INTRODUCTION
General Introduction
Construction industry is one of the most important industries in the world and is considered to be one of the most economy contributing (El Bassuony, 2018) Schedule and cost are considered as two important objectives that need to be quantified and maintained in the construction project (El-kholy, 2013) Usually, the direct cost will raise up in accordance with shortening the project duration On the contrary, the indirect cost will increase as the project duration increase Hereafter, the schedule plays a critical role because a delay in one activity may increase the total project duration as well as the total cost This at the end may cause a claim disputes among parties (Tran, 2020) The capability of handling the time ± cost tradeoff (TCT) problem gives an opportunity to a construction company to be superior over its rivals (Chen & Weng, 2009) Since the cost and time are two of the most important objectives which are easily quantified in a construction project, time-cost tradeoff problem has been researched for a long time (Hu & He, 2014) However, quality performance is being condsider in recent contract in addition to time and cost factor (Afshar, Kaveh, & Shoghli, 2007) Finally, the time, cost, and quality are usually three contradictive objectives which are often traded off in project practices (Hu & He, 2014) Getting a balance time, cost, and quality within the project scope then become a significant criterion to judge whether the project is successful (L Zhang, Du, & Zhang, 2014)
Being a project manager requires having an accurate plan of allocating resources to the tasks involved in a project Different resource allocations to the tasks will directly affect the project duration, project cost, and the project overall quality (Ahari & Niaki, 2013) Nowadays, most construction projects are behind the schedule, it is not an easy task for a project manager to finish the project on time and within the budget (M.Kashid & Jamgade, 2019) It needs a certain strategy, techniques, and tools to be adopted to achieve the goal as what it is planned Project management is the application of knowledge, skills, tools, and techniques to project activities to meet the project requirements Optimization of construction projects is one of the tool to provide the project manager a systematic way to improve the project results under a given circumstances in a construction project It allows the project manager to select one of the best option to assign to the tasks which include the construction methods, equipment and materials type, and also the size and productivity of the labor
Nowadays, repetitive construction project is dominant in construction industry Repetitive construction projects are projects with activities repeated in similar or identical units (-DĞNRZVNL) Repetitive construction is commonly found in high-rise buildings, housing projects, highways, pipeline network, and bridges (El-Rayes & Moselhi, 2001) In this project, the construction crews are required to move and repeat the same activity in a defined number of units (floors, house, spans, etc) Because of the frequent movement of crews, available scheduling methods for repetitive construction projects are geared toward maximizing crew work continuity by allowing each crew to finish work in one location of the project and move on to the next as soon as possible in order to minimize work interruptions (Hyari & El-Rayes, 2006) These complicated issues, of course need some strategy and a lot of consideration before implementing the project
One important factor to be considered when planning a construction project, especially when developing the project schedule is uncertainty Uncertainty is something unpredictable that may happen in our project It may give positive impact or negative impact to the project REMHFWLYHV8QFHUWDLQW\WKDWPDWWHUWRWKHSURMHFWảVREMHFWLYHVLVWKHULVNZKLOHWKHXQFHUWDLQW\ that gives a good thing lead to the opportunity for a project (Hillson & Yanjuan, 2019) Due to XQFHUWDLQW\WKHDFWLYLWLHVảGXUDWLRQDQGFRUUHVSRQGLQJFRVWare not certain and seldom the exact estimation are precisely known This conditon at the end may comes as errors estimation (Zheng
& Ng, 2005) Construction projects are frequently carried out in the uncertain environment due to some factors such as weather, site conditions, equipment condition, material delivery delays, worker productivity, inflation, etc (Eshtehardian, Afshar, & Abbasnia, 2009) All of these uncertainties will have the effect on the duration, cost, and quality of the project Thus, it is critical to consider uncertainty when planning and estimating the project in order to arrive at a more realistic and applicable implementation solution
This study will present a time cost quality trade off in repetitive construction project under uncertainty considering soft logic in the scheduling the project Fuzzy logic is adopted to model the uncertainty in the project Finding the optimum solution which minimize the total duration and the total cost, while maximize the overall quality of the project is the point of this study As previous study in this field utilize various kinds of algorithm, this study will apply Symbiotic Organism Search (SOS) algorithm which developed by Cheng and Prayogo in 2014.
Problem Statement
It is a challanging task to balance among the time, cost, and quality in construction project It is obvious that a short project duration can not be in the same point with the minimum total cost and maximum quality For instance, to do a project with a shorter duration will need additional resource which will cost higher On the other hand, keeping the project with a few resource will take a longer time, which also will increase the indirect cost of the project When deal with quality, a high quality can be acquired by applying a high quality material and a proper construction method which may cause a higher cost These three variables become a contradicting issue (El Bassuony, 2018)
The uniqueness of a construction project is the different condition of each project that may lead to the uncertain time, cost, and quality There are many factors that cause the uncertainty, such as weather, equipment malfunction or equipment maintenance, less skilled worker, etc Different level of uncertainty need to be calculated because it will produce different project time, cost, and quality In summary, a more realistic model is needed to represent the uncertainty in the construction project and solve for the time cost quality tradeoff problem
However, many research has been done for both time cost tradeoff and time cost quality trade off in construction project Table 1.1 summerize the previous research related to this topic
As can be seen in the Table 1.1, most researches conducted in this field are in deterministic condition and not considering uncertainty One conspicious thing is that more problems or parameter can be considered when the uncertainty is not included Whereas, when considering uncertainty the problems are limited Further, for most researches, repetitive project is seldom be used when considering uncertainty This study is considering uncertainty in the time and cost of each activity in the construction project Soft logic is applied in the scheduling for as a method to search for the shortest project duration Then the tardiness cost and reward are calculated as a feedback of the late completion and earlier completion This are considered to get a more realistic solutions Specifically, following research questions are addressed to be solved in this study: a How to schedule and estimate construction project under uncertainty? b How is the uncertainty affect to the total duration, total cost, and overall quality of the project?
Table 1.1 Previous Researches in Time ± Cost Tradeoff and Time ± Cost ± Quality Tradeoff
4 Eshtehardian et al (2009) x x T, C x x x x Fuzzy and
13 This Study x x x T, C, Q x x x x x x Fuzzy and SOS
Objective of the Study
The objective of this research is to develop an effective model in scheduling and estimating repetitive construction project under uncertainty The developed model is arranged to minimize the total project duration and total cost, while maximize the overall quality Further, the model will be able to generate a set of optimum solution which consist of the project schedule, estimated cost, estimated quality, and the optimum resource utilization option for each activity.
Scope of the Study
In order to limit the research problem, the scope of the study are defined as follows: a Time cost quality trade off being analyzed is in repetitive project b The scheduling arrangement is based on soft logic c Fuzzy logic is used to model the uncertainty d Cost to be considered are direct cost, indirect cost, tardiness cost and reward e Project target time is determined f Project resource is assumed to be single resource for each activity g Models are implemented by Symbiotic Organism Search (SOS) algorithm in
MATLAB h Cases study being used are adopted from previous research
Scientific and Practical Significance
The model will be valuable to the academician and industry practitioners in developing a better practice and tools for time cost quality tradeoff problem in construction project It will provide a comprehensive review of project scheduling under uncertainty that can be used in future practice Furthermore, it will help to investigate and quantify the performance of each execution options in the project.
Research Methodology
In order to achieve the research objectives, this study use methodology as follows: a Literature Study
Literature study of recent research development is conducted to investigate and analyze the relavant topic related to time cost and quality optimization in terms of the techniques and tools, then looked for potential improvement that can be made The literature study serve general overview about the time cost tradeoff and time cost quality trade off both in deterministic and undeterministic form in construction project and the specific circumtances on it b Model Development
Based on the literature study of potential improvement, the model of multi objective optimization for time cost quality trade off then developed in MATLAB software The purpose of this model is to find a set of optimal solution to conduct the repetitive project in minimum time and cost, while maximizing the quality in uncertain project condition c Validation of Developed Model
The developed model then applied to cases study in order to demonstrate the capability of the model The cases study are appointed from the previous study, and later the result will be compared to the previous result of the origin research This is to validate the results and illustrate the efficiency of this model to solve the problem Two case study are being analyze and developed One of them is a simplified model to find a satisfactory result compare to previous study, then the other one is to illustrate the ability of the model to solve a more complicated project d Conclusion
The result of the developed model is then analyzed Contribution and the significance of the study are discussed The capabilities as well as the limitation are listed for the behalf of the future study.
