Machine Cost-Effectiveness in Earthworks: Early Warning System and Status of the Previous Work Period

Abstract

Estimating earthwork costs is challenging due to the use of high-cost construction machines, the performance of works in dynamic, changing, and uncertain conditions, and the issues of machine actual productivity. In earthworks, there is a constant need to track, control, and analyze the progress to reduce costs. The management of machines’ work on construction sites is complex due to an unknown or insufficiently accurate assessment of their actual productivity, and it relies heavily on the site manager’s (in)experience. The cost-effectiveness of the contracted price for the operation of the machines may be questionable. This paper proposes a model for machine cost-effectiveness in earthworks. The proposed model consists of an Early warning system and Status of the previous work period. The Early warning system can provide timely and reliable detection of cost-effectiveness and profitability thresholds for excavators and tipper trucks during the excavation and material removal. The Status of the previous work period is time-dependent and provides a final assessment of the cost-effectiveness of excavators and tipper trucks for the past month or a more extended time. Applying the proposed model at the construction site of the infrastructure project demonstrated its practicality and purpose.

1. Introduction

The success of a project, in general, is achieved when it is completed with the lowest possible costs, in the shortest time, without accidents, and with the required quality [1]. Successful project management must strongly emphasize the efficient utilization of labor, material, and equipment in construction projects in order to deliver a successful project on time, within the budget, and as per the defined quality standards [2]. Productivity plays a key role in the success of a construction project because high productivity leads to a lower unit cost for performing activities [3]. The profitability of most construction projects critically depends on construction productivity, which can lead to project cost overruns and schedule delays if not fully addressed [4].

The term sustainability is used to describe the functionality, systems, and stages involved in efficiently utilizing resources [5]. Sustainable construction refers to the integration of environmental, social, and economic consideration into construction business strategies and practice [6]. From an economic standpoint, sustainability can be viewed as a sustained increase in productivity [7]. Sustainability indicates the proper utilization of technology to improve productivity and reduce costs, as well as the environmental impact [8].

Despite its urbanization and economic significance, the civil construction sector faces a range of challenges that undermine productivity and efficiency, including cost overruns, project delays, and quality issues [9]. Due to its large consumption of energy and materials, the civil construction sector is a major contributor to sustainability challenges [10], and it is under pressure to make construction processes more sustainable, aligning them with economic, social, and environmental sustainability [11].

Earthworks are among the most important types of construction works, which need to be analyzed because they take place in an extremely uncertain environment and conditions, involving a large volume of work and the intensive use of construction machines, with extremely high costs [12]. Earthworks include excavations and removal of large quantities of soil, they take place in the early phase of the project, and the activities are carried out by machines, the most important of which are excavators, dump (tipper) trucks, etc. [13].

Machine productivity assessment is significant for estimating the cost and time of earthworks [14]. It is important to manage earthmoving machinery effectively for its impact on project costs and duration, business profitability, the environment, health, and safety. However, current machinery management practices still heavily rely on the experience of the site manager [15]. During earthworks, the need for constant machine productivity monitoring and the application of corrective measures is highlighted to ensure performance within the frames of the estimated unit costs and duration outlined in the contract [16].

Cost-effectiveness is based on the requirement to achieve the highest possible output with a certain amount of input, while profitability is based on the requirement to achieve the greatest possible profit with the least amount of resources engaged [17]. The cost-effectiveness of the unit price contract that includes the operation of machines can be questionable, especially if the price was assembled based on rough subjective estimates, the (in)experience of the responsible person, and inaccurate or outdated data on the machine’s productivity. Therefore, the cost-effectiveness of the unit price contract, which includes the operation of machines, may remain unknown or be discovered too late.

In the concept of sustainability, the selection of construction machines must involve rational solutions that have a positive impact on operational efficiency, productivity, cost, environment, and human well-being [18]. The optimization of mechanized construction processes has a very important impact on economic and environmental sustainability [19]. In light of the growing worldwide consciousness regarding environmental issues and the depletion of resources, attaining sustainability in the construction sector has become a necessity [20].

