Minimizing Delay in Construction Project at PT Freeport Indonesia using Crashing CPMPERT Approach and Monte Carlo Simulation
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This research aims to develop an acceleration solution to improve the delayed construction project at PT Freeport Indonesia. The study integrates Critical Path MethodProgram Evaluation and Review Technique (CPMPERT) using Primavera software and Monte Carlo simulation to analyze the delayed schedule and improve project scheduling practices. These methodologies help identify critical activities, consider different time estimates, and predict the probability of multiple outcomes of the improved schedule. The study shows a 13.9% chance that the construction will be completed in 164 days, determined by the Crashing CPMPERT method combined with the Monte Carlo simulation. The findings provide a robust framework for enhancing project scheduling practices, leading to more accurate schedule analysis and better schedule performance.
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Introduction
By 2050, the projected annual demand for essential minerals in lowemission energy technologies will exceed $400 billion (International Energy Agency, 2023). Mining is fundamental in the worldwide transition to lowemission energy. More mining is required for the transition, not less. Providing resources for the energy transition involves more than mining more of the same materials in the same way. Instead, these critical minerals and raw materials must be mined sustainably to power the future global economy.
In recent years, the Government of Indonesia (GOI), through regulation, has consented to a downstream mining policy that prohibits the export of unrefined mineral commodities such as copper. The philosophy of implementing the downstream of the mining industry in Indonesia follows the spirit mandated by Pancasila on the fifth principle, which demands the social welfare of every person in Indonesia (Krustiyati & Gea, 2023).
PT Freeport Indonesia (PTFI) is a limited liability company organized under the laws of the Republic of Indonesia that operates the mines in the Grasberg minerals district (Isselet al., 2023). The Grasberg open pit ceased production at the end of 2019 and transitioned to underground mines. The Mill Optimization Electrical System (MOES) construction project adds power supply and transformer capacity at the millsite to support the planned increase in concentrating and underground loads. The scope of the MOES construction project is divided into two subscopes: 230 kV Transformer Addition and SAG3 to Amole 115 kV Interconnect.
The 230 kV Transformer Addition scope of work intends to supply power to the latest Copper Cleaner facility. Therefore, the facility can only operate once the 230 kV Transformer Addition scope is done. When the Old Mine Tram Demolition project starts, the SAG 3 to Amole 115 kV Interconnect scope of work will be used as a redundant power line for the underground mines. Therefore, the Old Tram Demolition project cannot be started until the scope of work for the SAG 3 to Amole 115 kV Interconnect is completed.
PTFI Management instructs the Central Services Division to construct the MOES project. Initially, MOES construction was scheduled to be completed on September 26, 2024. However, the construction progress has yet to achieve its target, as shown by the MOES project’s earned value management (EVM) chart as shown in Fig. 1. As of April 28, 2024, the target construction progress is 62.78%, and earned progress is just 34.98%, making it 27.8% behind schedule. The MOES construction completion date is forecasted to be delayed to November 6, 2024.
The delayed completion date of the MOES construction project will impact the two projects mentioned before. The Copper Cleaner project needs the power from the MOES project on July 1, 2024, and the Old Tram Demolition will start on October 1, 2024. In this research, the problem is the delayed construction schedule of the MOES project and how to accelerate it to improve schedule performance.
This study addresses this problem by integrating the Critical Path MethodProgram Evaluation and Rating Technique (CPMPERT) and the Monte Carlo Simulation. These methodologies provide a comprehensive approach to identifying critical activities, considering different time estimates, and predicting the probability of multiple outcomes of the improved schedule. Ultimately, they enhance project scheduling practices, leading to more accurate schedule analysis and better schedule performance.
Literature Review
It is essential to approach construction projects in remote areas like other project management to ensure the acceleration from a delay, considering time, cost, and scope as crucial criteria for success. Time in project management identifying effective project management practices is the way to optimize success as a vital metric for information systems development initiatives (Sanchez & Terlizzi, 2017). It is essential to estimate time precisely to allocate resources efficiently, manage the budget and schedule, and mitigate risks (Huang & Chen, 2006). In remote areas, construction contractors have trouble attracting and retaining skilled workers, are exposed to different climates, and have a longer delivery time (McAnulty & Baroudi, 2010). The factor that primarily influences the productivity of construction projects in PT Freeport Indonesia is labor management (Almuntadzaret al., 2021).
