Study on the Optimization Modeling of Construction Time Considering the Dependence of Durations

2018 International Conference on Modeling, Simulation and Analysis (ICMSA 2018) ISBN: 978-1-60595-544-5

Study on the Optimization Modeling of Construction Time Considering

the Dependence of Durations

Jun-wen MO, Jing ZHAO

and Zhao-ze HE

School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou Gansu 730070, China

*Corresponding author

Keywords: Duration dependence, Pearson product-moment correlation coefficient, Nonlinear structural equation, Time optimization.

Abstract. In order to solve the problem of project time optimization considering the dependence of durations, and on the basis of the existing literature the Pearson product-moment correlation coefficient and the nonlinear structural equation model are adopted to measure serial duration dependence and parallel dependence separately in the construction projects, and which are used to update the duration data. The mathematical model of the optimization of construction time is set up while the cost as a constraint, at the same time the optimization model is modified by considering the duration dependence, and finally the time optimization is achieved by using genetic algorithm. By taking into account the optimization modeling of construction time considering the dependence of durations, an empirical study is carried out to get the ideal results. This method, which has good guidance and practicability, can be used to solve the problem of time delay in the actual project.

Introduction

Domestic and foreign scholars have studied the project time optimization problem from different angles. Önder Halis Bettemir and Rifat Sonmez [1] use the strategy proposed aims to integrate parallel search ability of genetic algorithms with fine tuning capabilities of the simulated annealing technique to achieve an efficient algorithm for the RCPSP. Wail Menesi [2] points out that the constraint programming (CP) optimization model can solve the problem of time and resource

constraints, and which is more rapid than the heuristic algorithm. Rana A. Al Haj and Sameh M.

El-Sayegh [3] shorten the duration of critical activities to reduce the overall project duration, anonlinear-integer programming model is presented that is developed to solve the time–cost

optimization problem.Uroš Klanšek [4] presents the mixed-integer nonlinear programming (MINLP)

model for nonlinear discrete optimization of project schedules under restricted costs. Wang et al. [5]

find that the amount of resources, the degree of risk as well as the technical complexity of the activities are seldom considered when the time is optimized, and the optimization method based on

AHP method considering above factors is established.Li et al. deeper step of optimization method

between the three goals of project management, combining with multi goal and incentive genetic algorithm together to schedule optimization in, but the specific operating procedures also need to further study [6-7].Chen et al. research on the relationship between the parallel work and rework

phenomenon, the time optimization model for the parallel work mode is established,and the genetic

algorithm is applied to solve it [8].

Previous research is based on the classic model of network planning technique as the background, optimizes the problem of construction period assuming each duration is independent in the network plan. In the process of the practical project, each duration of process is not independent of each other, but acting on each other. Battaineh [9] evaluated the progress report of 164 construction

projects and 28 highway projects,the results show that the delay resulted from the mutual influence

between each duration is universal:average ratio of highway engineering and construction projects

to the actual construction period and the duration of the contract plan is 160.5% and 120.3% respectively. Investigation and analysis of Literature [10] shows that, in the practical project management, there is very common dependence between different duration variables, the most

this paper establishes the model of the time optimization considering the dependence of durations, and carry on the empirical research by Genetic Algorithm.

Time Model Considering the Dependence of Durations

Based on the research of literature [11], this paper puts forward the following assumptions:

① The cost is not divided into direct and indirect costs, but is considered as a whole;

② Assuming the relationship between cost and time of the project presents a non-linear

relationship (the two relationship): C_i  at_i2 bt_i d;

③ Due to the nature of the quadratic function, a decides the direction of the opening of the image function, symmetry axes of function is decided by a and b, and d decides the intercept function in Y axis. The upper and lower translation of the cost -time function image will not affect the position and the value of the best time for a project.

④ Only considering the duration dependence of the same project, the dependencies between

different projects are not considered. Defining variables:

M is for the total number of work, i is for the current work, nti is for normal working duration,

and nci for the normal cost of the case; sti and sci are respectively duration and cost under the

working state, siand sj are for the start time of the first i, j work; ti and ci are for duration and cost of

i, T is for the total project time. Then,





T Max s t i｜  m (1) In Eq. (9), si=Max{sh+th},h is for working i tight front work set.

Based on the above assumptions, the relationship between the cost and the duration of the work presents the relationship of quadratic function, namely:

 2  

i i i

c at bt d (2)

wherethere are three parameters;the actual work cost and duration of the data are only two groups,

then only through the elimination of parameters will the value of other parameters be gotten.The

image of the cost duration function down translates Δunits to make it through the origin of the coordinates (shown in Fig.1).

