Engineering project control of comprehensive unit price fluctuation-time limit fluctuation-process adjustment

Abstract

When an engineering project requires a lot of time and the construction environment is complex, the unit price of materials and personnel will change, the project construction will be hindered, and the construction plan of the project should be adjusted. These uncertain interference factors will cause the earned value analysis results are quite different from or even contrary to the actual situation, so there will not be enough impartial data to help managers to control project. To this end, this paper analyzes how the price fluctuations, process adjustment and the abnormal construction period will affect the construction schedule and cost effect respectively, and further studies the corresponding methods of earned value correction. Based on case analysis, this paper studies the comprehensive correction method of earned value when cost unit price changes, working procedure is adjusted and construction period fluctuates in an abnormal manner. The method improves the theory of earned value and provides reference for engineering practices on project management.

Keywords

Engineering project multifactor interference modified earned value project control

1. Introduction

In construction projects, progress control, cost control and quality control are known as the “three controls” of the project. On the premise of ensuring the project quality, when managers control the project, the efficiency of project progress control and cost control will determine whether the project can start smoothly according to the plan, and its effect will directly affect the success or failure of project construction. Therefore, project cost-progress control is the most important work in the whole project management process. Therefore, in order to make project control real and efficient, we must comprehensively consider the corresponding relationship between project cost and progress control.

For the research of cost control, foreign research started earlier than domestic research. Alvarado put forward the “five step management method”, which focuses on the research, the active use of various effective means to strengthen management and control, focusing on the control of material cost, in order to pursue the minimum cost [1]. Bagherpour et al. based on the information construction, constructed the cost control information system operation platform, evaluated the implementation effect of the system platform, and put forward the cost management mode with effective use of information platform and competitive advantage [2]. Kang based on modern control theory, combined with dynamic control theory, constructed the cost control model, established the corresponding database to facilitate the selection of cost objectives, and then realized the dynamic control of construction project cost [3].

The earned value methodology can comprehensively consider the project progress to control the project cost. The methodology uses three basic variables, two deviation indexes and two performance indexes. Through the statistics of the actual data of quantities and costs at each monitoring point and the comparison and analysis of the planned value, the whole project can finally achieve the purpose of efficient cost control. This method has the characteristics of simple and intuitive, overall consideration and dynamic control. Therefore, the earned value methodology has also been greatly favored by managers in modern engineering project control. However, the traditional earned value methodology itself still has some limitations. In addition, the application of earned value methodology in China’s engineering project control also exposes some inherent defects, which limits the breadth and depth of earned value methodology in China’s project management practice. Therefore, combined with the actual situation of engineering projects in China, it is of great practical significance to modify and improve the traditional earned value methodology.

This paper first led out from the introduction that this paper is to improve and modify the traditional earned value methodology. Then the middle chapter of the article studied the interference of unit price change, construction period fluctuation and process adjustment on project control, put forward the corresponding correction and improvement methods, and studied the effect of the improvement methods in practical application with examples. Finally, the paper summarized the conclusions of this paper, and explained whether the improvement and correction methods proposed in this paper are relatively effective.

2. Research status

In 1967, the US department of defense published the US department of defense directive DODI700.2. This document included the principle of earned value management, and proposed the “Cost/Schedule Control System Criteria (C/SCSC)” [4]. In 2000, the Project Management Institute from U.S. included the concept of “Earned Value Management” in its revised “PMBOOK 2nd edition”, which marked that the project earned value theory has been comprehensively and extensively applied. Lipke has a deep attainments in this respect, and he was also a book called “Earned Schedule”, which has been spread and studied by scholars all over the world. At the 2007 International Metrics Congress, Lipke made a report entitled “Earned Schedule – an emergency enhancement to EVM”, which made a systematic and comprehensive description of the Earned Schedule [5]. Lipke et al. proposed a reliable forecasting method of the final cost and duration by using EVM, earned schedule (ES) and statistical prediction and testing methods [6]. Byung-Cheol and Kenneth proposed to use Kalman filter into the application of earned value technology, and elaborated to use the recursive processing of the prediction method of Kalman filter to modify the earned value data [7]. Yong-Woo and Glenn put forward to integrate the earned value theory and the final planning system, so that every task in the project can be effectively coordinated [8]. Khamooshi and Golafshani developed the Earned Duration Management (EDM) in which they decoupled schedule and cost performance measures and developed a number of indices to measure progress and performance of schedule and cost, as well as the efficacy and efficiency of the plan at any level of the project [9]. Byung-Cheol figured out a CPI stability probability analysis model to evaluate individual projects within the project construction duration based on simulation model [10].