Construction project delay in Indonesia, based on research investigation through questionnaires, was found to be a factor related to inaccurate resource planning (Susanti, 2020). 17 risks can cause delays in construction projects at PT Freeport Indonesia (Mulianoet al., 2021).
Integrating CPMPERT and the Monte Carlo simulation provides a comprehensive approach to accelerating delayed project schedules. CPM allows for the identification of critical activities in the project schedule. PERT estimates the activity time and obtains a probability estimate for completion time for the entire network. The Monte Carlo simulation then runs multiple scenarios of the project schedule.
Critical Path AnalysisProgram Evaluation and Rating Technique
The critical path of activities in a project is the sequence of activities that form the longest chain in terms of their time to complete (Jacobs & Chase, 2018). If any of these activities in the critical path is delayed, the overall project is delayed. Multiple paths of the same length through the network are also possible, so numerous critical paths exist. Determining scheduling information about each activity in the project is the primary goal of CPM techniques. The techniques calculate when an activity must start and end, together with whether the activity is part of the critical path.
PERT is the best procedure if a single estimate of the time required to complete an activity could be more reliable. These three times allow analysts to estimate the activity time and obtain a probability estimate for completion time for the entire network (Jacobs & Chase, 2018). A feature of using threetime estimates is that it enables the analyst to assess the effect of uncertainty on project completion time. The following are the appropriate steps to demonstrate the PERT approach:
1. Identify each activity in the project and estimate how long it will take to complete each activity. The three estimates for an activity time are a = optimistic time, the minimum reasonable period in which the activity can be completed; m = most likely time, the best guess of the time required; b = pessimistic time, the maximum reasonable period the activity would take to be completed.
2. Determine the required sequence of activities and construct a network reflecting the precedence relationships. A way to do this is first to identify the immediate predecessors associated with an activity. The immediate predecessors are the activities that need to be completed immediately before an activity.
3. Calculate the expected time (ET) for each activity based on the beta statistical distribution and, in the simplified version, permits straightforward computation of the activity mean and standard deviation:
4. Determine the critical path using the expected times. Consider each sequence of activities that runs from the beginning to the end of the project. The critical path is the most extended sum of the activity times. The entire project will be delayed if any critical path activity is delayed. For some activities in a project, there may be some leeway in when an activity can start and finish, which is called the slack time in an activity. The variance, σ^{2}, associated with each ET is computed as follows:
5. Apply the standard normal distribution to Determine the probability of completing the project on a given date by summing the variance values associated with each activity on the critical path.
6. Substitute this figure, the project due date, and the expected completion time into the Z transformation formula, where D is desired completion date for the project, T is expected completion time for the project, $\sum {\sigma}_{cp}^{2}$ is sum of the variances along the critical path, with the formula:
7. Calculate the value of Z, which is the number of standard deviations of a standard normal distribution that the project due date is from the expected completion time.
8. Using the value of Z, find the probability of meeting the project due date using a table of normal probabilities. The expected completion time is the starting time plus the sum of the activity times on the critical path.
Monte Carlo Simulation
Monte Carlo simulation is a term applied to stochastic simulations that incorporate random variability into the model, either discrete, realtime, or some combination thereof (Bonate, 2001). The term ‘Monte Carlo’ was first coined by a group of scientists during their work on developing the atomic bomb during World War II and was a reference to the gaming city in Monaco. To perform Monte Carlo Simulation, the sampling distribution of the model parameters must be defined a priori, for example, a normal distribution with mean $\mu $ and variance σ^{2}. Monte Carlo simulation repeatedly simulates the model, drawing a different random set of values from the sampling distribution of the model parameters, the result of which is a set of possible outcomes (Bonate, 2001).