Ci’=ati2+bti cost

A

B

sti nti duration

A’

B’

O

t*

Ci=ati2+bti+d

Figure 1. Time-cost translation image.

＇ 2

i i i

c  at bt (3)

where, to make d=Δ, c_i＇  c_i  . The solution is:

＇ ＇

t i t i

2 ＇ 2 ＇

t i t i a=

s ( s )

s ( s )

t i ci t i ci

t i t i

t i ci t i ci

t i t i

n s s n

n n

s n n s b n n    _       _  ＇ ＇

c i c i

c i c i

s s n n           (4)

The objective function is:

＇ ＇

t i t i

a=

s ( s )

t i ci t i ci

t i t i

n s s n

n n

 

2 ＇ 2 ＇

t i t i

s ( s )

t i ci t i ci

t i t i

s n n s

b

n n

 

 (5) ＇

i i

c  c  

0

j i i

s s t 

t i i t i

s t  n

, ＞0

t i t i

s n

, 0, 1, 2, ,

i i

t s  i  m

where,Δ is the translation amount of cost,the scope of the delta hypothesis:

(6) where,  ( 0, 1) _{is a correction coefficient, random number can be used to instead of it in the} empirical research.

In the above model, solved cost resulting minimum duration is optimal duration, finally, the durations after the optimization of all lines in the project can be added to the total project duration and the most is the optimal time.

Time Optimization Model Considering the Dependence of Durations

When the time is optimized, the appropriate consideration of some influence factors or constraints will make the optimization results closer to the actual situation. Inherent dependencies exist

between serial durations,whichhave an important impact on each line of the network plan,and it is

likely to adversely affect the overall project time.At the same timeof network time optimization,

the duration dependence of the serial durations is taken into account, which can buffer the negative impact on the duration of the project and have a positive impact on the implementation of the follow-up works; at the same time if the pipelining construction is implemented, there may be a positive dependence between the serial working procedure due to the same construction methods and other reasons.

It is proposed that there are parallel advantage and disadvantage dependency relation existing in

Minc′i= ati2 + bti

s.t. si = Max{sh + th}, h is the set of tight front works of the work i.

MinT=Max{si + ti | I = 1, 2, ..., m}

the parallel durations.It is also mentioned in this paper, the influence degree and the trend of the

influencing factors on the parallel duration dependence are different;it is appropriate consideration

of these effects to establish the model of time optimization. The optimization model is as follows:

s.t.

＇ ＇

t i t i

a=

s ( s )

t i ci t i ci

t i t i

n s s n

n n

 

2 ＇ 2 ＇

t i t i

s ( s )

t i ci t i ci

t i t i

s n n s

b

n n

 

 (7) ＇

(1 )，

i i i j

t  t  k

if the relationship is favorable, kij∈（0,1） if the relationship is unfavorable, kij∈（-1,0）

＇

i i

c  c  

0

j i i

s s t 

t i i t i

s t  n

, ＞0

t i t i

s n

, 0, 1, 2, ,

i i

t s  i  m

where,kijis the dependence between work i and j,other symbols are ditto.

Time Optimization of Genetic Algorithm Considering the Dependence of Durations

Using the time optimization model considered duration dependence to optimize the practical example in literature [11],optimization model in accordance with the Eq.(7) achieves the final time

optimization by the C# programming language,the data of each node is introduced into the program

by the import node button, each route in the single node network plan is introduced into the

program by the import path button,andthe optimal duration and the total duration of each work can

be calculated As shown in Fig.2 and 3.

The optimized total project time is 508 days, saving 72 days than originally planned network, and the critical path optimized is B→H→I→M→O→U.

MinT = Max{si + ti′ | I = 1,2,.... m}

,h is the set of tight front works of the work i.

si = Max{sh + th}

Figure 2. Node data in the single node network.

Figure 3. Operation results.

Conclusions

dependence of durations has good applicability and high efficiency to solve delay in the

construction period.But there are still some problems that need further improvement and research:

(1) The time optimization model proposed in this paper does not consider the condition that optimal time of the project beyond the prescribed time limit, and without considering the problems of overdue fines. In this case, it is necessary to recheck the established model, or to classify different types of construction projects.

(2) At the time of updating durations, the next step needs to consider the cost as constraint condition changing with duration and updating problem.

Acknowledgement

This project was supported by the National Natural Science Foundation of China, Project No. 70961004.

Reference

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