Schedulers can compress the schedule of construction projects by overlapping design and construction activities. However, overlapping may induce increased total cost with the decrease of duration. To solve the concurrencybased timecost tradeoff problem effectively, this paper demonstrates an overlapping optimization algorithm that identifies an optimal overlapping strategy with exact overlap rates and generates the required duration at the minimum cost. The method makes use of overlapping strategy matrix (OSM) to illustrate the dependency relationships between activities. This method then optimizes the genetic algorithm (GA) to compute an overlapping strategy with exact overlap rates by means of overlapping and crashing. This paper then proposes an integrated framework of genetic algorithm and building information modeling (BIM) to prove the practice feasibility of theoretical research. The study is valuable to practitioners because the method allows establishing a compressed schedule which meets the limited budget within the contract duration. This article is also significant to researchers because it can compute the optimal scheduling strategy with exact overlap rates, crashing degree, and resources expeditiously. The usability and validity of the optimized method are verified by a test case in this paper.
The demand for a shorter project completion time has led to a variety of techniques adopted on schedule compression in the construction field: activity crashing, substitution, and overlapping [
To date, there are many studies on timecost tradeoff in schedule compression [
Here, this paper describes the mechanism of a combinatory model in which the construction information can be precisely delivered into and whereupon subsequently an optimal scheduling strategy of this construction project can be obtained. Distinct from the previous reports, the presented model can give out a precise overlapping rate about what percentage of an activity should be overlapped for the optimal solution and the accurate crashing rate with a completely new method of integrating the genetic algorithm with Overlapping Strategy Matrix. Apart from the first optimized overlapping strategy, the authors proposed a framework combining the traditional algorithm with BIM to realize second optimization and dynamic control of schedule. The concept of this new model involves (1) using OSM to express the overlapping relationships in a project schedule clearly, (2) getting precise overlap rates of coupled activities and crashing rates with an improved expression and utilization of chromosomes, (3) proposing an integrated framework of GA and BIM to prove the feasibility of the research in practice, and (4) providing the comparison of different optimization methods.
Overlapping is an effective tool widely used in different fields to reduce the completion time. There are two types of researches on overlapping: product development and project execution [
Project contract duration and project completion cost are two key objectives for the success of a project. So, there is a pressing need for the contractor to recognize these two objectives and achieve them effectively [
However, the existing studies related to timecost tradeoff analysis in overlapping has not reached academic and practical maturity [
Figure
The mechanism of overlapping.
Overlapping Strategy Matrix (OSM) is first introduced by Hossain [
The comparison of OSM and DSM.
Since both duration and cost have to be minimized, overlapping timecost tradeoff is a multiobjective optimization problem. Some researchers [
Equation (
The equivalent rework is defined by multiplying the rework probability (
In this function,
Correlation between overlapping rate and rework probability under different attributes.
Meanwhile, in the resource collaborative crashing condition, project duration and project coast after crashing can be represented as follows:
However, in terms of the practical conditions, crashing will have bad effects on project quality inevitably. So, this paper defines the project quality with
The above paragraphs illustrate that there are a great amount of possible scheduling strategies. Therefore, the process of continuous optimization will be tedious and complicated. In the following section, a hybridized optimization algorithm is introduced and explained to figure out the multiparametric problem. The algorithm is designed to assess all kinds of overlapping strategies and makes the optimal decision.
There are two different scenarios in the timecost tradeoff problem. The first one is when the project contract duration (
In this combinatory research model, the researchers begin by developing a schedule optimization model to facilitate scheduling, then get all the information needed about some cases, and express the dependency relationship of activities using the DSM. After that, the OSM can be derived from a list of estimable activities and the DSM. In the OSM, each dependency relationship is expressed by tens of genes to figure out the exact overlap rate as well as crashing rate and then all of them form a chromosome. After achieving all information of the project, GA initializes ‘
The algorithm generates a collection of random overlapping strategies, and each of them encompasses several overlap rates, the number of which is the same as dependency relationships. While in the binary coding system, the gene can only represent “0” or “1”, which means the result can only be “Not overlap” or “Overlap”. Hence, in the existing researches, a fixed overlap rate is given to all overlap activities for calculation. To make the calculation more accurate, this research proposes a new method to express the chromosome creatively. Each gene in the previous method is further represented by tens of binary numbers. Therefore, the original result of “overlap or not overlap” can be refined to exact overlap rates as percentages. Likewise, the exact crashing rate can be obtained by the algorithm. For the convenience of illustration, Figure
The genes in a random chromosome.