Newbyet al. (2010) conducted a Monte Carlo simulation based on estimates when activity durations follow known probability distributions. Meanwhile, Karabulut (2017) conducted a Monte Carlo simulation with 9,000 iterations of a construction project in which the activity duration estimates were obtained from PERT. Monte Carlo simulations are also utilized to evaluate duration variability for project scenarios, including anticipated or most probable time durations. Deshmukh and Rajhans (2018) compare the PERT technique and Monte Carlo simulation with 1320 iterations for probabilistic estimation of a project’s completion time. Wijaya and Sulistio (2019) conducted a Monte Carlo simulation with 10,000 iterations for an apartment construction project in Indonesia. Monte Carlo simulation takes the deterministic time durations obtained and puts them in long repeatable trials by iterating over long repeat durations. These coincidental values for each probabilistic distribution were used to estimate the completion time for a project with different durations between some frequencies (Karabulut, 2017).
Research Methodology
This study employs a mixed methods approach to integrate CPMPERT and Monte Carlo simulation to minimize project schedule delay. Data were collected through a questionnaire with project control experts, analysis of the current project schedule in Primavera software, observation of the project progress report, and field observations. The crashing of the CPMPERT process involved identifying critical activities, assigning most likely and optimistic time estimates, and resulting in an accelerated completion date.
The current schedule in Primavera is filtered to show only onprogress and notstarted activities. The researcher requested project control experts to input the optimistic and most likely time duration in these activities based on the current time duration to calculate the expected time duration as a crashed time duration using the PERT approach in Microsoft Excel. This method involves project control experts drawing on their experience with each construction activity to evaluate the duration.
The expected duration of each activity will then be updated into the current schedule in Primavera to make the crashed schedule. After running the schedule, Primavera can show the activities in the critical path. The sum of the critical path activities variances will be used to calculate the probability of meeting the project completion date.
After the crashing PERT is completed in Primavera, the crashed schedule is simulated with a Monte Carlo simulation utilizing Microsoft Excel with 10,000 iterations. The mean µ and variance σ^{2} from the PERT method are used in the Monte Carlo simulation for each critical path activity. These remaining time durations for each probabilistic distribution were used to estimate the completion time for the MOES project construction.
Result
The research methodology used Crashing CPMPERT to identify critical activities while considering different time estimates systematically. The results in Table I show optimistic, most likely, and pessimistic time estimates obtained from the questionnaire. Table I also shows the current work sequence established in the MOES construction project by showing the activity predecessor.
Activity ID  Predecessor ID  a  m  b  ET  σ ^{ 2 } 

1050  1510  1  1  1  1  0 