LITERATURE REVIEW
Definition and Concepts
Three factors play a significant role in planning and controlling construction projects: time, cost, and quality (Cristóbal, 2009) Construction management is critical to the success of a construction project because it possesses the knowledge that is necessary to manage the project's cost, quality, schedule, and resources Effective planning in terms of scheduling, budgeting, safety, and quality is important to be employed from the early stage of the project's life cycle because it enables control over the process from start to finish, minimizes delays and cost overruns, and aids in efficiently achieving the project's objectives (M.Kashid & Jamgade, 2019) Following segment will describe more detail about schedule, cost, and quality in construction project
In project management, a schedule is a tool that most commonly used to plan the project step by step (Gould & Joyce, 2009) Schedule in a simply way is the timetable that show when each action in a project will occur By sistemmatically analyzing each activity and its relationship to the other activity, the project manager will be able to build a project in a paper before starting it Schedule determine the start, duration, and the finish date of activities in the project Knowing precisely the duration of the activities will have an impact to the project cost For instance, renting an equipment to do an activity without knowing clearly how long the activity will take, will quickly reduce the planned profit So, the project manager must schedule the whole activities properly and effectively to meet the deadline and not reducing the profit
Below are the process to schedule the project (Gould & Joyce, 2009): a Identify project activities b Determine activities sequence c Determine actvities duration d Perform schedule calculation e Revise and adjust f Monitor and control
There are many methods that are often used in scheduling construction project Following are some of them a Critical Path Method (CPM)
The critical path is the sequence of activities that results in the longest total duration
It is the shortest possible time for the project's completion (Sarajevo & Herzegovina, 2012)
When any activity in the critical path is delay, it will impact to the overall duration of the project There is two way to do CPM, they are AOA (Activity on Arrow) and AON (Activity on Node) In AON, an activity is denoted by a box or node, whereas in AOA, the activity is denoted by an arrow AON, on the other hand, is preferred over the AOA network due to its simplicity (Daramola, 2015) Figure 2.1 and Figure 2.2 describe the scheduling for AON and AOA respectively
Figure 2.1 Activity on Node (AON)
Figure 2.2 Activity on Arrow (AOA) b Program Evaluation and Review Technique (PERT)
PERT is a statistical method to analyze the task involved to complete a project It is used to schedule complex and uncertain projects, when details and durations of all activities are not defined precisely Generally, it is used by assigning three time estimates for each activity: the optimistic time estimate (To); the most likely or normal time estimate (Tm); and the pessimistic time estimate (Tp) (El Bassuony, 2018) The expected time can be defined as:
Standard deviation is calculated to see the probability to finish the project within the expected time Standrard deviation and variance can be calculated as:
In the perspective of contractor, the price of a project consist of total cost and markup Total cost is the direct and indirect cost, while markup consist of profit and risk contingency
Direct cost is the cost that directly associated with activities in the construction site The total direct cost is the summation of the equipment cost, labor cost, and materials cost that was used in all of the activities in the project (Hegazy, 2002) Direct cost of an activity depends on site conditions, utilized resource productivity, and the construction method (El Bassuony, 2018) Indirect cost is not specifically identified, but they are being associated with a particular work item It includes site management, supervision, offices, canteen, storage sheds, cars, temporary roads and services, HWF3URILWLVWKHFRQWUDFWRUảVDGGHGIHHZKLOHWKH risk contingency is the safeguard cost agains uncertain conditions in the project In addition, there are tardiness and reward Tardiness cost is the cost that the contractor have to pay because of the delay of the project completion, and reward is the bonus due to the early completion of the project Usually these cost is defined in the contract before starting the project (M.Kashid & Jamgade, 2019) Figure 2.3 show the price in construction project
Direct Cost Indirect Cost Figure 2.3 Price of Construction Project
The consumption of the direct cost in a project is decreasing as the project duration increase, while the indirect cost is increasing as long as the project proceed (El Bassuony, 2018) As a management team, it established the most efficient project duration by crashing to minimize the cost Crashing means the process to accelerate an activity in the project to shorten the project duration Shorten the project duration will increase the direct cost but will decrease the indirect cost If the indirect cost cut for the project is higher than the crashing cost of an activity in the project, then the total project cost can be reduced
Quality is an important parameter which highly corelated with time and cost of each activity in the project However, quality is not a quantitative parameter in the nature (Hu &
He, 2014) Quality can be defined as meeting the legal, aesthetic and functional requirements of a project In the construction industry, quality can be defined as the degree of meeting the requirements of the designer, constructor, and regulatory agencies as well as the owner Project quality relies on the quality of every activity in the project When there is a poor quality in the project, it may cause to the failure or rework to a certain activity It will direct to an increasing cost or known as failure cost The failure cost in a project could be occurred as internal and external failures Internal failure cost includes rework, crap, reinspection, re- testing, redesign, material review etc while external failure cost includes processing customer complaints, customer returns, warranty claims and repair costs (Mallawaarachchi & Senaratne, 2015) Many company associated with ISO9000 to ensure customer worldwide that quality will be consistently high The ISO is International Organization for Standardization This group published international standards to define quality management concept and guidance Registration with the ISO means that there will be an accredited auditor as a third party involved in the project to examine the works and ensure that it meet the standard (Gould & Joyce, 2009)
The quality of the work closely related to the productivity The productivity of the construction worker are highly impacted by the duration of the work Some studies suggest that the productivity will be likely to decrease as the more hours the construction workers have to work If in normal condition of 40 hours per week can achieve 100% of the productivity, increasing the working time to 50 or 60 hours per week may decrease the productivity into 80% and afterwards depend on the total weeks they have to work Further, this will lead to a higher cost in which it needs more resource or to pay the overtime fee of the workers (Mubarak, 2010)
Estimating and quantifying quality of each activity as well as the total quality of a construction project is a more challenging task than predicting the total duration and total cost of the project (El-Rayes & Kandil, 2005b) Cristóbal (2009); El-Rayes and Kandil (2005b); Luong, Tran, and Nguyen (2018); Wang, Abdallah, Clevenger, and Monghasemi (2019) employed Analytical Hierarchy Process (AHP) method which is based on quality breakdown structure to quantify the quality This method described that the total quality of a project is depend on the weight and quality of each activity in the project, whereas the quality of each activity in the project depend on the quality indicators as well as the weight of the indicators of that activity For instance, there are three indicator in concrete pavement work, that is compressive strength, flexural strength, and ride quality the quality of the concrete pavement work will depend on the sum of the quality and weight of aforementioned indicator It ranges from 0 to 100 Following equation was used to estimate the overall quality of the project
Beside, Fang and Chao (2014); Tran et al (2018) (L Zhang et al., 2014) evaluate the total quality of a project based on the average of the quality from all activity The quality of each activity depend on the executing time of that activity The quality will increase when duration is extended, but after some point, the duration extension will decrease the quality slightly Following equation was used to quantify the whole project quality:
Repetitive construction project is a project that consist of activities repeated in some units When an activity is completed in one unit, it must be repeated in the other unit There are two types of repetitive project, they are (L.-h Zhang & Zou, 2015): a Horizontal Repetitive Project
The activities in this project are repeated due to their geometrical layout For example, the highways, tunnels, and pipeline project b Vertical Repetitive Project
This project involves activities repetition in a descrete steps High rise building and multiple similar house are examples of this project
Figure 2.4 represent the structure of repetitive project A, B, C, D, and E indicates the activities in the project Vertical axis is the number of unit, and the horizontal axis is the duration Each unit has the same activities, which are activity A, B, C, D, and E The duration of the same activity in different unit may not be the same, due to the work volume of corresponding unit It can be seen from Figure 2.4Figure 2.4 Structure of Repetitive Project, when activity A in unit 1 is finished, then activity A in the next unit can be started, and so on for the other activities In the repetitive project, the activity work order is not only depend on the activity dependency, but also the unit dependency In Figure 2.4, when activity E in unit
2 is finished, it can not immediately start to the activity E in unit 3 This is because the previous activity of activity E in unit 3, which is activity D is not finished yet, so it should wait until this activity is finished, then it can be started
Figure 2.4 Structure of Repetitive Project
Some common scheduling method such as linear scheduling and line of balance are used in scheduling repetitive project These methods are providing a graphical interface that enables users to identify and interpret the production rates, durations, and relationships between repeating tasks quickly (Tokdemir, Erol, & Dikmen, 2019) From the characteristic, linear scheduling method (LSM) represent the schedule in 1 line, while the line of balance (LOB) do it in 2 paralel lines For some analytical equation, these two methods are complitely different (Su & Lucko, 2015) LSM and LOB can be graph can be seen in Figure 2.5 and Figure 2.6 respectively
Figure 2.6 Line of Balance Method
Soft Logic
Soft logic is a condition where the activities in the project can be done in any order, but still based on its dependencies This is mostly done in a repetitive project For example, a foundation work must be done for 4 units, A, B, C, and D Considering soft logic, this work can be done from A-B-C-D, D-C-B-A, A-C-D-B, A-D-B-C and so on After that, the next activity which is the successor of foundation work is carry out in the same manner to the unit that finish first in the previous activity In repetitive project scheduling, when an activity in one unit is finished, the resource must be transfered to the other unit to do the same work But then, it must consider the work dependencies When the next unit has not finished in previous activity, then the resource should wait until it finish so it can begin to work In the other condition, when an activity in one unit is ready to be executed due to the finish of the previous activity in that unit, the resource may not available because it has not finish in previous unit
So, the execution time in that unit must be delay due to unavailable resource These two condition will result in a longer project duration Another condition, when the resource is available and the unit is ready to start, the activity can be executed immediately This may produce a shorter project duration comparing to the previous two condition That is why changing the sequence of the activity in the project may produce a longer or shorter duration (see Figure 2.7) However, the aim of the soft logic in this study is to search for the shortest project duration
35 days Working time Resource transfer time
Figure 2.7 Soft Logic in Project Scheduling
Fuzzy Logic