The relevant research started quite late in China. In 1994, Hu reviewed the application of the earned value methodology in the construction of foreign engineering projects, and expounded the principle of the method of earned value in the management of project schedule and cost [11]. Qi put forward a method to integrate the management on project schedule, cost, quality, risk and other elements based on the earned value methodology [12]. Chang put forward the theory of multi-stage earned value methodology and studied the analysis method of cost overruns and schedule delays [13]. Lu built the project cost control process based on the improved earned value methodology, and verified the feasibility and effectiveness based on the case study [14]. Liu put forward the multi-factor performance evaluation model based on the multi-factor comprehensive analysis method for indexes in statistics [15]. Liu proposed the concept of earned value for effective construction period in view of the inconsistency between the actual project completion and the plan in the integrated control research on the cost/schedule of large water conservancy projects [16].

In conclusion, it can be seen that China’ engineering projects are developing rapidly, and the theory of earned value is widely used for project management in modern engineering projects. However, the distortion information displayed by the interference of multiple factors of the earned value theory for project management in practical projects will mislead managers and decision-making, and affect the efficiency of project management. At present, according to the characteristics of engineering projects in China, the research on the improvement and modification methods of earned value theory is still not comprehensive enough.

Therefore, in this paper, the research method of combining theory with practice is used to analyze the influence of three common interference factors on cost and schedule separately, and then combined with an example to study the project control method of modifying the traditional earned value analysis under the interference of multiple factors. Considering that many factors concurrently interfere with earned value analysis, the project control is studied. By modifying the relevant evaluation indexes of the existing earned value methodology, the modified earned value methodology is used to analyze the project from two aspects of schedule and cost. As far as possible, the earned value methodology can provide more accurate prediction value in engineering construction projects, so that managers can make more realistic judgment on the process of engineering projects. It has certain theoretical and practical significance for the research of cost schedule control method in the field of project management in China.

3. Interference of unit price changes on cost control

In the project construction, the unit price of labor, materials and equipment may change due to the large time span and complicated resource composition of the construction project. When using the earned value methodology to predict the cost, the staff fail to analyze the cost variation of personnel, materials and equipment respectively, so there is a large deviation in the cost prediction in the construction process and the management on the whole project has been deteriorated [17].

Definition 1: the cost deviation performance index CPI refers to the ratio of the budgeted cost to the actual cost of the completed project.

$\displaystyle\textit{CPI}=\frac{\textit{BCWP}}{\textit{ACWP}}$ (1)

Definition 2: EAC refers to the ratio of the total cost of budgeted project completion to cost deviation performance index.

$\displaystyle\textit{EAC}=\frac{\textit{BAC}}{\textit{CPI}}$ (2)

The dynamic variable cost of unit price influencing factor $i$ is $\Delta C_{i}$ , then:

$\displaystyle\Delta C_{i}=\left\{{\begin{array}[]{l}\sum\limits_{j=1}^{n}(% \textit{AP}_{ij}-\textit{BP}_{ij})\times Q_{ij}(\textit{The unit price of }i\textit{ is only affected by the }\\ \textit{amount of work})\\ \sum\limits_{j=1}^{n}(\textit{AP}_{ij}-\textit{BP}_{ij})\times T_{ij}(\textit{% The unit price of }i\textit{ is only affected by the}\\ \textit{construction period})\\ \end{array}}\right.$ (3)

$Q$ is the quantity of the project, $T$ means the construction period, AP refers to the actual unit price, BP represents the budgeted unit price. Divide the project planned duration $T$ into $n$ integer calculation units, which can be year, month and day, $j=1,2,3\ldots n$ .

