculating the latest start and the latest end of each work according to the topological reverse order of the planned network:
for each work, e.g. its immediately following work is empty, its latest end time is the total duration T e If not, the latest ending time is the latest starting time of the earliest started work in the immediately following work;
LS i ＝LF i -T i
step 4.3.3) if the total time period is greater than the time limit, adding the sample to the failure record;
step 4.4) calculating the failure probability of the plan:
wherein N is f N is the number of samples that fail, N is the number of all samples;
step 4.5) recording the floating time of each work in the sample and whether the work is a key work or not;
calculating a float time for each job:
F i ＝ES i -ES i ＝LF i -EF i
the work with the floating time of 0 is the key work;
the key coefficients and average float time of each key work are calculated as follows:
wherein sigma i For average lag timeSigma under three-point estimation i ＝(U i -M i ) 3, key coefficientThe average impact of work i on project lag is described, and the average float describes the average adjustable buffering time of each work; more critical work will have larger key coefficients and smaller average float times;
5) And carrying out risk prediction according to the failure probability calculation result of the plan, if the failure probability of the plan exceeds a set control standard threshold value, indicating that the risk exceeds the expected value, and if the risk is not acceptable, carrying out construction by using the plan.
If the failure probability of the plan exceeds the set control standard threshold, optimizing workflow related to key work or adjusting resource investment of the workflow, re-estimating working time of each work under the new plan, and repeating the step 4) until the failure probability meets the control requirement;
6) And 4) carrying out importance dyeing on the work in the planning network by utilizing the key coefficient obtained in the step 4), and making a Gantt chart to be exported.
The invention has the beneficial effects that:
the method can quickly and effectively calculate the possibility of out-of-date failure of a given plan in a fixed delivery period, find out the work which is easy to cause failure, assist project managers to carry out plan optimization, solve the problem that the plan optimization cannot be quantified purely by experience, greatly improve the evaluation efficiency and the optimization quality in large-scale projects, and have higher practical value.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a schematic diagram of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a planning network in accordance with an embodiment of the present invention;
FIG. 3 is a Gantt chart of an embodiment of the present invention;
FIG. 4 is a schematic diagram of a planned network calculation result according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of the calculation results of an optimized planning network according to an embodiment of the present invention;
fig. 6 is a schematic diagram showing the change of the failure probability before and after the time limit is extended according to the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The construction progress risk prediction method based on the random probability is characterized in that under the condition that the completion time of each work meets the three-point distribution, the planned overdue failure refers to the possibility that the duration of a critical path is longer than the given cut-off time under the condition that the work duration is given, and the failure probability refers to the possibility that the total duration is longer than the cut-off date under the condition that the work duration is a random variable meeting the three-point distribution. To describe the uncertainty of the work, the invention is described by three-point distribution assumption, namely, the least work time (marked as L), the general work time (marked as M) and the longest work time (marked as U), and the mathematical expression is as follows:
since three-point estimation is employed, the case where the operation time period is smaller than the shortest estimation time period and larger than the longest estimation time period is not considered in the present invention.
The invention models a work plan using a plan network model, wherein each work is regarded as a node (V) and the dependency between works is regarded as a directed edge (E), which together form a directed graph G (V, E). Each node contains all information of the work itself, such as three-point parameters (L, M, U) of time, work number, work name and the like, and each side contains work dependency information, such as A work is connected to B work, then A is the immediately preceding work of B, and B is the immediately following work of A. For each job, the job can only be started if all immediately preceding jobs are completed; if the job is not completed, all immediately following jobs cannot be started.
As shown in fig. 1, a construction progress risk control method based on random probability includes the following steps:
step one: reading a work plan network file and a work time length estimated value thereof which are given by a project manager, and constructing a plan network;
in the first step, the user needs to provide the immediately preceding work and the immediately following work of each work, and three-point estimation is used for estimating the working time length, so that the most optimistic (shortest), the most pessimistic (longest) and the most probable (general) time are needed to be provided. The detailed steps are as follows:
step 1.1: reading in project plan files, wherein all works form node sets of a plan network, all work attachment relations form edge sets of the plan network, and the node sets together form the plan network G (V, E):
v= { u|u is the work in the plan }
E= { (u, v) |u, v has a work dependency }
Step 1.2: three-point estimation is carried out on each working time length:
T i ～P(L i ,M i ,U i )i∈V
the samples for each variable are noted as t i The distribution of samples satisfies the above-mentioned three-point distribution.