1060  1050  1  1  1  1  0 
1070  1110  1  1  1  1  0 
1080  1070  1  1  1  1  0 
1090  1080  1  1  1  1  0 
1100  1090  1  1  1  1  0 
1110  1120  1  1  1  1  0 
1120  1060  1  1  1  1  0 
1210  1200  1  3  3  2.67  0.11 
1270  1260  1  1  1  1  0 
1280  1270  1  1  1  1  0 
1290  2130  1  1  1  1  0 
1300  1290  1  1  1  1  0 
1310  1300  1  1  1  1  0 
1320  2460  1  1  1  1  0 
1330  1320  1  1  1  1  0 
1340  1330  1  1  2  1.17  0.03 
1440  2530  1  1  1  1  0 
1480  1590  1  1  2  1.17  0.03 
1500  1490  4  5  5  4.83  0.03 
1510  1500  1  3  3  2.67  0.11 
1520  1310  1  1  2  1.17  0.03 
1530  1540  1  1  2  1.17  0.03 
1540  1520  1  1  1  1  0 
1550  1530  1  1  1  1  0 
1560  1550  3  4  4  3.83  0.03 
1570  1580  8  11  12  10.67  0.44 
1575  1620  1  1  3  1.33  0.11 
1577  1650  3  3  4  3.17  0.03 
1610  1690  1  1  1  1  0 
1620  1660  1  1  1  1  0 
1630  1670  1  1  1  1  0 
1640  1680  1  1  1  1  0 
1650  2090  1  1  1  1  0 
1660  1590, 1430  1  1  1  1  0 
1670  2110  1  1  1  1  0 
1680  1770  1  1  1  1  0 
1690  1780  1  1  1  1  0 
1760  2540  1  1  2  1.17  0.03 
1770  1760  1  1  1  1  0 
1780  1820  1  1  1  1  0 
1790  1600  1  1  1  1  0 
1800  1810  1  1  2  1.17  0.03 
1810  1800  1  1  1  1  0 
1820  2460, 1420  1  1  1  1  0 
1830  1840  1  1  1  1  0 
1840  1850  1  1  1  1  0 
1850  1860  1  1  1  1  0 
1860  1870  1  1  1  1  0 
1870  1880  1  1  1  1  0 
1880  1890  1  1  1  1  0 
1890  1560  1  1  1  1  0 
1900  1910  1  1  1  1  0 
1910  1920  2  2  4  2.33  0.11 
1920  1930  1  2  3  2  0.11 
1930  1960  1  1  1  1  0 
1940  2130  1  1  1  1  0 
1950  1900  1  2  2  1.83  0.03 
1990  2010  3  3  4  3.17  0.03 
2010  2050  1  2  2  1.83  0.03 
2050  2060  1  1  1  1  0 
2060  2070  1  1  1  1  0 
2070  2210  1  1  1  1  0 
2080  2120  1  1  1  1  0 
2120  2060, 2460  1  1  2  1.17  0.03 
2130  2140  3  4  4  3.83  0.03 
2140  2150  21  26  30  25.83  2.25 
2150  2140  8  9  12  9.33  0.44 
2160  2090  10  11  14  11.33  0.44 
2170  2180  1  3  3  2.67  0.11 
2180  1510  3  4  6  4.17  0.25 
2190  2200  1  1  2  1.17  0.03 
2200  1610  1  1  3  1.33  0.11 
2210  2270  1  2  3  2  0.11 
2270  2280  3  3  4  3.17  0.03 
2280  2290  1  2  3  2  0.11 
2290  2300  3  4  4  3.83  0.03 
2300  2310  1  2  3  2  0.11 
2310  2320  2  3  4  3  0.11 
2320  2330  1  2  2  1.83  0.03 
2330  2340  1  1  1  1  0 
2340  2350  1  1  1  1  0 
2350  2360  1  1  2  1.17  0.03 
2360  2370  1  2  2  1.83  0.03 
2370  2380  1  1  1  1  0 
2380  2390  1  1  1  1  0 
2390  2400  1  1  1  1  0 
2400  1210  1  1  1  1  0 
2410  2420  1  2  2  1.83  0.03 
2420  2430  1  2  2  1.83  0.03 
2430  2440  1  1  1  1  0 
2440  2450  1  2  2  1.83  0.03 
2450  2500  1  2  2  1.83  0.03 
2460  2470  1  1  1  1  0 
2470  2140  5  7  7  6.67  0.11 
2480  2490  5  7  7  6.67  0.11 
2490  1510  4  6  7  5.83  0.25 
2500  2530  5  6  7  6  0.11 
2510  1360  3  4  4  3.83  0.03 
2560  2570, 1180  1  2  3  2  0.11 
2620  3000  1  2  2  1.83  0.03 
2900  2700  5  6  7  6  0.11 
2910  2600  4  5  7  5.17  0.25 
3200  2750  5  7  7  6.67  0.11 
1180  2630  0  0  0  0  0 
1360  2640  1  2  3  2  0.11 
1370  2590  4  5  5  4.83  0.03 
1380  1390  16  17  21  17.5  0.69 
1390  2690  3  5  5  4.67  0.11 
1400  2580  6  9  10  8.67  0.44 
1410  3170  4  5  7  5.17  0.25 
2550  2610  1  2  2  1.83  0.03 
2580  3180  1  2  2  1.83  0.03 
2590  2720  1  2  2  1.83  0.03 