4. The disturbance of abnormal fluctuation of construction period on schedule control

In the project implementation, if price adjustment and project change are not taken into consideration, when the project is completed, BCWS $=$ BCWP, SV $=$ 0, SPI $=$ 1. Therefore, SV and SPI in the construction process cannot accurately predict the time needed for the construction. In order to better manage the progress, this paper adopts the concept of construction Earned Schedule value (ES). The earned value of construction period is used to replace the cost index in the earned value methodology with time index, so as to obtain a more objective progress performance index and more reasonably predict the project duration.

Definition 3: the construction Earned Schedule (ES) refers to the time when the EV value of AT time equals to the PV value, and the expression is as follows:

$\displaystyle\textit{ES}=C+\frac{\textit{EV}_{\textit{AT}}-\textit{PV}_{C}}{% \textit{PV}_{C+1}-\textit{PV}_{C}}$ (4)

where $C$ refers to the adjacent time point before ES, and AT means the actual duration from the beginning of the project to the evaluation of the project status.

The progress deviation based on the earned value of construction period is SV, and the progress performance index is SPI. It is speculated that the project completion period is $\textit{IEAC}(t)$ . The equation is as follows:

$\displaystyle\textit{SV}(t)=\textit{ES}-\textit{AT}$ (5) $\displaystyle\textit{SPI}({t})=\frac{\textit{ES}}{\textit{AT}}$ (6) $\displaystyle\textit{IEAC}({t})=\frac{\textit{PD}}{\textit{SPI}(t)}$ (7)

In Eq. (7), PD means the meaning of the planned completion period of the project.

Lipke found that SPI disobeyed the normal distribution, but it obeyed the right skew distribution. As long as it was corrected and logarithmicized, it could approach the normal distribution [18]. Based on Bayesian inference method and expert opinions, Yang and Hao proposed a dynamic prediction model of schedule performance from the perspective of statistics [19]. So we assume when the project duration fluctuates abnormally, the project progress performance index SPI (t) follows the law of the normal distribution, that is, $\textit{SPI}(t)-f(\mu,\sigma^{2})$ [20]. All the parameters in the normal distribution are selected according to the actual situation.

Definition 4: Effective frequency $P$ refers to the effect of $\textit{SPI}(t)$ on the future work.

Based on weighting (w), the adjusted effective progress performance index $\textit{SPI'}(t)$ is obtained. The method for weighting is as follows:

$\displaystyle\textit{SPI'}(t)_{1}=\textit{SPI}({t})_{1}$ (8) $\displaystyle\textit{SPI'}(t)_{n}={w}_{n}\times\textit{SPI}(t)_{n}+w_{n-1}% \times\textit{SPI}(t)_{n-1}$ (9) $\displaystyle\textit{IEAC'}(t)=\frac{\textit{PD}}{\textit{SPI'}({t})}$ (10)

where ${w}_{n}+w_{n-1}=1$ , and in the equation ${n}\geqslant 1$ .

5. Interference of process adjustment to progress control

In the project implementation, in order to improve efficiency, managers will allocate idle work resources to other work, so the sequence in the work completion is inconsistent with the plan. When there is unfinished work before ES, or the work completed after ES should be revised because ES preorder work fails to provide enough information, there will be great deviation between the predicted value and the actual value of the construction period. Therefore, the continuity of the actual completed work and the consistency between the work and the plan should be considered [21, 22, 23, 24]. The consistency index $S$ is adopted, then:

$\displaystyle S=\frac{\sum\limits_{i=1}^{k}{\textit{EV}_{i}}}{\sum\limits_{i=1% }^{k}{\textit{PV}_{i}}}$ (11)

The value of $i$ is $1,2,3\ldots k$ , where $k$ means the amount of work before ES, $\textit{EV}_{i}$ represents the cumulative value of EV when the work is actually completed at ES, and $\textit{PV}_{i}$ refers to the cumulative value of PV in the planned budget at ES. The greater $S$ value, the higher the consistency, $S\in[{0,1}]$ .