Step two: estimating the failure probability of the planning network by using the algorithm and the input parameters;
in the second step, the three-point estimation parameters provided in the first step are used for sampling the working time, a Digestron algorithm (Modified Dijkstra Algorithm) is adopted for solving the total time, a Markov chain Monte Carlo Method (MCMC) is used for carrying out state transition, a subset simulation method (Subset Simulation) is used for estimating the failure probability, and the average floating time and the average lag time of each point in the failure sample are recorded. The detailed steps are as follows:
step 2.1: the planned network is topologically ordered using the Kahn Algorithm Algorithm (Kahn Algorithm), which steps are as follows:
step 2.1.1: the ingress of each node is calculated, defined as the number of directed edges pointing to that node:
d i ＝|N i |,N i ＝{n|(n,i)∈E}
step 2.1.2: finding out a node with the degree of incidence of 0, removing the node from the planning network, and placing the node in the sorting;
step 2.1.3: if all nodes are removed, the resulting ordering is the topological order of the planned network.
Step 2.2: and sampling the working time of each work.
Step 2.3: the total duration of the planned network is calculated using the modified dijkstra algorithm (Modified Dijkstra Algorithm) as follows:
step 2.3.1: calculating the earliest start and earliest end of each work according to the topological positive sequence of the planning network:
for each job, if its immediately preceding job is empty, its earliest start is 0, if not empty, and its earliest start is the earliest end of the latest end of the immediately preceding jobs. The earliest end is the earliest start plus the working time of sampling:
EF i ＝ES i +T i
the end time of the work that ends the latest among all works is the total duration of the planned network:
step 2.3.2: calculating the latest start and the latest end of each work according to the topological reverse order of the planned network:
for each work, e.g. its immediately following work is empty, its latest end is the total time length T e If not, its latest start is the latest start of the earliest start of the immediately following work.
LS i ＝LF i -T i
Calculating the floating man-hour for each job:
F i ＝ES i -ES i ＝LF i -EF i
the operation with a float time of 0 is a critical operation.
Step 2.3.3: if the total time period is greater than the time limit, the sample is added to the failure record.
Step 2.3.4: record the sample's float time and whether it is critical.
Step 2.4: the planned failure probability is defined as follows:
wherein N is f For the number of samples that fail, N is the number of all samples.
Step 2.5: the key coefficients and average float of each job are calculated as follows:
wherein sigma i For average lag time, σ in three-point estimation i ＝(U i -M i ) The criticality factor describes the average impact of the work on project lag, and the average float describes the average adjustable buffering time of each work. More critical jobs will have a greater key coefficient and a smaller average float.
Step three: evaluating the failure probability under the condition of a given control level, if the control requirement is met, performing a step six, otherwise, performing a step four;
in the third step, the user needs to give a reference standard according to the risk bearing capacity of the user, if the calculated failure probability is larger than the value, the risk is beyond expectations, and the plan needs to be improved, otherwise, the risk is acceptable, and the plan can be used for execution.
Step four: prolonging the deadline, or positioning the key work by utilizing the key coefficient obtained in the step three, adjusting workflow related to the key work or adjusting resource investment of the workflow, re-estimating working time of each work under a new plan, and repeating the step two until the failure probability meets the control requirement;
in the fourth step, if the plan cannot control the excessive risk under the given time limit, the time limit can be prolonged or the plan can be adjusted to improve the reliability of the plan; if the adjustment plan is selected, the key coefficient obtained by calculation in the second step can be calculated from the recorded failure sample, so as to represent the average overdue time of the total progress overdue caused by the working overdue, and the working relationship or resource investment of the working with high coefficient can be optimized in the fifth step.