Information of activities’ attributes.
Activity  Predecessors 

Direct cost (dollars 








1  —  24  2,400  Fast  High  —  —  0.5  25  12 
2  —  25  1,000  Slow  —  —  0.333  12  25  
3  —  33  3,200  Slow  Low  —  —  0.5  12  25 
4  —  20  30,000  Fast  Low  —  —  0.333  25  12 
5  1  30  15,000  Fast  High  0.0  0.65  0.5  12  38 
6  1  24  40,000  Slow  High  0.0  0.3  0.333  50  25 
7  5  18  22,000  Fast  High  0.0  0.5  0.666  25  12 
8  6  24  120  Slow  Low  0.0  0.5  0.5  12  12 
9  6  25  300  Slow  Low  0.0  0.6  0.333  25  25 
10  2, 6  33  450  Slow  Low  0.0  0.8  0.666  25  12 
11  7, 8  20  350  Slow  High  0.0  0.6  0.5  12  25 
12  5, 9, 10  30  2,000  Fast  Low  0.0  1  0.5  12  38 
13  3  24  1,800  Slow  High  0.0  0.5  0.666  25  12 
14  4, 10  18  2,200  Slow  Low  0.0  0.75  0.5  12  12 
15  12  16  4,500  Slow  High  0.0  0.8  0.333  25  25 
16  13, 14  30  1,000  Fast  High  0.0  0.65  0.5  12  38 
17  11, 14, 15  24  4,000  Slow  Low  0.0  0.7  0.666  50  12 
18  16, 17  18  3,000  Fast  High  0.0  1  0.5  25  25 
Apart from these variables in objective function, there are also some genetic algorithm parameters to be set. These variables can largely affect the efficiency of calculation. For the case in this paper, the number of individuals (NIND) means the number of project schedules in the scheduling context and is set as 100 to make sure the population size is big enough to decrease the error in random selection overlapping strategies. The maximum generation (MAXGEN) is 1000, which means the process of selecting, crossing, and mutating random overlapping strategies will iterate 1000 times for a relatively accurate and optimal solution. In the scheduling problem, a chromosome represents a solution of overlapping strategy and a gene means an exact overlap rate in the strategy. Hence, the length of chromosome (NVAR) in the scheduling context depends on the number of dependency relationships in a project, which in this case is 23, and the optimal overlapping strategy contains 23 exact overlapping rates. And, the precision of variables (PRECI) represents the accuracy class in refining the overlap rates and is set as 20 in the case of this paper. The specific explanation of chromosome is further described in the next subsection. In addition, the gap (GGAP) is defined as 0.9, while the crossover probability (
Since the optimization process described above is based on theoretical research, this paper proposed a brand new thought of combing the GA and BIM platform to prove the practical meaning of the research. As can be seen in Figure
Optimize the project schedule using the improved objective function and genetic algorithm, and then optimize the result for the second time by integrating with 4D BIM visualization.
Implement the schedule and track the onsite data and project requirements, and then analyze whether the project need adjustment.
If the schedule need adjustment due to delay or requirement change, optimize the schedule again with the updated information.
If there are any changes in the building, modify the BIM model according to the newest design and then analyze the unreasonable schedule or conflicts through dynamic simulation. Finally output the optimal schedule and realize the dynamic loop control of schedule.
Dynamic schedule optimization and control based on GA and BIM.
The advantages of integrating GA with BIM come from four aspects:
The visualization function of BIM can represent the schedule intuitively, showing the probable conflicts in project schedule. The project participants can then estimate the feasibility of the schedule.
After estimation, the scheduler can make some adjustments and optimize the schedule for the second time.
Engineers can collect onsite data, track the project requirements, and upload all information on the realtime integrated 4D BIM platform, so that the BIM platform can analyze the schedule variance and adjust the schedule dynamically according to practical conditions.