The cost earned value of completed or partially completed work based on the plan is $\textit{EV}_{s}$ , then

$\displaystyle\textit{EV}_{s}=S\times\mathop{\sum}\limits_{i=1}^{k}\textit{EV}_% {i}=S\times\textit{EV}$ (12)

The cost earned value of completed or partially completed work that fails to follow the plan is expressed as $\textit{EV}_{r}$ , then

$\displaystyle\textit{EV}_{r}=\textit{EV}-\textit{EV}_{s}=({1-S})\times\textit{EV}$ (13)

Definition 5: Effective cost earned value ( $\textit{EV}_{e}$ ) refers to the index that is built based on the continuity of actual work and the consistency between the work and the plan so as to improve the accuracy of time limit prediction. It is expressed as:

$\displaystyle\textit{EV}_{e}=\textit{EV}_{s}+({1-R})\times\textit{EV}_{r}=S% \times\textit{EV}+({1-S})\times({1-R})\times\textit{EV}$ (14)

where, $R$ is the probability that the completed work inconsistent with the planned process needs to be reworked in the future.

Definition 6: $I$ refers to the difference between the earned value $\textit{ES}_{e}$ of the effective construction period and the adjacent time point $C$ of ES, therefore

$\displaystyle I=\frac{\textit{EV}_{e}-\textit{PV}_{C}}{\textit{PV}_{C+1}-% \textit{PV}_{C}}$ (15)

In the equation, $C$ means the adjacent time point less than ES. $\textit{PV}_{c}$ refers to the accumulated plan cost at time point of $C$ , and $\textit{PV}_{{C}+{1}}$ refers to the cumulative plan cost at time point of $C+1$ .

The earned value of the effective construction period is:

$\displaystyle\textit{ES}_{e}=C+I$ (16)

The effective progress performance index is:

$\displaystyle\textit{SPI}_{{te}}=\frac{\textit{ES}_{e}}{\textit{AT}}$ (17)

The project completion period is predicated to be:

$\displaystyle\textit{IEAC}_{{te}}=\frac{\textit{PD}}{\textit{SPI}_{{te}}}$ (18)

where PD means the planned period of the project completion.

6. Project control case analysis under multi-factor interference

6.1 Project profile

In terms of water conservancy project, there are ten tasks of A, B, C, D, E, F, G, H, I, J, the key path is A $\to$ B $\to$ C $\to$ F $\to$ G $\to$ H $\to$ I $\to$ J. Among them, the prework of work $F$ is work $C$ and $D$ , and work $E$ is an independent and non-critical work. The total planned duration of the project is 10 months. The Transverse Lined Diagram of project planning progress is shown in Fig. 1.

In the implementation, the low temperature in autumn and winter has hindered the progress of A, B, C and D. The delay in the material supply hinders A and B work progress, and land expropriation immigration can make it impossible for C and D. In order to reduce the impact on progress, the manager shall first implement the work E and F. After the work of E and F is finished, the land expropriation problem is solved. The work C and D is implemented, but at this time schedule cannot be finished due to the temperature and moderate F cohesion processing. Other work is completed according to the schedule, and the actual progress diagram is shown in Fig. 2.

During construction, the price of materials, and equipment and labor cost for each work also fluctuates due to the fluctuation of the market and various other reasons. The dynamic change of unit price is shown in Table 1.

According to the earned value method analysis, the index parameters were obtained, and the index parameters of earned value were demonstrated in Table 2.

The predicted completion period of the 11th and 12th months in Table 2 is the inherent flaw in the traditional earned value method in the progress management, but the earned value method can reduce the deviation. The earned value curve is drawn according to the parameters in Table 2, and the earned value curve is shown in Fig. 3.

Table 1
Dynamic change of unit price

Job number		A		B		C		D		E		F		G		H		I		J
Estimated quantity of	Q	50		50		140		80		150		200		50		60		100		100
work
Unit price		BP	AP	BP	AP	BP	AP	BP	AP	BP	AP	BP	AP	BP	AP	BP	AP	BP	AP	BP	AP
Material	P ${}_{1}$	1	1.5	1	1.5	2	3	3	2	4	2	6	5	2	2	2	2	3	3	3	3
Personnel	P ${}_{2}$	4	5	4	5	4	8	5	5	5	4	5	4	4	4	4	4	4	4	4	4
Equipment	P ${}_{3}$	4	6	4	6	4	6	8	4	6	4	5	5	3	3	4	4	3	3	2	2
Planned duration (days)	T	30		30		60		45		30		60		30		30		30		30

Figure 1.