Optimizing the working relation or resource investment comprises optimizing the working time of the work, so that the labor investment can be increased, the time can be reduced, and the required time can be updated based on the manual time required by the workload; or the working sequence is adjusted, the workflow is simplified, and the work before and after the work is updated. The new plan should be recalculated and evaluated in step two.
Step five: and (3) carrying out importance dyeing on the planned network by utilizing the key coefficient obtained in the step (III), and making a Gantt chart to be exported.
Fig. 2 and 3 are plan networks for use with the embodiments, the networks comprising 10 jobs and 13 job dependencies. The project manager now has to evaluate the possibility of delivering it on schedule under given time constraints, such as the difficulty of quantitatively evaluating the objective empirically alone, which can be obtained relatively easily by means of the method of the invention.
Example item estimation values (Unit: tian) for professional construction
The following is a description of specific implementations and predictive applications of the invention.
1. Adjusting work with definite time period
Step one: importing a plan and selecting a demonstration case;
step two: setting the most pessimistic and the most optimistic time and general time for each work respectively;
step three: setting the cut-off date as 100 days, controlling the failure probability standard as 0.5%, clicking an evaluation button, and evaluating the work plan;
step four: the planned failure probability is calculated to be about 1.02%, the control requirement is not met, the critical value is set to be 0.5 day, the critical coefficient of construction work of the building 2, the building 3 and the roof is found to be higher, and the optimization is selected;
step five: re-planning the work selected in the steps, compressing the work to 18 days when the structure specialty is the most pessimistic, compressing the work to 24 days when the roof construction is the most pessimistic, and calculating the work when the work is re-estimated;
example project time-consuming estimation values (Unit: tian) after optimization of each professional construction
Step six: the resulting failure probability was found to have fallen to 0.00%, indicating that the current schedule has met the control requirements, and that the work schedule was derived for execution.
Comparing fig. 4 and 5, it can be seen that the modified plan, while substantially identical from a general time perspective, is safer because the latter has less variability in critical work and is easier to control overall. In more complex schedules, the method can easily find out the work which is easy to run away, thereby ensuring the on-time delivery of the project.
2. Estimating required completion time given planning information and control objectives
Step one: importing a plan and selecting a demonstration case;
step two: setting the most pessimistic and the most optimistic time and general time for each work respectively;
step three: setting a control failure probability standard as 1%, primarily estimating the total time for 95 days, clicking an evaluation button, and evaluating a work plan;
step four: the planned failure probability is calculated to be about 24.66%, and the control standard is not satisfied, so that the time required for the increase is up to 100 days. The new time-consuming and re-evaluating schedule is set to obtain the failure probability of approximately 0.98 percent, which is smaller than the control standard, so that the time-consuming project is expected to take 100 days to ensure that the project can be delivered smoothly.
Step five: the plan is exported and executed.
As can be seen by comparing the time limit of fig. 6 before and after the time limit is extended, since most samples fall into 86 days to 100 days, when 95 days are selected as project time nodes, there is a high possibility that on-schedule delivery cannot be achieved, and the time limit is re-formulated according to the distribution, so that the requirements can be met. The method can assist a project manager to better expect the time required for completing the project when the project combination is not signed, and provides a basis for formulating a scientific and controllable target.
It will be understood that modifications and variations will be apparent to those skilled in the art from the foregoing description, and it is intended that all such modifications and variations be included within the scope of the following claims.