This paper aims to propose a model for machine cost-effectiveness in earthworks. It should be used by contractors on construction sites with large amounts of earthworks. The proposed model enables the careful management of machines, aligned with sustainability principles, and represents an innovative, unique, and practical approach for tracking and monitoring the progress of earthworks. Applying the model, it can be determined whether the contracted unit prices for machine work are favorable for the contractor. With the timely detection of non-cost-effective work and non-profitable use of machines, it is possible to make the right decisions and effectively reorganize the work of machines on the construction site. The model requires data from commonly used documentation on the construction site, an accurate assessment of the machine’s actual productivity, and geodetic measurement data of the volume of material removed.

2. Background

Earthworks are usually an essential process in most construction works, with a significant impact on construction cost and productivity [21]. They usually account for about 20% of the total construction costs [22] or even more than 30% [23]. In earthworks, there is a constant need for improvements in the performance of work operations and management, in order to reduce the costs associated with earthworks [24].

Estimating earthworks costs is challenging, time-consuming, and demanding [25]. Making decisions during earthworks to reduce costs and time is not easy [26]. Some studies whose main focus was, among other things, the costs of earthworks and construction machinery are highlighted below.

Parente et al. [27] proposed an integrated system for earthworks tasks comprising equipment, as well as spatial and optimization modules to minimize the execution cost and duration while reducing carbon emissions. They pointed out that their system can output several different resource distribution solutions regarding the deadline, budget, and carbon emissions. Future work should focus on expanding the system’s modeling capabilities and exploring the potential development of a new module (or the improvement of already-developed modules), in line with the importance of sustainability in construction.

Lee et al. [28] presented an easy-to-use computerized system called Eco-Economic Excavator Configuration (E3C), which allows the collection of large amounts of input data and the selection of the most favorable excavator configuration. They highlighted that their system instructs earthwork managers to make more informed decisions for controlling economic excavating and fuel efficiency. The limitations are related to development issues (arbitrarily selecting the percentage of the ease of loading the material and its ambiguity and uncertainty in quantifying) and the case of overtime hours. Future work should focus on adapting the system to the specifications of other equipment manufacturers, implementing an automated method that measures the actual digging depth (instead of a fixed value of the average digging depth), integrating E3C with an earthwork grid system, and integrating E3C with an earth allocation planning (EAP) method that identifies the optimal cut–fill pairing and sequencing.

Gwak et al. [29] proposed a new computational method, which identifies optimal cut–fill prism pairs and their sequence, to minimize the earthmoving cost. They emphasized that their method presents a practical and useful tool. Some of the prominent limitation include the absence of a rock–earth loss factor when moving a cut prism to a fill pit, and insufficient inclusion of geological variability and soil type uncertainty. Other limitations include an insufficiently precise graphical model of the earthwork job and the absence of the comprehensive identification of all global solutions that minimize the cost required to correct the nonconforming prisms. Finally, it is desirable to simultaneously incorporate the 3D contour data, the values of the equipment’s physical attributes, and the job site’s geological attributes.

Krantz et al. [30] presented a new concept, labelled “Eco-Hauling”, for reducing the costs and CO₂ emissions of earthmoving activities. They highlighted that the results of their study can help earthmoving contractors to conduct a trade-off between costs, CO₂ emissions, and productivity, based on specific project requirements and constraints. The limitations are related to the complex implementation and non-intuitive applications. Future work should focus on facilitating the implementation of Eco-Hauling by developing a digital production control system, which would enable the management of production in real-time.

Lu et al. [31] proposed a “lean and green” framework to support equipment use planning and equipment costs, considering productivity performance and greenhouse gas emissions. They pointed out that their framework provides an analytical and systematic approach in assessing the production rate and environmental impact. Future research should focus on applying sensor technology and establishing sophisticated mathematical models or predictive analytics models.

Jassim et al. [32] presented a model based on mass hauling distance for the optimal planning and assessment of earthmoving equipment configurations considering cost, duration, energy, and CO₂ emissions. They emphasized that their model is suitable for planners, construction managers, and contractors in the pre-construction phase and offers useful guidance for effective decision-making. Their study also indicates that trucks represent significant contributors to earthmoving costs and environmental impacts. More case studies, particularly involving a greater number of equipment configurations and alternative fuels, are needed to enable the approach to be applied more generally.