Transverse Lined Diagram of project planning progress.

Figure 2.

Actual progress diagram.

In the Table 1, AP means actual unit price and BP means budget unit price.

Table 2

Index parameters of earned value

Time	1	2	3	4	5	6	7	8	9	10	11	12
BCWS	290	580	1245	2165	3995	4895	5205	5565	6075	6555	6555	6555
BCWP	232	406	1510	2410	3310	3940	4624	4895	5205	5565	6075	6555
ACWP	390	765	1680	2450	3220	4110	5030	5600	5910	6270	6780	7260
CPI	0.59	0.53	0.90	0.98	1.03	0.96	0.92	0.87	0.88	0.89	0.90	0.90
EAC	11019	12351	7293	6664	6377	6838	7131	7499	7443	7385	7316	7260
SPI	0.80	0.70	1.13	1.07	0.93	0.82	0.73	0.77	0.81	0.79	0.82	1
IEAC	12.5	14.29	8.83	9.38	10.81	12.15	13.66	13.03	12.34	12.60	12.22	10

In the implementation of the project in this case, there are factors, such as unit price change, process adjustment and abnormal fluctuation of construction period. According to the curve of earned value, the predicted completion cost deviates greatly at the second, third, fifth and sixth time points. In the forecast of completion cost, the predicted completion cost cannot reflect the cost increase caused by the delay of the whole project. At the same time, due to the adjustment of working procedure, abnormal fluctuation of construction period occurred in the second, seventh and eighth months.

Figure 3.

Earned value curve.

In Fig. 3, BCWS is the budget cost of planned quantities, BCWP is the budget cost of completed quantities, and ACWP is the actual cost of completed quantities.

6.2 Project management under multi-factor interference

As the labor and equipment cost is calculated based on working hours and cost for per working hour, the change of construction period will affect the labor and equipment cost. Therefore, in the case of multi-factor interference, the interference factor of schedule control should be considered first, and then the interference factor of cost control.

6.2.1 Progress control under multi-factor interference

(1) Progress management under the interference of process adjustment

The process adjustment is made in the third, fourth and fifth month. The third month is taken as the prediction for consistency calculation. The calculation table of the third month expense plan is obtained from Fig. 3. The calculation of the third month expense plan is shown in Table 3.

Table 3
Expense plan calculation table for the third month

Project	PV	PV at ES	EV at AT	EV-PV	I/C or R
A	50	50	50	0
B	50	50	50	0
C	70	100	0	$-$ 100	I/C
D	30	50	0	$-$ 50	I/C
E	0	0	150	150	R
F	0	0	0	0
G	0	0	0	0
H	0	0	0	0
I	0	0	0	0
J	0	0	0	0
Total		250	250	0

In Table 3, when EV-PV $>$ 0 is 0, it means that there is unfinished work on the left side of ES, while the completed or partially completed work on the right side of ES may cause rework due to the change of unfinished part of its immediate work or the failure to provide sufficient connection information. The rework rate is expressed by R. When EV-PV $<$ 0, it means that there are interference factors for the construction, resulting in the actual construction progress lagging behind the planned progress, which is expressed by I/C. The cumulative value of PV at ES is 250, the difference between EV and PV at ES is 150, and the sum of EV at ES is 250 $-$ 150 $=$ 100. According to Eq. (11), the consistency of work completed in the third month is S $=$ 0.4. Considering the actual situation of prework C and D, the value of the rework rate of completed part of F for current work is R $=$ 0.8. According to Eqs (14)–(18):

The effective earned value is calculated as follows:

$\displaystyle\textit{EV}_{e3}=S_{3}\times\textit{EV}_{3}+({1-R_{3}})\times({1-% S_{3}})\times\textit{EV}_{3}=785.2$ (19)

The calculation parameters $I$ and effective duration are as follows:

$\displaystyle I=\frac{\textit{EV}_{e3}-\textit{PV}_{3}}{\textit{PV}_{4}-% \textit{PV}_{3}}=-0.5$ (20) $\displaystyle\textit{ES}_{e}=C+I=2.5$ (21)

Calculate the effective progress performance index as:

$\displaystyle\textit{SPI}_{e3}=\frac{\textit{ES}_{e3}}{3}=0.8333$ (22)

The predicted project completion period can be calculated as:

$\displaystyle\textit{IEAC}_{e3}=\frac{\textit{PD}}{\textit{SPI}_{e3}}=12$ (23)

Finally, the planned completion period ( $\textit{IEAC}_{{3e}}$ ) in the third month was calculated to be 12 months, same to the actual completion period. Similarly, the predicted completion period of the fourth and fifth months is calculated to obtain the forecast data for the progress of the whole project. The calculation of the earned value under process adjustment is shown in Table 4.

Table 4

Calculation table of earned value under process adjustment

Time	1	2	3	4	5	6	7	8	9	10	11	12
BCWS	290	580	1245	2165	3995	4895	5205	5565	6075	6555	6555	6555
BCWP	232	406	1510	2410	3310	3939.7	4623.6	4895	5205	5565	6075	6555
ACWP	390	765	1680	2450	3220	4110	5030	5600	5910	6270	6780	7260
SPI	0.80	0.70	0.83	0.84	0.84	0.82	0.73	0.77	0.81	0.80	0.82	0.83
ES	0.80	1.40	3.40	3.96	4.55	4.94	5.12	6.14	7.29	8	9	10
IEAC	12.5	14.29	11.99	11.86	11.93	12.15	13.66	13.03	12.88	12.5	12.22	12
S	1	1	0.40	0.30	0.50	1	1	1	1	1	1	1
R	0	0	0.80	0.50	0.50	0	0	0	0	0	0	0
EV ${}_{\text{e}}$	232	406	785.2	1587.6	2515	3939.7	4623.6	4895	5205	5565	6075	6555
I	0	0	$-$ 0.5	0.37	0.19	0	0	0	0	0	0	0
ES ${}_{\text{e}}$	0.8	1.4	2.5	3.37	4.19	4.9	5.1	6.1	7.3	8.0	9.0	10.0

It can be seen from Table 4 that the improved effective duration earned value methodology has little deviation between the predicted value of project completion duration (IEAC) in the third, fourth and fifth months under the condition of work process adjustment and the actual duration results, which shows that the predicted value calculated by introducing parameter I and rework rate R is more objective and realistic.

(2) Schedule management under abnormal fluctuation of construction period

From Table 4, it can be seen that there is still a large deviation in the predicted completion period of the second, seventh and eighth months, due to the disturbance factor of abnormal fluctuation of construction period. According to the real situation of the project, the influencing factors are decided and an estimated progress performance index (SPI) is determined. Normal distribution adjustment method is adopted for adjustment. According to the actual situation of the project, from the beginning of the project to the sixth month, the work of A, B, C and D was affected by the low temperature in autumn and winter. The construction efficiency reduction lasts for a long time, and the impact effect is relatively stable. Experienced managers can make a rough estimate of the impact of the efficiency reduction effect on the progress. After analyzing and discussing the case, it was assumed that the estimated progress performance index (SPI) was 0.8.

As a reference to calculate the SPI value of the first month, the expected value of the normal distribution was determined and the standard deviation was set as 0.2, $\textit{SPI}(t)-f(0.8,0.2)$ . Parameters at each time point were obtained based on normal distribution adjustment method and data in Table 4. The data of normal distribution adjustment method were shown in Table 5.