Construction projects consist of the complex and unique tasks which also take place in a dynamic environment (Bakry, Moselhi, & Zayed, 2016) Due to this, the construction project often faces uncertainty during the project implementation and influence the project objectives (Zhong, Chen, Zhou, & Hu, 2018) Some instance such as bad weather, equipment condition, resource availability, site condition, and labor efficiency are likely to occur Thus, these factors are important to be considered when planning the project There are two kinds of method that can be used when considering the uncertainty in the project scheduling The first method is probability-based method This method use the historical data of some typical activities that has been done in the past The data in the normal distribution will be used to determine the probability a project can finish in a certain time In other way, the other method, which is fuzzy-based method lies on the expert knowledge and estimation (Long & Ohsato, 2008) In the probability method, one might say that the probability for a certain activity in the project to be finished in eight days is 0.7 and the probability it will last in eleven days is 0.3 This measures that after repeating the activity in several time in the past, the activity duration was eight days in 70% cases and eleven days in 30% cases Because the total of the probability must be 1.0, so there is no other possible duration the activity can end up with (Liberatore, 2002)
One challanging thing when using the probability method is that the process of gathering the historical data is tough For some projects, there may be some activities that seldom and have not been performed before Thus, this method seems can not work for this condition (Ke & Liu, 2010) Due to this issue, the fuzzy method as the other alternative is used Fuzzy method is a more simple method that rely on the human estimations (Masmoudi
& Hạt, 2013) In the fuzzy logic, the occurance of an uncertain and imprecise event can rely on the expert knowledge (Elbarkouky, Fayek, Siraj, & Sadeghi, 2016) In this method, an expert may state that an activity should take between 8 and 12 days to complete, but due to uncertainty, the activity could take as long as 15 days or as little as 6 days A membership value within the fuzzy number is used as a degree of measurement to which an event occurs, not whether it occurs or not This is why fuzzy theory is a widely used technique for incorporating uncertainty into project scheduling
Some researchers has analyzed and estimated the project schedule under uncertainty Some researches added buffer to the schedule to reduce the effect of the uncertainty (Bakry et al., 2016; Long & Ohsato, 2008; Uddin, Miah, Khan, & AlArjani, 2021), some other researches are done it with fuzzy number which as the estimate to forms the activitiesả duration in the project (Eshtehardian et al., 2008, 2009; Kalhor et al., 2011; Leu, Chen, & Yang, 2001;
H Zhang & Xing, 2010; Zheng & Ng, 2005) The researches that used the fuzzy numbers mostly will result in fuzzy numbers, except defuzzification is utilized at the end to get the exact result While, using buffer can result in the exact solution by predicting the exact buffer number needed to protect the project from delay and ensure the date of completion
Fuzzy logic was first introduced by Lotfi A Zadeh in 1965 This technique can provide a definite conclusion from vague and inaccurate information (Al-Zarrad & Fonseca, 2018) Problems involving linguistic description may be effectively solved by fuzzy Fuzzy logic is the extension of Boolean logic, which things are defined as 1 or 0; yes or no; true or false In fuzzy logic, the things are more flexible that some of the element may be partly include into a set A membership value, range from 0 to 1 is given to each element in order to define how much the element belong to the set The process in fuzzy logic include three main steps, they are: a Fuzzification
Fuzzification is the process to convert a crisp value, which is the original value of the variable that intend to be analyzed into fuzzy numbers Fuzzy number can be expressed in various ways, such as triangular fuzzy number (TFN), trapezoidal fuzzy number (TrFN), and gaussian fuzzy number (GFN) Among these, fuzzy triangular number is the most popular (Al-Zarrad & Fonseca, 2018) It defines the fuzzy numbers and membership value in a triangular shape Figure 2.8 depict the fuzzy triangular number The triangular fuzzy number may be symmetrical or anti-symmetrical, depend on the data There are three number in fuzzy triangular number, that is a, b, and c The membership value of a and c is 0, while b has the membership value of 1 The membership value of the other fuzzy number between a to c can be calculated by equation (2.6)
Figure 2.8 Triangular Fuzzy Number (TFN)
Trapezoidal fuzzy number is a set of fuzzy number that consist of 4 number with the membership function in a trapezoid form (see Figure 2.9) Different from TFN, the TrFN has several number in the middle that has membership value of 1 The membership value of each fuzzy number in TrFN is formulated in equation (2.7) Beside, gaussian fuzzy number is based on normal distribution (Anggreainy, Widyanto, Widjaja, & Soedarsono, 2018) This method is quite complex and difficult in terms of the arithmatic operation comparing to the other two method GFN can be seen in Figure 2.10
Figure 2.9 Trapezoidal Fuzzy Number (TrFN) a b c
Figure 2.10 Gaussian Fuzzy Number (GFN) b Fuzzy Operation
In this step, the fuzzy number are being processed The basic operations for fuzzy number with more than one variable are union, intersection, and complement These operation however depend on the fuzzy rules For a single-variable fuzzy set, operation such as summation, substraction, and multiplication are common These operstions are formulated below Assume there are two fuzzy set, A and B The summation, substraction, and multiplication of Aand Bis done in equation (2.10), (2.11), and (2.12)
Defuzzification means to convert the fuzzy numbers back into a crisp number This crisp number will be used as the output to compare all of the alternative solutions There are many method can be used for defuzzification, some of the methods are: x Maximum Membership Principle
Maximum membership principle use the value with the highest membership value as the crisp value This method is also known as height method Figure 2.11 described defuzzification using max membership principle method z* is the defuzzified value, which derived from the value of the highest membership value
Z* ȝ x Figure 2.11 Maximum Membership Principle Method of Defuzzification x Centroid Method
Centroid method also known as center of gravity method or center of area method This method has been widely used by researchers (Ross, 2004) This method calculate the centroid of the fuzzy output and then set it as the crisp value (Figure 2.12) Centroid method can be calculated by Eq (2.16)
Figure 2.12 Centroid Method of Defuzzification
The weighted average method is done by weighting each membership function in fuzzy output by its corresponding maximum membership value (see Figure 2.13) Weighted average method of defuzzification can be calculated by Eq (2.17)
Figure 2.13 Weighted Average Method of Defuzzification x Mean Max Method
Mean max method also known as middle of maxima This method use middle of fuzzy number with the highest membership value as the crisp value (see Figure 2.14) Mean max method can be calculated by Eq (2.18)
Figure 2.14 Mean Max Method of Defuzzification
Optimization in Construction
Optimization means a process to find the maximum or minimum value of an objective from a feasible set mathematically More general, optimization is the process of finding the best available values from a certain set according to the given criteria These criteria then expressed in mathematical function, called objective function ()ULGJHLUVVRQ 5RVáRQ) Optimization play a significant role for the construction project due to the complexity and the nature of the construction project It provide a fast way to do simulation for analyzing and planning the project (Salimi, Mawlana, & Hammad, 2018) There are two types of optimization, they are: a Single Objective Optimization
This kind of optimization only have one criteria or objective function to be reach May be it is to minimize the project duration, or minimize the total cost of the project, or maximize the profit of the project The goal of single objective optimization is to find the best solution of the proposed objective This will find one best solution as the output This is useful as a tool which should provide decision makers with insights into the nature of the problem, but usually cannot provide a set of alternative solutions that trade different objectives against each other (Savic, 2002) b Multiple Objective Optimization
Multiple objective optimization allows to optimize the problem which has more than one objective to be achieved For instance time cost optimization Which has two objective function, minimize time and minimize cost; and time cost quality optimization, which minimize time and cost, while maximize the quality Not solely in time, cost, and quality, there are many objectives ofter traded off in planning and analyzing construction project, such as energy, environment, risk, and even life cycle performance (Jung, Heo, & Lee, 2021) To be noted here, the objectives are in a contrary This means when we want to minimize the duration, it will cause a higher cost because of additional resource added to the project Meanwhile, this is not happen in every point, because shorten the project duration will cut the indirect cost which can reduce the total cost of the project But again, when the duration is very short it will increase the cost (see Figure 2.15)
Figure 2.15 Direct Cost, Indirect Cost, and Total Cost in Construction
Optimizing in multiple objective optimization cause conflicting objectives, there is no single optimal solution, but many different solution These solutions called pareto optimal, which represent the best tradeoff among the objectives (Chou & Truong, 2020) When comparing the different solutions, there are 3 possibility, they are:
3 X1 and X2 are not dominated each other
A non-dominated solution is the solution that can not be displaced by the other solution The set of non-dominated solution is called the Pareto front (Tran, Cheng, & Prayogo, 2016) Because this problem rarely presents a unique solution, decision makers are expected to choose a solution among the set of efficient solutions (Tran et al., 2016)
There are three most used optimization method for time cost trade off problem (TCT) and time cost quality trade off problem (TCQT), they are: b Exact Method
Exact method sometimes called mathematical method This method guarantee to find the optimum solution of the problem But it needs higher effort and it grows polinomially with the problem size (Rothlauf, 2011) This method usually solve the problem by deviding it into simpler problems Example of this method is Linear Programming and Dynamic Programming Figure 2.16 describe the mathematical optimization under two constraints
Figure 2.16 Optimization in Exact Method c Heuristic Method
Aside from exact method, there is a heuristic method which employs a practical method within a shorter time than exact method However, it does not guarantee to catch the optimal solution, but still sufficient to the goal Many researcher found that this algorithm can result to get trapped in local optima, and further can not discover the global optimum solution ()ULGJHLUVVRQ 5RVáRQ ) Local optima means the optium solution (for example it generates the minimum point) comparing to its nearby points, while global optimum means that it is the minimum point over all points, no other point is better than it Thus, this algorithm then developed The developed algorithm so called metaheuristic algorithm d Metaheuristic Method
Metaheuristic is the upper level of heuristic This method can be applied and has been applied to solve almost any optimization problems Metaheuristic algorithm can explore the solution space more throughly and find a better solution
Recently, the application of meta-heuristic algorithms to project development has been lauded (Garg, 2015) Numerous researchers from a variety of fields of science and engineering have used metaheuristic algorithms to solve optimization problems encountered in their respective fields Garg (2016) proposed a hybridization of two well-known algorithms for constrained optimization, the genetic algorithm (GA) and particle swarm optimization (PSO) Garg (2019) recently combined gravitational search and genetic algorithms to solve constrained optimization problems Nine well-known structural engineering design problems were used to validate the proposed algorithm GSA-GA Rahimian (2019) evaluated the efficiency of data envelopment analysis (DEA) using the differential evolution (DE) There are so many kinds of metaheuristic algorithm, some of them are:
The Multi Objective Symbiotic Organism Search Algorithm (SOS) algorithm is used in this study The SOS algorithm was developed for the first time by (Cheng & Prayogo, 2014) It is an optimization algorithm that adapts the way organisms interact in nature The SOS algorithm is a relatively new and popular global optimization technique that has gained widespread acceptance among researchers working in both continuous and discrete optimization domains in recent years (A E Ezugwu, Adeleke, & Viriri, 2018) There has been some outstanding research in optimization field that use SOS algorithm as a tool (Cheng, Prayogo, & Tran, 2016; Absalom E Ezugwu & Prayogo, 2019; Han & Zhou, 2019; Liu, Li, Wang, Qi, & Rose, 2020) The input needed to be determined by the user to run the process in SOS algorithm are: the ecosystem size, number of generation, decision variables, objective functions, upper bound and lower bound
The selection process of this algorithm are as follow: a Define an initial ecosystem, which include a set of organism The number of organism in this ecosystem is defined by the user Each organism in this ecosystem represents one possible solution of the problem b The search is start Each organism in the ecosystem will interact each other within three phases: x Mutualism symbiosis
Mutualism symbiosis between two organism will give benefit to both organism One example of this interaction in nature is the interaction between the flower and the bee The bee land to the flower to gather the nectar which will turn into its food This is benefit to the bee At this time, the bee will got some pollen on its hairy body, then when it land to the other flower, some of the pollen rubs off and pollinating the flower, which also benefit to the flower x Commensalism symbiosis
This is benefit only to one organism, while the other organism is not affected Not get benefit nor loss For instance, the bird that live in the hollows of tree Their presence does not affect the tree, but the tree provides protection for them x Parasitism symbiosis
This symbiosis only benefit to one organism, while the other organism is got harm on it The mosquitoes that feed on blood of human body is the example of parasitism symbiosis in the nature In SOS algorithm, parasite vector is made by duplicating one organism, then the parasite vector will interact to the other organism
If the parasite vector dominates the other organism, then it will replace the organism and move into the next population, otherwise the parasite vector will be removed and the other organism will be moved to the next population
Time Cost Tradeoff (TQT) and Time Cost Quality Tradeoff (TCQT)
Tradeoff between time and cost allow the project stakeholder to build a project in an optimal schedule and leads to the minimum cost (Alavipour & Arditi, 2019; Cho & Kim, 2021) Furthermore, in order to balance the completion time and cost while maintining the quality of the works, many researchers already proposed different methodologies to solve both time cost tradeoff problem and time cost quality tradeoff problem (Choi & Park, 2019) Below are some of them
El-Rayes and Kandil (2005b) investigated deterministic time-cost-quality optimization in highway construction The study takes into account the multiple resource utilization factors such as material type, employee productivity, and equipment Each of the resource option then has its own time, cost, and quality The total time to be minimized is coming from the summasion of all activity duration based on selected resource utilization option The cost is considering the direct cost and indirect cost which form combined into one for each option For the quality, this study considering quality of each indicator in each activity The total quality is calculated for the sum of the weight of each indicator and each activities in the project Genetic Algorithm was conducted to find the optimum solution Then a set of optimum solution which is minimizing time, minimizing cost, and maximizing quality then showed in a form of pareto front
(Cristóbal, 2009) strive to find the optimal balance of time, cost, and quality in road construction projects in order to meet the specified time, budget, and quality goals The solver performs the analysis in integer programming The objective is to select the most cost- effective resource option for each activity in a road construction project that meets the specified objective The result find only one optimal solution as the method used is integer programming However the result was meet the requirement
(L Zhang et al., 2014) introduce a new particle swarm optimization (PSO) to analyze stochastic time cost quality trade of in a three storey building The developed PSO algorithm is Immune Genetic Particle Swarm Optimization (IGPSO) which add mutation and crosover operators in PSO The algorithm then used to find the optimum solution for minimum time, minimum cost, and maximum quality with one resource option Actually the data being analyzed in this study served in shortest duration, initial duration, and longest duration Activity duration was used as decision vector to be determined So the objective is to find the best duration of each activity ranging from the stortest and longest time that could generate the shorter project duration and lower total project cost Target time and cost are determined, that whenever the solution exceed the target time, it will be punished by penalty, otherwise it will get reward The total cost of the proposed solution must be less than or equal to the target cost Then quality performance index (QPI) is used to calculate the quality of each activity based on the shortest and longest duration of the activity Finally a set of optimum solution is shown in pareto front
(Huang et al., 2016) analyze time cost trade off in repetitive construction project to meet the deadline considering soft logic Soft logic means that the task in the project can be carried out in any order According to the research, soft logic is applied for each units in the project So there is no restriction that a certain unit must be started first that the other specific unit following the previous one All unit can start first as long as it reduce the time and cost The cost is calculated considering direct cost, indirect cost, resource transferring cost, and idle cost Then by the help of genetic algorithm, the study presented a set of optimal solution which has shorter duration and lower cost than previous study conducting the same case study without soft logic
(Tran et al., 2018) conduct an analysis of the time, cost, quality, and continuity of work in repetitive projects Simultaneously, time cost quality and work continuity are optimized Work continuity aims to minimize project interruptions The method used is Opposition Multiple Objective Symbiotic Organism Search, which is based on the concept of opposition- based learning Opposition-based learning is a machine-intelligence strategy that takes into account both the current estimate and its opposite estimate in order to arrive at a better solution The result is then presented based on two case studies, and a superior solution is obtained when compared to previous studies
(Altuwaim & El-Rayes, 2018) conducted a study to aiming for minimizing the project's time and cost by minimizing the project's interruption day So as the interruption day minimized, the idle cost which is added to the direct cost can be minimized The study conduct with the help of Genetic Algorithm to identify the best total shift can be done to an activity based on its interruption in accordance with its predecessor After finding the optimal shift day, the project then rescheduled again, the high interruption day is kept, and not being shifted The solution for this is to move the crew to the other project, so the cost for the interruption only determined by mibilizing and demobilizing the crew from the project site In comparison to previous research, the result generates the same duration but at a lower cost
Above mentioned researches are in deterministic condition, which indicate that all process will be done smoothly with no uncertainty However, there are some uncertainty that appear in the construction project and affect the project performance, whether the project duration, project cost, and even the quality of works of the project Some uncertainty factors like bad weather, bad site condition, bad equipment condition, less resource availability, and inferior labor efficiency often arise and hereafter, a good strategy is needed to save the project performance as what has been planned Thus, considering uncertainty in the analysis makes the stochastic analysis more suitable for TCT and TCQT problem rather than the deterministic analysis (El Bassuony, 2018)
Generally, fuzzy logic approach is used to present the uncertainty As mentioned before, fuzzy logic has the membership function that will indicate the membership degree of DQHOHPHQW,QWKLVSUREOHPWKHPHPEHUVKLSYDOXHĮFXWZKLFKKDV range from 0 to 1 are used to describe the uncertainty level of the project This concept shows the degree of how the decision maker (project expert) wish to bound the uncertainty in the analysis The uncertainty level will be drawn for all activities of all alternatives in the project Later, the uncertainty level will be decide by the decision maker to choose the best option to implement the project Figure 2.17 describe the cost and time range due to the uncertainty level
Figure 2.17 Cost and Time Range in Different Uncertainty Level 7KHORZHUWKHYDOXHRIĮPHDQVWKHORZHUWhe optimism of the decision maker that the project will be in a good condition This indicates a high uncertainty and end up with a wider UDQJHRIWKHGXUDWLRQFRVWDQGTXDOLW\,QRWKHUZRUGVWKHKLJKHUWKHYDOXHRIĮWKHJUHDWHU the optimism of the dHFLVLRQPDNHUZKLFKPHDQVWKDWWKHUHLVQRXQFHUWDLQW\Į
(Eshtehardian et al., 2008) proposed time cost tradeoff considering uncertainty in construction project A deterministic project data is convert into stochastic data in terms of the project cost, which generate the minimum and maximum cost of the activity In this study, the uncertainty is only considered in the project cost Fuzzy shape was determined for each activity in the project Alpha cut from 0 to 1 is done to represent the level of the uncertainty Schedule and cost then calculated considering the maximum and minimum cost for all alpha cut 2 models were studied The first one, for all solution, the fuzzy cost were convert first to the crisp value before rank it While in the second model, the fuzzy numbers are directly ranked Finally Genetic Algorithm is used to calculate all possible solution and generate a set of optimal solution for every alpha cut
(Eshtehardian et al., 2009) study another variable to consider, namely the degree of optimism A new variable with a range of 0-1 is used to model the decision maker's optimism level To rank the solution, fuzzy logic approach based on left and right dominance is used Then, using a Genetic Algorithm, a set of optimal solutions is determined A stochastic analysis was done in terms of time and cost, comparing various levels of uncertainty and optimism degree (H Zhang & Xing, 2010) analyzed the time-cost-quality trade-off in the presence of uncertainty using fuzzy multi-attribute utility functions that determine the optimal solution based on the weight assigned to each activity The uncertainty manifests is modeled using stochastic project data (time and cost) There is no degree of uncertainty PSO is used to determine the optimal solution, which is determined by the options' highest attribute uitlity
(Ahari & Niaki, 2013) proposed a fuzzy logic method to define the quality in a time cost quality trade off of a multiple resource option project The way is deviding 5 descrete level for the time and cost, that is very low, low, medium, high and very high While the level for the quality is only 3, they are low, medium, and high Then quality is determined based on if-then rule from the fuzzy set of duration and cost For instance, if the activity is done with very low cost and low time, then the quality will be low This is based on the fuzzy operation of intersection, that define the output as the minimum of two variable of fuzzy set After getting the membership value of quality, the quality level will be determined based on the membership value in a given fuzzy number (see Figure 2.18) These indicator is developed based on expert opinion Cplex Solver of GAMS then used to calculate the optimum solution This research generate one optimum solution that select the best resource to be used to have minimum project time with minimum cost and maximum quality
Figure 2.18 Fuzzy to Define Quality (Ahari & Niaki, 2013) (Acar Yildirim & Akcay, 2019) conduct a study on time cost trade off in roof house project with multiple resource option considering uncertainty along the construction time, such as weather condition, worker productivity, etc Uncertainty is determined by alpha cut in fuzzy logic from 0 to 1 Then based on original data (normal time) from the site, compressed and delay time and cost are calculated based on the number of the crew and the productivity of the crew The time and cost data then presented in triangular fuzzy number Then optimization is done by genetic algorithm generating a set of optimum solution for time and cost in different uncertainty level.