BIM platform can store a large amount of data relevant to schedule management effectively, making it possible to generate and recommend schedule automatically through data mining in the future.
To investigate the practicability and applicability of the method in the realworld construction project, an illustrative sample is presented herein to explain the proposed algorithm with full details and appreciate the impact on total project duration and total amount of project cost. This case was originally reproduced from [
Table
The dependency relationship of this project can be represented intuitively using the OSM matrix in Figure
The OSM matrix of the case.
For the case example, the population with 23 solutions has evolved for 1000 generations to produce an approximately optimal schedule. The crossover probability is set to 0.7 and the mutation probability in GA optimization is set to 0.01. In addition, the targeted completion date of the project is 110 days and the penalty coefficient is set to 2 so that expected project completion duration remains within project contract date. Setting of penalty coefficient will discard those schedules with completion time higher than the project contract date.
To understand how optimal overlapping strategy can optimize the project schedule better, Figure
Comparison of four overlapping scenarios.
The optimal overlapping strategy of the case.
Overlap activity  Overlap rate  Overlap duration (days)  Rework duration (days)  Rework probability  Rework cost (dollars) 

1–5  0.218026  6.54  1.31  0.10  256.69 
1–6  0.299989  7.20  1.44  0.46  388.77 
5–7  0.21767  3.92  0.78  0.10  153.51 
6–8  0.499969  12.00  2.40  0.41  1079.86 
6–9  0.599973  15.00  3.00  0.45  1619.86 
2–10  0.799835  26.39  5.28  0.52  3800.03 
6–10  0.799959  26.40  5.28  0.52  3801.21 
7–11  0.599985  12.00  2.40  0.58  1295.93 
8–11  0.599974  12.00  2.40  0.58  1295.89 
5–12  0.285024  8.55  1.71  0.10  438.69 
9–12  0.286209  8.59  1.72  0.10  442.35 
10–12  0.285853  8.58  1.72  0.10  441.24 
3–13  0.499996  12.00  2.40  0.55  1079.98 
4–14  0.749908  13.50  2.70  0.50  1822.06 
9–14  0.749951  13.50  2.70  0.50  1822.26 
12–15  0.8  12.8  2.56  0.64  1843.2 
13–16  0.217192  6.52  1.30  0.10  254.73 
14–16  0.218397  6.55  1.31  0.10  257.57 
11–17  0.699977  16.80  3.36  0.48  2116.66 
14–17  0.699992  16.80  3.36  0.48  2116.75 
15–17  0.699999  16.80  3.36  0.48  2116.80 
16–18  0.216634  3.90  0.80  0.10  152.05 
17–18  0.218784  3.94  0.79  0.10  155.09 
The aforementioned discussion shows the difficulty of determining an optimal overlapping strategy. The superiority of the optimized method is mainly represented in two aspects: (1) the total duration is much shorter than the one before optimization. Although it is a bit longer than the results in scenario 2 and scenario 4, the duration satisfies the contract required date and makes the overlapping strategy acceptable. (2) the total duration is largely reduced compared to other scenarios since the proposed model can eliminate unnecessary rework. This kind of optimization is of value to practical construction projects.
Under the circumstances of applying the combinatory method, this paper assumes that overlapping and crashing is independent and does not consider the mutual influence. Table
The optimized duration and resource of each activity with the combinatory method.
1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  


12.3  25.0  33.0  20.0  30.0  11.0  18.0  24.0  25.0  25  20  23.4  24  18  7  30  18.9  15.8 

3.8  1  1  1  1  3.2  1  1  1  2.4  1  1.6  1  1  3.5  1  2  2.3 
The optimized overlap rate of each activity pair with the combinatory method.