Claims (3)
1. The construction progress risk control method based on the random probability is characterized by comprising the following steps of:
1) The method comprises the steps of obtaining decomposition work of a construction project plan, wherein the least work time L, the longest work time U and the general work time M of each work are obtained;
2) Setting a control standard threshold value of construction project cut-off date and failure probability;
3) Modeling the works by adopting a planning network model, wherein each work is regarded as a node V, the dependency relationship between the works is regarded as a directed edge E, and the two are combined into a directed graph G (V, E); each node contains all information of work, including three-point parameters (L, M, U) used, work number and work name; each edge contains work dependency information, if work A is connected to work B, then A is the immediately preceding work of B, B is the immediately following work of A, for each work, only if all the immediately preceding works are all completed, the work can be started;
4) Sampling the working time length through three-point estimation parameters, solving the total time length of a sample by using a Digestrot algorithm, performing state transition by using a Markov chain Monte Carlo method, estimating the failure probability by using a subset simulation method, recording whether each work in the failure sample is CPM key work and the floating time thereof, and calculating the average floating time and key coefficient of the key work by using the sample;
in the step 4), the failure probability is estimated by using a subset simulation method, whether each work in the failure sample is a CPM key work and the floating time thereof are recorded, and the step of calculating the average floating time and the key coefficient of the key work by using the sample is as follows:
step 4.1) performing topological ordering on the planned network;
step 4.2) sampling the working time of each work to obtain a sampling sample;
step 4.3) according to the topological order of the planning network, calculating the total duration of the planning network of each sample, and recording failure samples;
for each sample, calculating the total duration of the planned network by using a Di Jie Style algorithm, and recording a failure sample; the method comprises the following steps:
step 4.3.1) respectively calculating the earliest starting time and the earliest ending time of each work according to the topological positive sequence of the planned network;
earliest start time ES of each job i ：
For each job, if its immediately preceding job is empty, its earliest start time is 0, if not empty, its earliest start time is the earliest end time of the job that ends the latest in the immediately preceding job;
wherein P is i All the immediately preceding working sets of the working i in the planning network;
the earliest end time EF of each job i As the earliest start time ES i Adding the sampling working time length:
EF i ＝ES i +T i ；
wherein T is i The working time length of the sampling of the working i is;
the end time of the latest work among all works is the total duration T of the planning network e ：
Step 4.3.2) calculating the latest starting time and the latest ending time of each work according to the topological reverse order of the planned network:
latest end time LF i ：
For each work, e.g. its immediately following work is empty, its latest end time is the total duration T e If not, the latest ending time is the latest starting time of the earliest started work in the immediately following work;
latest start time LS i Subtracting the sampling working time length from the latest ending time;
LS i ＝LF i -T i ；
step 4.3.3) if the total time period is greater than the time limit, adding the sample to the failure record;
step 4.4) calculating the failure probability of the plan
Wherein N is f N is the number of samples that fail, N is the number of all samples;
step 4.5) recording the floating time of each work in the sample and whether the work is a key work or not; calculating key coefficients of key workAnd average float +.>
Calculating a float F for each job i ：
F i ＝LS i -ES i ＝LF i -EF i
The work with the floating time of 0 is a key work in CPM, and the key work in the sample can be used for calculating the key coefficient of the work;
calculating key coefficients of key workAnd average float +.>The formula is as follows:
wherein sigma i For average lag time, σ in three-point estimation i ＝(U i -M i ) 3, key coefficientThe average impact of key work i on project lag is described, and the average floating time describes the average adjustable buffer time of each work; more critical work will have larger key coefficients and smaller average float times;
5) And carrying out risk prediction according to the failure probability calculation result of the plan, if the failure probability of the plan exceeds a set control standard threshold value, indicating that the risk exceeds the expected value, and if the risk is not acceptable, carrying out construction by using the plan.
2. The construction progress risk control method based on random probability according to claim 1, wherein in the step 4.1), a constellations algorithm is used for topological ordering of the planned network, specifically as follows:
step 4.1.1) calculating the degree of ingress of each node of the planning network model, wherein the degree of ingress is the number d of directed edges pointing to the node i i ：
d i ＝|N i |,N i ＝{n|(n,i)∈E}
Wherein N is i For a node set of a node i adjacent to and pointing to the node i, i·| is the cardinality of the set, representing the size of the set;
step 4.1.2) finding out a node with the degree of entry of 0, removing the node from the planning network, and putting the node into the sorting;
step 4.1.3) if all nodes are removed, the resulting ordering is the topology order of the planned network.
3. The construction progress risk control method based on random probability according to claim 1, wherein the improvement of the plan is required in the step 5), specifically comprising the following steps:
if the failure probability of the plan exceeds the set control standard threshold, optimizing the workflow related to the key work or adjusting the resource investment of the workflow, re-estimating the working time of each work under the new plan, and repeating the step 4) until the failure probability meets the control requirement.
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