RESEARCH METHODOLOGY
Data Processing
This step is to process the raw data, which is the fuzzy number Fuzzy number in time, and cost data are processed to be generated 6 level of uncertainty (0; 0.2; 0.4; 0.6; 0.8; 1) These data, later will be converted into deterministic data by using defuzzification method The exact data in all uncertainty level will be used for the next step In this study, fuzzy number of time and cost data consist of three number that represent the optimistic, most likely, and pessimistic condition These numbers then modeled in Fuzzy Triangular Number (TFN) and will be defuzzified using one of defuzzification method, in this case is centroid method Beside, Quality Performance Index (QPI) is run to get the quality of each activity corresponding to the time data that it has The whole process of data processing is described in Figure 3.2
Time, cost, and quality data in uncertainty condition
Figure 3.2 Flowchart of Data Processing
Centroid method of defuzzification as already mentioned in previous part is the defuzzification that based on the center of gravity of the two-dimentional membership function shape A detail explaination about these method which will be utilized in this study is drawn in Figure 3.3 It describes that by cutting the alpha between 0 to 1, new numbers are generated as the lower and upper bound of the duration of the corresponding activity These numbers, t- to t+ reflect the possible duration an activity usually done under the uncertainty OHYHORIĮ But then, the area below the cutting line is being defuzzified to get the most possible time to do the activity t- and t+ can be calculated from the basic formula mentioned in previous part (equation (2.6)), and generated:
Figure 3.3 Centroid Defuzzification Then t is calculated based on centroid method of defuzzification by Eq (2.16) This process is done for all fuzzy numbers in terms of time and cost data Defuzzification for each fuzzy set will result in deterministic number The deterministic number will then be used to the next step, which is scheduling the time and estimating the cost and quality The scheduling and estimating by the deterministic number after defuzzification will result the same as the schedulng and estimating using fuzzy number then defuzzifying it For instance, the summation of A 3, 4, 6 which has crisp number of 4.33 and B 4, 5, 7which has crisp number of 5.33 will result in C 7, 9,13in which by defuzzifying it will lead to 9.66 This is the same as if the summation is using the crisp number, that is 4.33 + 5.33 In this study, the scheduling and estimating process is done after defuzzification process of each fuzzy set.
Scheduling and Estimating
In this step, the total project time, total project cost as well as the overall quality works are estimated This step is done for each alpha cut from 0 to 1 As mentioned earlier, soft logic is utilized as the method to the schedule the project The scheduling of the project time is based on the soft logic as already metioned before Figure 3.4 described the steps of scheduling and estimating using soft logic The input to this system will be the project data that has been processed before by defuzzification The system will generate an arrangement of resource option for each activity in the project This resource arrangement are later to be controlled as decision variable, because it will generate a different project output for a different resource arrangement After that, a random unit sequence for those activities is determined Based on this sequence, the system will do the scheduling for the project and estimate the project duration, cost, and quality This steps will be repeated for 6 case of alpha cut (0; 0.2; 0.4; 0.6; 0.8; 1) Following subsection describes the steps for the scheduling and estimating subsystem
Extract resource option for each activity
For each activity in the project
Unit sequence = unit sequence of predecessor activity
Last activity in last unit?
Determine activity start and finish time Yes
Calculate total project duration, total cost, and quality
Figure 3.4 Scheduling and Estimating Subsystem a Determine the resource option
Since the activities in the project has multiple options, the option will be initialized by the model to be used for that activity Equation (3.3) illustrates an example of a resource option arrangement that could be used for each project activity This equation indicates that the second resource option will be utilized to the first activity, the third resource option will be utilized to the second activity, and so on Remember that the resource for doing activity 1 is different from the resource in other activity, but once a resource for one activity is choosen, that resource will be used to all units in the project The other condition of this study is that there is only single resource working in each activity, so this resource will do the same activity in all unit The number of resource option for each activity may be different depend on the resource availability
The unit sequence are determined randomly by the system, but will not be controlled like the resource option in the optimizer The unit sequence will be generated for the first activity in the project For the following activity, the sequence will be based on the previous activity and the resource availability of that activity Figure 3.5 described the unit sequence determination
Figure 3.5 Unit Sequence in Repetitive Project with One Leading Activity Using Soft Logic
As can be seen in Figure 3.5, the opening activity is activity A, then followed by the activity B A3 and B3 indicate activity A and activity B in unit 3 respectively When the A3 is finished, B3 can start immediately From the example in this figure, the system determined the unit sequence for activity A to be 3;2;1 So for the successor of activity A, the unit sequence will depend on the unit sequence of activity A and at the same time considering the resource availabilty If activity A continue to unit 2, then activity B will also be continued to unit 2 after activity A2 and B3 are finished Activity A2 act as the predecessor activity of activity B2, while activity B3 is being considered due to the condition of the single resource option The starting time of each activity in the project can be calculated by Eq (3.4) to (3.6) It is worth to note, that when there are multiple initial activities, the unit sequence of these activities may vary Thus, the sequence of the succeeding activity will be altered Figure 3.6 illustrates how to determine the sequence of activities when there are multiple leading activities
E1=Max (B1,D1) The minimum of ((Max B3,D3), (Max B2,D2), (Max B1,D1)) that is the unit which will start first
Figure 3.6 Unit Sequence in Repetitive Project with More Than One Leading Activity Using
From Figure 3.6, it is described that activity A and C are the first activities and without predecessor Activity B come up after activity A and activity D is the successor of activity C The system will define the unit sequence for activity A and activity C Then the successor of each activity (activity B and D) will continue with the unit sequence of its predecessor Activity E is the next activity that can only be started when activity
B and D are finished The unit sequence of activity E will depend on the unit sequence of activity B and B The system will search for which among these unit that finish first Then the activity E will continue on that unit For example, the early finish of B3, B2, and B1 are 7,13, and 19 respectively While the early finish of D3, D2, and D1 is 15,8, and 12 respectively The maximum of (B3,D3), (B2,D2), and (B1,D1) are then 15, 13, and 19 respectively So, these numbers will be sorted, and the unit with the lowest finished date will be started first In the case of this example, unit 2 will be the first unit to be started in activity E, then followed by unit 3 and unit 1 So, the unit sequence of activity E will be 2-3-1 c Calculate the total project duration
The project duration is calculate based on forward method Eq (3.4) to (3.7) are used to calculate the project duration
Where ES i,j and EF i,j indicate the early start and early finish of activity i in unit j respectively d i,j is the duration of activity i in unit j The early start of an activity is determined by the maximum between the early finish time of predecence activity which is the job logic of the activity, and the finish time of previous unit which represent the resource availability In this study, the relationship among activities is fixed by finish-to-start Then, these equations will be repeated for all activity in the project The total project duration is then determined based on the last activity in the last unit, which can be seen in Eq (3.8) Total project duration is the early finish of the last activity in the last unit of the project
T EF I J (3.8) d Calculate the total project cost
As mentioned earlier, some type of cost such as the direct cost, indirect cost, tardiness and reward are cosidered in this study The total direct cost of a projet can be obtined by summing all the direct cost from each activity in each unit While, the indirect cost is usually a constant cost that increase as the duration of the project extend In this study, the indirect cost of an activity is calculated by multiplying the constrant number per day to the total duration the corresponding activity can be finished To determine the tardiness cost and reaward, a project target time must be set The target time will be a benchmark to decide whether the project will be punished by penalty or will be given daily reward/bonus The tardiness cost may be considered due to late project completion or cost overrun incurred by the contractor But this study only calculates the tardiness cost due to schedule delay The amount of the tardiness and reward should be depend on the contract It should be sufficient enough to encourage the contractor to finish the project earlier But again, the risk level may increase if the works are done in rush The tardiness cost is calculated in exponential equation, while the reward/bonus set as a constant/determined cost per day Equation (3.9) to (2.12) show how this model calculate for these costs
In above equation, Dc is the total direct cost of the project and c i,j is the direct cost of activity i in unit j Ic represents the total indirect cost, that calculated by multiplying c in which is a determined indirect cost rate per day to T, the total project time that has been derived from scheduling the project c p describes the tardiness cost, which will be calculated using equation (3.11) This equation is an exponential equation in the basis from previous study by (L Zhang et al., 2014) Further it is modified to be the original formula divided by 10 to maintain the tardiness cost rate per day The reward (c r ) due to early completion is assumed to be c 1 per day, and T t is the target finish time of the project Then, the total cost of the project is calculated by following equations:
As in equation (3.13) and (3.14), the total cost for a project if it can finish earlier than the target time (T t ) will be lower than the total cost if the project is finished later than