Table 5

Data table of normal distribution adjustment method

Time	1	2	3	4	5	6	7	8	9	10	11	12
BCWS	290	580	1245	2165	3995	4895	5205	5565	6075	6555	6555	6555
BCWP	232	406	1510	2410	3310	3940	4623	4895	5205	5565	6075	6555
ACWP	390	765	1680	2450	3220	4110	5030	5600	5910	6270	6780	7260
SPI	0.8	0.70	0.83	0.84	0.84	0.82	0.73	0.77	0.81	0.80	0.82	0.83
ES	0.8	1.40	3.40	3.96	4.55	4.94	5.12	6.14	7.29	8	9	10
IEAC	12.5	14.29	11.99	11.86	11.93	12.15	13.66	13.03	12.88	12.5	12.22	12
SPI’	0.81	0.80	0.83	0.84	0.84	0.82	0.81	0.81	0.81	0.81	0.82	0.83
1W	1
2W	0.9	0.1
3W			1
4W				1
5W					1
6W					0.1	0.9
7W						0.9	0.1
8W							0.9	0.1
9W								0.9	0.1
10W									0.9	0.1
11W										0.1	0.9
12W												1
IEAC’	12.28	12.45	12.00	11.86	11.93	12.13	12.26	12.34	12.39	12.40	12.24	12

After the SPI value is adjusted through normal distribution adjustment method, the SPI’ value is obtained. The comparison between SPI’ and SPI is shown in Fig. 4.

In Fig. 4, SPI is the schedule performance index, and SPI’ is the effective schedule performance index after weighting.

According to Fig. 4, the predicted completion period calculated by the SPI’ values of the second, seventh and eighth months adjusted by normal distribution adjustment method is slightly deviated from the actual completion period. The influence of abnormal fluctuation of construction period on the progress performance index has been removed.

6.2.2 Multi-factor interference cost control

According to the data obtained from the progress control, the total construction period of the whole project is determined. This part will analyze the interference caused by the change of unit price based cases, and consider the impact of the change of personnel, equipment and materials on the cost control respectively.

(1) Material cost analysis

The data on material cost earned value analysis and calculation are shown in Table 6.

Table 6
Material cost earned value analysis and calculation data

Time	1	2	3	4	5	6	7	8	9	10	11	12
BCWS	50	100	330	620	1820	2420	2520	2640	2940	3240	3240	3240
BCWP	40	70	700	1300	1900	2100	2320	2420	2520	2640	2940	3240
ACWP	60	105	450	950	1450	1650	1880	2030	2130	2250	2550	2850
CPI	0.67	0.67	1.56	1.37	1.31	1.28	1.23	1.19	1.18	1.17	1.15	1.14
EAC	4860	4860	2083	2368	2473	2546	2626	2718	2739	2761	2810	2850

The amount of each work task has not changed, so the change of material cost is only affected by the unit price rather than the change of progress. The change of material unit price is shown in Table 7.

Table 7

Material unit price change table

Work	A	B	C	D	E	F	G	H	I	J	Total
Q	50	50	140	80	150	200	50	60	100	100
BP	1	1	2	3	4	6	2	2	3	3
AP	1.5	1.5	3	2	2	5	2	2	3	3
$\Delta$ C	25	25	140	$-$ 80	$-$ 300	$-$ 200	0	0	0	0	$-$ 390

Figure 4.

Comparison diagram of SPI’ and SPI.

According to Table 7, the change of total cost is $-$ 390 for the sake of the change in the unit price of materials. $\textit{EAC}=\textit{BCWS}+C=3240-390=2850$ . Therefore, the total cost of finished materials is predicted to be 2850, which is in line with the actual cost. It should be noted here that various materials may have different cost unit prices at each forecast time point. The actual unit price at the forecast point used in the above table of material unit price change is just equal to the actual unit price in the actual construction, so as to reflect the applicability of this method. In practical application, the dynamic total variable cost will have a slight deviation due to the different forecast time points, which generally has little influence on the calculation and control of expenses.

(2) Labor cost analysis

The data of labor cost earned value analysis and calculation are shown in Table 8.

In Table 8, BCWP is the product of the estimated unit price and the actual construction period, while BCWP’ refers to the product of the estimated unit price and the earned value of the construction period. As the construction period of a project changes, personnel cost is not only affected by schedule change, but also affected by unit price. The change table of personnel unit price is shown in Table 9.