2600  2730  1  3  3  2.67  0.11 
2610  2740  1  3  3  2.67  0.11 
2630  2780  1  2  2  1.83  0.03 
2640  2760  1  2  2  1.83  0.03 
2650  2820  1  1  2  1.17  0.03 
2660  2770  1  2  3  2  0.11 
2670  2670  13  14  21  15  1.78 
2680  2800  6  8  11  8.17  0.69 
2690  2810  15  16  20  16.5  0.69 
2700  1410  4  6  6  5.67  0.11 
2710  2850  15  17  21  17.33  1 
2720  2860  5  5  6  5.17  0.03 
2730  2710  1  1  1  1  0 
2740  2670  1  1  1  1  0 
2750  3090  1  1  1  1  0 
2760  2830  2  3  4  3  0.11 
2770  2890  2  3  4  3  0.11 
2780  2920  3  4  5  4  0.11 
2790  2930  1  2  2  1.83  0.03 
2800  3090  7  9  10  8.83  0.25 
2810  2950  5  5  7  5.33  0.11 
2820  3100  1  3  3  2.67  0.11 
2830  2970  4  5  7  5.17  0.25 
2840  2980  3  3  5  3.33  0.11 
2850  2710  1  1  2  1.17  0.03 
2860  2940  1  3  3  2.67  0.11 
2870  3010  7  10  12  9.83  0.69 
2880  3020  1  1  1  1  0 
2890  3030  7  9  11  9  0.44 
2920  3040  5  7  7  6.67  0.11 
2930  3050  5  5  7  5.33  0.11 
2940  3080  5  6  9  6.33  0.44 
2950  3100, 3160  1  2  3  2  0.11 
2960  2680  1  1  1  1  0 
2970  3090  1  1  1  1  0 
2980  2930  1  1  1  1  0 
2990  3110  1  1  1  1  0 
3000  3120  3  4  5  4  0.11 
3010  3130  1  1  1  1  0 
3020  3010  1  2  3  2  0.11 
3030  1350  4  5  8  5.33  0.44 
3040  1180  1  2  2  1.83  0.03 
3050  1370  3  4  4  3.83  0.03 
3060  1380  2  4  4  3.67  0.11 
3070  2660  1  1  3  1.33  0.11 
3080  3150  1  1  2  1.17  0.03 
3090  3100  5  7  8  6.83  0.25 
3100  3160  1  2  3  2  0.11 
3110  2700  4  6  7  5.83  0.25 
3120  2780  5  7  7  6.67  0.11 
3130  3190  5  5  7  5.33  0.11 
3140  2420  4  6  7  5.83  0.25 
3150  2560  5  6  8  6.17  0.25 
3160  2910  1  1  3  1.33  0.11 
3170  3200  1  2  3  2  0.11 
3180  2090  1  1  2  1.17  0.03 
3190  1575  19  24  28  23.83  2.25 
The construction schedule in Primavera is then updated with each activity’s expected time (ET) to analyze the crashing PERT schedule. After updating the expected duration of each activity and running the schedule in Primavera, the MOES project will be completed in 165 days. This accelerated construction duration shows that the crashingPERT method can minimize the delay from 192 to 165 days.
The Primavera software generates a resource assignment to calculate the earned value of the crashed construction schedule. Fig. 2 shows an EVM chart comparing the current schedule and crashingPERT results. The EVM curve of the crashingPERT schedule is higher than the current CPM curve, which indicates the delayminimizing effect of the crashingPERT method.
The variances associated with critical activities shown in Fig. 3 obtained from Primavera will be used to find the probability of completion in Microsoft Excel. Thus the $\sum {\sigma}_{cp}^{2}$ = 0.11 + 0 + 0.027 + 0.44 + 2.25 + 0.027 + 0 + 0.027 + 0.027 + 0 + 0.11 + 0.11 + 0.25 + 0.11 + 0.25 + 0.11 + 0.11 + 0.11 + 0.25 + 0.44 + 0.11 + 0.11 + 0.25 + 0.11 + 0.11 + 0.25 + 2.25 = 7.972. The probability of completing the construction on October 10, 2024. D, then, is 164. The expected completion time was found to be 165. Substituting into the Z equation and solving, we obtain:
Looking at the table of areas under cumulative standard normal distribution, the Z value of −0.35 yields a probability of 0.36317, which means that the Central Services Division has about a 36% chance of completing the project in 165 days.