T t This is because this project will get a reward, and those reward will be considered as a plus-money Whereas, when project is late, an additional cost is added which will cause cost overrun e Calculate the total project quality
Due to a wide different measurement units of quality in real construction project, each of the measurement units then transformed into a unified system to make a consistent evaluation of the quality (El-Rayes & Kandil, 2005b) Generally, researchers present the quality in their research as a percentage level from 0 to 100% or 0-1 100% means the highest quality, that can be reached by doing the activity in the best duration So, the benchmark here is the best duration mode The quality is changing as the decreasing or increasing of the duration (Jeunet & Bou Orm, 2020)
Quality of every activity were investigated and identified based on previous experience and researches In this study, to evaluate the quality of the project, the model used Quality Performance Index (QPI) that was introduced by (L Zhang et al., 2014) The QPI is calculated for each activity of each unit in the project The overall project quality will be defined as the integration of all quality of all activity In QPI, the quality of each activity is calculated from the function of time The best quality will come up if the activity is executed in the best duration If the activity are extended till the longest duration, the quality will decrease to 80%, as it is not efficient anymore to do the activity In the different condition, if the activity is rushed and finished earlier until the shortest duration it can be, the quality will also decrease until 50% Figure 3.7 shows the quality determined from QPI method
Figure 3.7 Quality Performance Index (QPI) The total quality of the project is calculated by equation (3.15)
The best duration of an activity can be defined as follow:
From above equations, QPI i,j is the quality of activity i in unit j The t i,j is the duration of activity i in unit j SD, BD, and LD are the shortest duration, best duration, and longer duration respectively The shortest duration and longest duration of an activity is respectively the shortest time and the longest time from all execution option that is available for that activity These coefficients can be derived from elimination of three equations a i,j ,b i,j ,c i,j are the coefficients determined by the quadratic function (see Figure 3.7) These three equations can be generated by substituting the t i,j with SD,
BD, and LD whose QPI are 50%, 80%, and 100% respectively
These steps are repeated in the algorithm until all uncertainty level being tested For each uncertainty level, these steps are also repeated in the MOSOS optimizer to test the resource option arrangement and unit sequence until the stopping condition is reached and a set of optimal solution is generated at the end.
Optimization Using Multiple Objective Symbiotic Organism Search Algorithm (MOSOS)
Decision variables are the things that will be controlled in the optimization It is the factors that may influence the result of the study Here, the decision variables are the factor that influence the time, cost and quality in the project being studied The decision varibles of this study is the resource utilization options Resource utilization option may include the material types, equipment types, construction method, crews formation, and the overtime work All these variables are combined into a single variable Each activity in the project has more than one resource ulitization option to be selected Each of these resource utilization will generate the different activity duration, ativity cost, and also the quality One of these options will be selected to execute the activity in the project based on its performance in the project Once a resource for an activity is selected, then it will be used to finish the activity in all unit of the project
Since the model in this study using the soft logic, the unit arrangement may affect to the starting time of each activity and later will give impact to the total project duration Repetitive project consist of some activities that being execute in many units This means that the crew in the project need to do the same activity repeatedly Resource availability and task dependency are the decision to start an activity in the project Actually, the unit sequence will just be determined randomly by the model In other words, it will not be maintained but still influence the project performance
The objective function of this model is to minimize the total project duration and cost while maximizing the project's quality of work The following section discusses these objective functions a Minimize the total cost
As mentioned before, the total cost consist of the direct cost, indirect cost, tardiness, and rewards TKHGLUHFW FRVWLVWKHVXPRIDOODFWLYLW\ảVGLUHFWFRVWDQGWKHLQGLUHFW cost is proportional to the duration of the project So, in this model, the indirect is assumed to be a constant per day Beside the direct and indirect cost, the other cost being consider to be added to the total cost of a final option are tardiness cost and incentives The tardiness cost is a penalty given due to the late completion time of the project, while the incentive is the bonus given to the contractor due to early completion of the project Following equation is formulated to minimize the cost
Minimize C Dc Ic Tc (3.17) b Minimize the total time
The second objective function is to minimize the project duration The total project duration is vary for all possible solutions due to the execution options of each solutions and also the unit sequence arrangement Following equation is used to minimize the total project duration
Minimize T EF I J , (3.18) c Maximize the quality
The overall quality of the project is depend on the quality of each activity in each unit of the project After determining these quality by applying Quality Performance Index (QPI) as described in equation (3.15) and (3.16), then the overall project quality can be TXDQWLILHGDVWKHDYHUDJHRIDOODWLYLWLHVảTXDOLW\LQWKHSURMHFWDVFDQEHVHHQLQ equation (3.19)
The optimization process by SOS algorithm is done by following steps a Information setting and initialization of the ecosystem
In this step, all the project data are being read by the algorithm The data includes WKHDFWLYLWLHVảGXUDWLRQFRVWDQGTXDOLW\WKDWKDVEHHQSURFHVVHGEHIRUHLQIX]]\ process; the generation number as well as the ecosystem size; the decision variables; and objective functions The generation number will represent for how many interation or repetition the algorithm will do to finish the problem On the other side, the ecosystem size is the number of solutions for each generation One organism represent one possible solution that can be used to execute the project This will end up as approximately the number of possible solution that come at the end These data and parameters are determined by the user
After that, the algorithm will initialize the organisms of the ecosystem Initialization will reveal the decision variables of each organism Then, using the decision variable, the resource option for each activity is determined From this information, the algorithm will automatically calculate the objective function value, which in this study are the total duration, total cost, and the total quality This calculation is done in scheduling and estimating subsystem The objective function value then sticked up together with the decision variable and form the organism Each organism in the ecosystem can be illustrated in equation (3.20)
Decision Variable Objective Function Valu
Index i indicates the i th activity in the project (n is the last activity) x i is the decision variable for activity i y 1 , y 2 , y 3 are the objective function value of project duration, project cost, and the overall quality respectively For this case, there are three objective functions, so that there are also three numbers present on the right side of the organism as the objective function value b Non-dominated Sorting
This step calculates the ranking of each organism as in the equation (3.20) based on the objective function value the organism has Each organism in the ecosystem is compared to the other organism in terms of the objective function values The organism with a better objective function value will have a higher rank One organism is said to be better and has a higher rank than the other organism if it meets condition in equation (3.21) and (3.22) Let say the comparison between organism X 1 andX 2 X 1 is better than X 2 if equation (3.21) which indicate that the objective function value of X 1 is no worse than X 2 in all objectives, and equation (3.22) that describe the objective function value ofX 1 is strictly better thanX 2 in at least one objective, are fulfilled
Non-dominated sorting will sort all organism based on the rank of the organism The rank of each organism depends on how many other-organism are being dominated by this organism Each rank in the ecosystem may consist more than one organism To compare the organism in the same rank, crowding distance is utilized The crowding distance of a particular organism is calculated based on the objective function value of the neighboring organism located in the previous and after the particular organism Then the total crowding distance an organism has is the sum of all crowding distance of all objective function as shown in Eq (3.23) Figure 3.8 depict the crowding distance of an organism (S1) Literally, the crowding distance an organism has is the division of the difference in objective function value of the next organism with the previous organism to the difference of the maximum objective function value with the minimum objective function value It depends on the number of objective function, where the total crowding distance should be the sum of all crowding distance in all objective function
Figure 3.8 Crowding Distance of an Organism
Above calculation for crowding distance is for all organism in the ecosystem, except for the first and the last organism The first and last organism only have one neighboring organism, thus the crowding distance of these organism is set to be infinitive
After sorting all organism in the ecosystem based on the rank and the crowding distance, organisms are put into a new ecosystem one by one starting from the upper organism (the best organism with the highest rank) The number of organism that enter the ecosystem is remain the same as the ecosystem size that has been determined in the first step When the ecosystem is full, all the left organism is not being used anymore c Evolution Process