1–5  1–6  5–7  6–8  6–9  2–10  6–10  7–11  8–11  5–12  9–12  10–12  3–13  4–14  9–14  12–15  13–16  14–16  11–17  14–17  15–17  16–18  17–18  


0.01  0.30  0.02  0  0  0.03  0.80  0  0.01  0.01  0.03  0.30  0  0.01  0.01  0.80  0  0.01  0.01  0.02  0.70  0.03  0.21 
The preceding sections clearly demonstrate a systematic schedule optimization strategy that can obtain a tradeoff between reduction in project completion duration and increase of cost. As the obtained result reveals, the rework probability and rework duration increase as the sensitivity to change in upstream activities increases, which is consistent with the hypothesis of Bogus et al. [
Finally, the proposed model based on hybridized algorithms provides an optimized approach to formulate a detailed construction schedule within the required contract duration. The project manager is given the optimization model, duration and dependency information, activity attributes, and the overlap constraints to make the schedule for the construction project case. And, when the contractor has an extremely strict requirement on project duration, the scheduler can apply overlapping and crashing comprehensively to utilize the advantage of each method to the largest extent. Then, the result of first optimization can be integrated with 4D BIM platform to simulate the schedule with visualization function. This kind of integration makes it more intuitional and dynamic to observe the implementation of optimized schedule. The practitioners can analyze the correlation between components and activities, especially those complicated processes, to make the theoretical schedule coincide more with the practical conditions in projects. The second optimization step ensures the rationality and practicality of the optimal schedule. Taking the construction joint and settlement joint as an example, according to the experiences, the influence and propagation of cross construction between these two processes are great due to the complexity of operation and large number of embedded parts. Therefore, after observing this condition in the BIM model, the practitioners can adjust the overlap rate between these two activities in the input parameters and obtain an updated schedule with exact overlap rates. After second optimization, the schedule can be implemented and onsite data can be tracked and updated in real time, finally realizing dynamic control of schedule.
Through all these phases and activities, this research finally creates a virtuous cycle in which researchers can achieve a satisfactory result and improve the optimization tool at the same time.
This paper presents a synthesized method that determines the optimal schedule with a set of exact overlap rates between coupled activities in the schedule network and exact crashing level. It considers the effect of evolution rate and sensitivity of activities on the rework probability and analyses the timecost tradeoff using a hybridized algorithm. A mathematical formula capable of outputting the optimal overlapping strategy with total duration, cost, and exact overlap rates enumerative is further presented. Then, the combination with crashing and the corresponding time and cost functions are given. Given this optimization model, the project manager can make a better construction schedule precisely without exceeding the required contract duration. Besides, in the process of schedule compression, the project manager can also compare the cost and duration of different plans under various project conditions like schedule information, activity attributes, and contract requirements. For the contribution to exact calculation in compressed scheduling under project constraints involved in budget and time, this research advances the knowledge system relative to exact activity overlapping and crashing in the field of construction scheduling, thus also contributing a little to the construction industry. And, the integration with 4D BIM provides a new idea and research direction for future work.
However, there are still some limitations of the study presented in this paper which need further improvements. The limitations are as follows:
Rework probability is calculated using an empirical formula in this research, while this calculation method may lead to inaccuracy of the result. Hence, in the future study, it would be commendable to simulate the rework probability in compliance with probability distributions like Poisson distribution.
It may be an additional progress in exact scheduling to build time model and cost model separately. In order to balance the duration and cost, the time model can be built from the angle of overlapping and activities dependencies based on DSM and the cost model can be built considering the negation cost. The sophisticated models may produce activities overlapping plans of better elaboration and accuracy.
It would be commendable to incorporate a change propagation predicting method to manage design changes in the multidisciplinary collaborative environment of construction. The exterior changes may lead to risk of completion within the contract duration. So, it may be encouraged to eliminate this kind of uncertainty using scientific modeling and analysis method.
Evolution of the activity
Sensitivity of the activity
Total cost of the project
Total direct cost of activity
Daily indirect cost of activity
Overlapping duration between activity
The maximum overlapping rate of the activity pair
The minimum overlapping rate of the activity pair
Overlap rate of the activity pair
Rework probability of activity
Penalty coefficient of delay
Rework duration of activity
Total duration of the project
Contract required duration of the project.
The paper is finished based on modeling. There are no extra data except for a case study.
The authors declare that they have no conflicts of interest.
This work was supported by a National Natural Science Foundation of China grant funded by the China government (No. 71671128). The contribution in project management, strategy, and information technology is gratefully acknowledged.