Furthermore, the study conducted a Monte Carlo simulation to run multiple project schedule scenarios in Microsoft Excel. According to the Monte Carlo simulation, the probability of completing the construction in 165 days, as determined by crashing CPMPERT, is about 13.9%, as shown in Table II. The probability is obtained from the frequency of 165 days from 10,000 iterations of the crashed schedule’s critical path. Fig. 4 shows the result of the Monte Carlo simulation in Microsoft Excel.
Remaining days  Frequency  Probability  Cumulative probability 

152  1  0.0001  0.0001 
153  0  0  0.0001 
154  3  0.0003  0.0004 
155  7  0.0007  0.0011 
156  19  0.0019  0.003 
157  39  0.0039  0.0069 
158  128  0.0128  0.0197 
159  216  0.0216  0.0413 
160  466  0.0466  0.0879 
161  733  0.0733  0.1612 
162  1062  0.1062  0.2674 
163  1252  0.1252  0.3926 
164  1391  0.1391  0.5317 
165  1342  0.1342  0.6659 
166  1135  0.1135  0.7794 
167  927  0.0927  0.8721 
168  593  0.0593  0.9314 
169  355  0.0355  0.9669 
170  185  0.0185  0.9854 
171  87  0.0087  0.9941 
172  39  0.0039  0.998 
173  11  0.0011  0.9991 
174  7  0.0007  0.9998 
175  1  0.0001  0.9999 
177  1  0.0001  1 
Discussion
The number of iterations in a Monte Carlo simulation depends on several factors, such as the complexity of the model, the number of variables and their relationship, the availability of time, and the convergence of the model. The more iterations run, the longer it will take and the more accurate the output response will be. The histogram begins to smooth out with more iterations. The gaps start to fill in, and a more stable and robust representation of the simulated output. However, there comes a time when, as the number of iterations increases, the smoothness of the histogram or the convergence does not necessarily increase significantly.
In their study, Newbyet al. (2010) presented a Monte Carlo simulation method to estimate the time involved in a mining project that has not yet started. This method employs Monte Carlo simulation to calculate the likelihood of a specific activity being part of the critical path, considering the uncertainty of activity durations. Meanwhile, the MOES construction project is still in progress and has already been delayed.
The basic idea of this technique is like that of CPMPERT, except that it is being crashed and focused on the critical path, not the probability of each activity being critical. In this research’s Monte Carlo simulation technique, the researcher assumes that each activity duration in the crashed critical path is a random variable that follows some probability distribution. Both studies consistently concluded that integrating Monte Carlo into the CPMPERT technique yields more accurate results than the classic technique alone. The Monte Carlo method effectively simulates the uncertainty in a construction project in a mining area.
The Central Services Division can implement the crashing CPMPERT method and Monte Carlo simulation to handle delayed construction projects. Their internal project control personnel will also benefit from implementing Monte Carlo simulation in their project reporting, not only enhancing their scheduling analysis but also informing the probability of the completion of a project to its client. The Central Services Division may need to conduct a Monte Carlo simulation before starting a construction project to determine the probability of a project being completed on time.
Conclusion
Utilizing the CPMPERT methodology, which integrates expert opinion in different time estimates, when crashing a delayed construction schedule presents numerous benefits. It has been empirically validated as a reliable timeestimating technique, and a simple analysis can be made quickly. More accurate time estimations can be attained by engaging knowledgeable and experienced specialists who profoundly understand the project’s uncertainties.
Integrating Monte Carlo simulation into the PERT Method offers an alternate technique to address the limitations of these classic scheduling methods in minimizing delay in a construction project. The MOES construction project case study demonstrates the effectiveness of this method in quantifying and simulating uncertainty in a construction project, hence providing more reliable estimations of construction completion time. The case study indicates that the Monte Carlo simulation provides a more accurate analysis than classic CPMPERT others, making it the viable choice for the construction project.
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