Evolution process is the process to search for the optimum solution In SOS algorithm, this process is done through three phases, as already mentioned before: mutualism, commensalism, and parasitism phase Each organism that will be selected sequently from the ecosystem will interact to the other randomly-selected organism and doing all these three phases x Mutualism Phase Reflecting the real symbiotic in the real life, mutualism phase in this algorithm will also give advantage for both iteraced-organisms The advantage in this terms are the mutual survival This means that both organisms will evolve into a new organism (Cheng & Prayogo, 2014) The new organism is formulated in equation (3.24) and (3.25) When two organisms (let say X i and X j ) interact each other in the mutualism phase, a mutual vector will be generated This reflects the characteristic of the relationship The mutual vector is formulated in equation (3.26) Further, each benefit gathered by each organism are indexed BF 1 and BF 2 the benefit obtained by the each organism may not be equal one another One organism may get more benfit than the other organism Thus, the benefit of BF 1 and BF 2 are randomly set to be 1 or 2 The mutual vector and the benefit of each organism will impact to the regeneration of the new organism The regeneration will present the decision variable of the new organism itself
From the above equation, rand(0,1) is a random number ranged from 0 to
1 X best is the best organism This organism has a good objective function value Usually it is in the first rank of the ecosystem If the organism in the first rank is not a single orgnism, X best will be selected randomly
MODEL IMPLEMENTATION AND VALIDATION
Model Implementation
The first case study being analyzed is a concrete bridge project that has been used before by (Hyari & El-Rayes, 2006; Selinger, 1980; Tran et al., 2018) Excavation, foundations, columns, beams, and slabs work are among the five activities included in the project The bridge is supported by four piers and has three main spans In other words, the project's activities will be repeated in four units The general information of the first case study with the predecessor activity is served in Table 4.1 The activity predecessor is the activity that must be finished before starting a certain activity In activity 1 to 4, the unit predecessor is the previous unit For example the unit arrangement for soft logic is 2 ± 3 ± 1 ± 4 ± 5, then activity in unit 3 can only be started when activity in unit 2 is finished, and so on with the other unit The unit predecessor for activity 5 is different, that is 2 previous unit This means that one unit can only be started when the 2 units in previous activity are finished
Table 4.2 shows the data from the first case study The data are in optimistic, most likely and pessimistic condition The indirect cost is set to be $5,000/day and the initial cost is $120,000 as the information from previous study
Table 4.1 Activity Predecessor of Case Study 1
Table 4.2 Data of Activities in Case Study 1
Activity Unit Alternatives Time (day) Cost ($)
The second case study involves a large-scale project with 19 activities and 5 sections
In other words, there are 95 tasks need to complete The goal of this case study is to investigate if the model can be applied to a real-world project with numerous activities This case study was first analyzed by (L Zhang et al., 2014) employing the initial duration, shortest duration, and longest duration However, to illustrate the repetitive project in this study, it was adjusted to be multiple-house project The project consists of 5 identical units, each of which is a three- story house Using the initial duration option in all activities, the overall project duration is
The target finish time for this case study is set at 235 days The project's indirect cost rate is $5,000 per day, while an incentive of $3,600 per day is offered for early completion Table 4.3 and Table 4.4 provide detailed project data for the second case study.
Table 4.3 General Information of Case study 2
Table 4.4 Data of Activities in Case study 2
Activity Unit Alternatives Time (day) Cost (¥)
The project data undergoes fuzzy logic processing to address uncertainty, with the output serving as input for project scheduling and estimation via the SOS algorithm The first model employs 100 generations and 50 ecosystem size, while the second model uses 150 generations and 50 ecosystem size Table 4.5 presents optimal solutions for minimum project duration, total cost, and total quality, considering trade-offs between these objectives Each solution assigns a single resource to each activity Notably, all solutions in Table 4.5 correspond to an uncertainty level of 1.
Verification of the model's accuracy is possible by comparing its solutions to those obtained in earlier studies This indicates certainty or a lack of consideration for uncertainty.
Table 4.5 Optimum Solutions from the Case Study 1
Sorted by Resource Option Unit Sequence/activity Project Performance
The first solution to this model is achieved by using resource option 1 1 3 1 1 for each activity with a unit sequence of 3-4-2-1, which results in a minimum total project duration of 104.4 days The second solution, which utilizes a different resource and unit arrangement, reduces the total cost to $1,898,500 but results in a longer duration compared to the first solution The third solution maximizes quality to 0.961, which is higher than the first and the second solutions, but requires more time and money The final solution strikes a balance between time, cost, and quality It is important to note that the unit sequence for activities 1 through 4 in Table 4.5 is identical, but differs for activity 5 This is because activity 5, which is slab work, contains only three units and has a task dependency of greater than one For instance, before beginning activity 5 in unit 3, activity 4 in units 2 and 3 must be completed
These solutions perform admirably when compared to those from previous studies As the model is based on previous research, particularly in terms of the cost, the solutions in Table 4.5 do not include the tardiness cost and reward/bonus in the total cost (Hyari & El- Rayes, 2006; Selinger, 1980; Tran et al., 2018) analyzed this project under hard logic conditions, finding that the unit sequence of 1-2-3-4 resulted in the shortest duration of 117.9 days, 106.8 days, and 106.8 days, respectively Only one of these studies (Tran et al., 2018) quantifies the cost and quality The outcomes of that research has the cost of $1,966,476 with the quality of 0.73 It is comparable to this study, which found that by following the unit sequence 3-4-2-1, the project could be completed in 104.4 days for a cost of $ 1,987,100 and a quality of 0.76 However, the model is superior because it provides solutions to the uncertainty condition
Table 4.6 Selected Optimum Solutions from Case Study 1
Sorted by Resource Option Unit
Figure 4.1 3D View in Time, Cost, and Quality of Optimum Solutions in Case Study 1 The optimal solutions for the first case that were fully generated by this model (including tardiness cost and incentives) are shown in Table 4.6 The project's target duration has been set to 108 days, based on the shortest duration generated in the previous study The incentive for earlier completion is 1,000 dollars per day, and the cost of tardiness is calculated according to the given formula Each solution in Table 4.6 is a distinct solution based on a resource option Each solution has six possible outcomes, that differs the uncertainty level The following levels of uncertainty are being examined: 0, 0.2, 0.4, 0.6, 0.8, and 1 Figure 4.1 illustrates the three-dimensional view of the solutions for levels of uncertainty 0, 0.2, 0.4, 0.6, DQG DV DQG [ UHVSHFWLYHO\ )LQDOO\ Figure 4.2 illustrates the time-cost relationship for the first case solutions from this study and the previous study The results from Hyari and El-Rayes (2006) and Selinger (1980) did not generate the total cost; rather, they are depicted in the figure to help to explain the result comparison
Figure 4.2 2D View in Time and Cost of The Solutions in Case Study 1
Table 4.7 Selected Optimum Solutions from Case Study 2
Solutions Uncertainty Time Cost Quality Execution Options Unit
Table 4.7 illustrates five solutions from a set of non-dominated solutions in the second case study Due to the modifications made to the project, the results of this study cannot be compared to those of previous studies The previous study completed the project in 136 days with only one building, whereas this study completed it in 191 days for five similar buildings by using a single resource In terms of quality, this model's output could reach as high as 0.98 in the previous study if the project is completed within 260 days
The first three solutions are chosen on the basis of their highest objective function values, while the fourth and fifth solutions are chosen to compare the effect of the quality performance index on the solutions In the first and second solution, it is obvious that as uncertainty increases, time, cost, and quality increase, whereas in solutions 3, 4, and 5, time and cost increase but quality decreases By comparison, the total duration of these three solutions exceeds the project's target duration and is significantly longer than the duration of the first and second solutions In analysis, this is the effect of the quality performance index, which quantifies the quality of each activity in this project as a function of its duration The quality increase as the execution time approaches the best duration, but after that, extending the project duration results in a decrease of work quality In other words, projects lasting more than 250 days are no longer effective Figure 4.3 depicts a three-dimensional view of the time cost quality relationship for the optimum solutions in the second case study
Figure 4.3 3D View in Time, Cost, and Quality of the Optimum Solutions in Case Study 2
Figure 4.4 Tradeoff in Time ± Quality and Cost ± Quality of the Optimum Solutions in Case Study 1
Figure 4.5 Tradeoff in Time ± Cost, Time ± Quality, and Cost ± Quality of the Optimum Solutions in Case Study 2
Figure 4.4 and Figure 4.5 illustrate the tradeoff objectives for each solution in case study 1 and 2 According to the figures, the shorter the project duration, the higher the total cost of the project, and vice versa; however, if the project duration extends and exceeds the target finish time, the cost of the project increases due to the effect of indirect costs and tardiness costs Additionally, it is demonstrated that the shorter the project duration, the lower the quality, and the longer the project duration, the higher the quality In both case studies, the cost-quality relationship demonstrated that the quality decrease as the cost decrease, but for some solution the quality keeps decreasing when achieving the highest cost This is correlated to the project duration, when the duration is too long and exceed the target time, cost overrun incurred and will result in lower quality of works Additionally, there is a significant cost increase that can be attributed to tardiness and indirect costs, primarily as a result of the longer project duration, that is why the solution with this characteristic will have a lower quality of work It is also interesting to note that as the solution moves from not considering uncertainty to considering it (i.e from uncertainty level 1 to 0), the total project duration, cost, and quality all increase dramatically in all solutions.