Table 8

Labor cost earned value analysis and calculation data

Time	1	2	3	4	5	6	7	8	9	10	11	12
BCWS	120	240	435	705	1005	1155	1275	1395	1515	1635	1653	1653
BCWP	96	168	390	540	690	871.1	1069	1155	1275	1395	1515	1653
BCWP’	120	240	510	660	810	1080	1350	1470	1590	1710	1830	1950
ACWP	150	300	570	690	810	1200	1590	1830	1950	2070	2190	2310
CPI	0.64	0.56	0.68	0.78	0.85	0.73	0.67	0.63	0.65	0.67	0.69	0.72
EAC	2555	2920	2390	2089	1919	2252	2431	2591	2501	2426	2363	2285

Table 9

Changes of personnel unit price

Work	A	B	C	D	E	F	G	H	I	J	Total
T	30	30	60	45	30	60	30	30	30	30
BP	4	4	4	5	5	5	4	4	4	4
AP	5	5	8	5	4	4	4	4	4	4
C	30	30	240	0	$-$ 30	$-$ 60	0	0	0	0	210

According to Table 9, the change of total cost is 210 due to the change of unit price of personnel. According to the period of each work plan and the unit price of actual personnel in each work, the average value is used to calculate the increased cost caused by the construction delay as follows:

$\displaystyle\Delta C_{D}=\frac{\sum\limits_{i=A}^{J}{\textit{AP}_{i}\times T_% {i}}}{\textit{PD}}\times\textit{DT}$ (24)

where PD is the planned construction period and DT refers to the delayed construction period.

From the equation, we can calculate that the average cost of personnel is 6.15, and the increased cost due to the delay of construction period is the product of the average cost of personnel and the predicted delay of construction period, which is 369. Finally, the total cost of completion personnel is 2232, which is 78.

(3) Equipment cost analysis

According to the labor cost analysis method, the change of total cost caused by the change of unit price of equipment is 90. According to the work schedule and the actual equipment unit price of each work and Eq. (19), the average value is used to calculate: if the increased cost due to the delay of construction period is 354, the predicted total cost of completed equipment is 2,106, with the difference of 6 from the actual cost.

To sum up, the predicted project completion cost of the whole project is 2850 $+$ 2232 $+$ 2106 $=$ 7188, with a difference of 72 from the actual completion cost (7240) and an error of 1% $<$ 2%. Therefore, it is objective and effective to use this correction method to control the project cost after improving the traditional earned value methodology.

7. Conclusions

Based on the traditional earned value methodology analysis, this paper proposes a method based on the dynamic unit price table to solve the data distortion caused by market price changes in earned value analysis. The prediction method is improved based on the value of effective construction period so that the prediction is more accurate. Normal partial weighted adjustment method is adopted to correct the disturbance in abnormal fluctuation of construction period. Also, this paper introduces a project example, which includes three common interference factors: cost unit price adjustment, abnormal fluctuation of construction period and working process adjustment. The situation of multiple interference factors occurring at the same time is analyzed, and can be universally applied to the modified earned value analysis. The correction method makes progress forecast and cost forecast deviation small and ensure that the data is objective, which provides effective project control data for managers.

There are many interference factors when using earned value analysis method for project control, and the three interference factors mentioned in this paper are only a part of them. In the future research, more and more complex interference factors can be analyzed and corrected. The data obtained from this dynamic analysis is more objective, which is more helpful for managers to correct and improve in time. It will also have greater reference value and practical significance for project control.

Footnotes

Acknowledgments

The authors are grateful to the support of the National Natural Science Foundation of China (No. 51709116). The authors would also like to express special thanks to the reviewers for their constructive comments and suggestions in improving the quality of this manuscript.

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Engineering project control of comprehensive unit price fluctuation-time limit fluctuation-process adjustment

Abstract

Keywords

1. Introduction

2. Research status

3. Interference of unit price changes on cost control

6.1 Project profile

Table 1 Dynamic change of unit price

6.2.1 Progress control under multi-factor interference

(1) Progress management under the interference of process adjustment

Table 3 Expense plan calculation table for the third month

(2) Schedule management under abnormal fluctuation of construction period

(1) Material cost analysis

Table 6 Material cost earned value analysis and calculation data

(2) Labor cost analysis

(3) Equipment cost analysis

Footnotes

Acknowledgments

References

Table 1
Dynamic change of unit price

Table 3
Expense plan calculation table for the third month

Table 6
Material cost earned value analysis and calculation data