Model Validation
To validate the solutions generated by this model, this study compared the SOS algorithm's performance to that of other widely used algorithms NSGA-II (non-dominated sorted genetic algorithm) and MOPSO (multiple objective particle swarm optimization) are also being evaluated After comparing the results of each algorithm, the robustness of the SOS algorithm used in this study is determined Additionally, the total number of optimum solutions generated by each algorithm is compared This is because multiple objective optimization seeks to discover a set of non-dominated solutions to the problem under investigation As a result, it is preferable for the algorithm to find as many optimal solutions as possible (Tran et al., 2016)
Table 4.8 Comparison of the Optimum Solution from the Three Algorithms
Sort by Algorithm Time Cost Quality
Table 4.8 summarized the results of the optimum solution generated by the three algorithms in case study 2 in terms of time, cost, and quality The algorithm's parameters, such as generation and population, remain constant, at 150 generations and a population size of 50
As can be seen from the table, when the optimum solution is sorted by time, the SOS algorithm generates the shortest time compared to the other algorithms, which is 191 days MOPSO can obtain 199 days, but this is still a long time in comparison to the result of SOS NSGA-II produces the longest duration of all of these algorithms, that is 202 days When sorted by cost, SOS came in at the lowest cost of 6,518,000, slightly higher than MOPSO, but with a shorter time and higher quality than MOPSO, whereas NSGA-II project's cost is quite high in comparison to SOS and MOPSO Moreover, when sorting the quality, the highest quality that MOSOS can generate is 0.98, which is significantly better than the other solutions from MOPSO and NSGA-II with the shorter duration and lower cost
Table 4.9 contains the other comparison that compares the number of optimum solutions generated by each algorithm According to the results in the table, the SOS algorithm can obtain a larger population size for the optimal solution than the other algorithms As a result, the SOS algorithm is capable of generating a greater number of optimal solutions than the other two algorithms Thus, the SOS algorithm is a robust algorithm that is extremely effective at resolving the problem at hand
Table 4.9 Comparison of the Total Optimum Solution from Three Algorithms
Algorithms SOS NSGA.II MOPSO
Result Discussion
The comparison results indicate that the newly proposed model utilizing MOSOS outperforms other popular studies with different multiple objective algorithms Additional discoveries discussed in the following sections
A time-cost-quality trade-off is one way to identify a suitable construction method for each activity in the project that aims to accomplish the same goal as the initial construction method within less time, at a lower cost, and with higher quality of work It is critical to select the most appropriate construction method for each activity in the project, as a different construction method will result in a different project outcome Additionally, considering uncertainty, which reflects a lack of certainty regarding the duration and cost of each activity in the project, is critical, as numerous uncertainty factors such as inclement weather, equipment failure, material availability, and poor site condition may manifest themselves during the project's implementation
The research objectives were met through the integration of the SOS algorithm and fuzzy logic The model used in this study included a fuzzy alpha cut to account for the project uncertainty The fuzzy sets in Triangular Fuzzy Number is used to model the time and cost of each project activity The quality of each activity in the project was determined by its duration of execution The first case study demonstrates the model's validity The model's solution is efficient and compares favorably with the previous study in terms of time, cost, and quality
The second case demonstrates the proposed model's suitability for a larger and real construction projects As a result of the model, a set of optimal solutions is generated
This study presents a methodology to determine optimal project solutions under uncertainty It offers a range of options tailored to different uncertainty levels, empowering decision-makers to select the solution that best aligns with their risk tolerance As uncertainty rises, projects typically experience increases in duration, cost, and quality requirements This methodology provides valuable insights for project planners by quantifying the impact of uncertainty on project outcomes, enabling them to make informed decisions that balance potential risks and rewards.
In other words, when a decision maker considers a higher level of uncertainty, implying that they will accept only a lower level of uncertainty for the project, they will have a greater range of time and cost If we wish to avoid the uncertainty that could jeopardize our project, we will increase our preparations (i.e we consider the risk contingency to handle if the uncertainty occurs) While disregarding uncertainty (uncertainty level = 1) implies that the decision maker accepts greater uncertainty, which results in reduced time, cost, and quality It is critical to note here that the uncertainty level does not describe the probability of the uncertainty occurring in the project or the probability of its occurrence being reduced; rather, it describes the impact of the uncertainty on the project When a decision maker considers the highest level of uncertainty, this does not necessarily mean that the project will last in the longest time or be the most expensive This means they have more safety in time and cost; when uncertainty occurs, project performance does not suffer; but, when uncertainty does not occur, project performance may improve
The analytical results established that the SOS algorithm is the most powerful optimizer because it achieved a more diverse display in non-dominated solutions, more compromising solutions, and a high level of satisfaction It is demonstrated that the SOS algorithm is the optimal and most applicable algorithm for solving the problem at hand
Moreover, the results indicate that SOS accurately reflects a clear relationships between the three considered objectives, that are time, cost, and quality It is recommended for future studies to use this algorithm From a practical standpoint, the total possible combination solution in case study 2 is approximately 1.22 10u 10 for each uncertainty level It is generated by 19 activities with either two or three alternative options for each activity in a total of five units This model was run for 150 generations and a total of 50 ecosystems It is also effective and intelligently searching for optimal solutions in a short period of time The run lasted for ten minutes As a result, it is believed that the model can be used to solve a real-world project involving a greater number of construction activities in a reasonable amount of time.
CONCLUSION AND RECOMMENDATION
Conclusion
Every construction project's objective is to complete it on time, within budget, and with the highest possible quality As a result, these three parameters (time, cost, and quality) are critical to estimate and control Optimization in this field enables the discovery of the optimal method from a plethora of available options for completing the project and meeting the project objective The primary goal of time, cost, and quality optimization is to strike a balance between increasing direct costs and decreasing indirect costs while maintaining the same level of quality as the project provision A different construction method will result in a different project performance, that is why it is critical to find the most optimal solution that combines the shortest time and lowest cost with the highest level of quality
This study developed a hybrid model that combines the fuzzy logic approach and the multiple objective symbiotic organism search algorithm to solve time-cost-quality trade-offs in repetitive construction projects that subjected to uncertainty Fuzzy logic is used to represent the uncertainty associated with the project's duration and cost, while the SOS algorithm acts as an optimizer, searching for the most optimal way to implement the project The model is based on two case studies The first case study is used to validate the model by comparing it to the previous study The model performed admirably and produced a superior result in terms of project time, cost, and quality when compared to previous studies The second case examined the model's ability to manage a larger construction project in order to ensure that it is applicable in real construction Additionally, this study compares the model's solution to those generated by other widely used algorithms, such as NSGA-II and MOPSO The results demonstrate that the SOS algorithm is the most effective and applicable method for resolving the problem under investigation
The model's output is a set of optimal solutions for implementing the project at various levels of uncertainty ranging from low to high for both cases studied The optimal solution set contains useful information such as the optimal resource option for each activity and the optimal unit arrangement for performing the activities The analytical results indicate that estimating the project under uncertainty will result in a longer project duration, costing more, but having a higher quality, than if it is not considered at all In other words, the uncertainty impact to the project might be lowered with a definite increase of project duration or project cost By a thoroughly searching utilizing soft logic, the model can find the optimal solution that minimizes time and cost while maintain a high level of quality This solution may assist the decision-maker in determining the optimal method for implementing the project By defining their tolerance for uncertainty, they can determine which solution best fits their circumstances.
Research Contribution
This study contributes to the enhancement of the construction project's planning The process of selecting the most appropriate method for completing the project based on the total time, total cost, and overall quality is carried out in a systematic manner This study applies fuzzy logic and the multiple-objective symbiotic organism search (MOSOS) algorithm to the academic field Fuzzy logic is used to model time and cost uncertainty, and the quality of each activity is calculated based on its execution time MOSOS is a free parameter multiple- objective variant of the original SOS that is used in this study to optimize for the most optimal solution This study developed a scheduling subsystem that takes into account the time and cost uncertainty, and results in varying levels of quality performance Additionally, this study used soft logic to schedule for a larger search space with the shortest duration Moreover, the cost of tardiness as a result of schedule delays and the reward, which accounts for the bonus received by the contractor for earlier project completion, are being considered in order to arrive at a more realistic solution The findings of this study will provide useful references for civil engineering field for both academic and industrial field in determining estimateing the project quickly and accurately.
Future Works
Despite the model's effectiveness and robustness, several recommendations could be made to enhance and improve the model's intent The first, this study only considered a single resource for each activity, which in the implementation, requires each unit's activity execution to pause and wait for the previous unit Multiple resources can be added to a project, especially for a larger project, this intend to reduce the project's duration Second, the unit arrangement for the soft logic was determined randomly and was not treated as a decision variable As a result, additional research is required to address these limitations by considering multiple resource utilization strategies for each activity in the project and using the unit arrangement as a decision variable to find the most optimal solutions For potential extensions, a hybridization of the current model with other multiple criteria decision-making techniques is also appealing
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