Pilger et al. [33] used a Life Cycle Analysis (LCA) for investigating the environmental impacts and the cost overruns of road construction. They pointed out that LCA is a tool that can assist in making more suitable decisions within the sustainability assumptions of road projects. In addition, they highlighted that most road construction projects have to be adjusted during construction due to poor and incomplete surveys and field work, which prolongs the duration of construction activities, increases costs, and changes the environmental impacts.

Kim S. K. et al. [21] proposed a methodology for automatically generating a moving path for construction equipment (a truck) based on BIM information for earthworks. Using their methodology, it is possible to efficiently control construction equipment, determine the overall moving cost, and automatically create one of the most efficient paths when deciding the location for a temporary road during construction. However, since the presented methodology cannot reflect all the special conditions of the site, it cannot always guarantee that the optimal temporary road location will be selected.

Shehadeh et al. [23] presented a multi-objective and multi-variable optimization mathematical model to optimize the time and cost of earthmoving activities. The presented model is based on the application of the genetic algorithm (GA) optimization technique. The authors highlighted that their model is (currently) restricted to a single earthmoving activity and deals only with excavation and soil transfer from a construction site to a dumping area. Future research should focus on developing further capabilities of the model, implementing new multi-objective optimization algorithms to compare the results, and adding the application of new technology (GPS, GIS, connected equipment, etc.).

3. Model for Machine Cost-Effectiveness in Earthworks

This paper proposes a model for machine cost-effectiveness in earthworks. The model consists of two interconnected steps. The first step is the Early warning system, which can provide timely and reliable detection of the cost-effectiveness and profitability threshold of excavators and tipper trucks. The second step is the Status for previous work period. Applying the second step is time-dependent and provides the final cost-effectiveness evaluation of excavators and tipper trucks for the previous work period. Figure 1 shows the steps of the proposed model.

The significant data for the model assessing machine cost-effectiveness in earthworks is the machine’s actual productivity assessment. Estimating the actual productivity of construction machines is very challenging [34]. Knowing the actual productivity, one can obtain the expected duration for completing the activity for a given amount of work [35]. The actual productivity of construction machines (e.g., excavators, dump/tipper trucks, etc.) plays an essential role in the progress of earthworks [36]. Productivity assessment is a significant issue because productivity assessment manuals provide averaged values, data collection from the construction site is demanding, and various unexpected situations and problems may arise [37].

Figure 1. Model for machine cost-effectiveness in earthworks with protocol proposal by Šopić et al. [38] (image created by the first author).

Figure 1. Model for machine cost-effectiveness in earthworks with protocol proposal by Šopić et al. [38] (image created by the first author).

The proposed model for machine cost-effectiveness in earthworks implies actual productivity assessment by applying the research of Šopić et al. (developed by the same authors as in this paper) [38]. Research by Šopić et al. [38] highlights the importance of a machine’s actual productivity and proposes a protocol for data collection and processing using audio-visual and location-sensing technology. The protocol proposal [38] consists of three steps. The first step involves collecting data on the construction site about the operation of excavators and tipper trucks. Data are collected using a video camera or a smartphone (audio-visual technology) and a GPS receiver (location-sensing technology). Applying the protocol proposal implies collecting data in terms of good (or excellent) working conditions and the use of working time. Otherwise, it is necessary to reorganize the operation of the machines. Therefore, the actual productivity of excavators and tipper trucks (which is obtained in the third step) represents the maximum possible (optimal/desired) productivity of the machines on the construction site. The application of the protocol proposal also involves tracking and monitoring the feasible (optimal) number of tipper trucks’ daily laps to the unloading place. The number of daily laps made by tipper trucks to the unloading place represents easily measurable data and can serve as one of the possibilities for assessing the actual productivity of earthmoving machines [39].

The second step consists of data processing from the construction site. Data processing requires software: MATLAB (for video analysis), GPS tracking software, Google Earth Pro, and software (or add-on) for statistical data processing. Applying the second step gives the values of the time cycle for the excavator and the tipper truck. The measurement of the time cycle of machines (with cyclical work) is essential for tracking and monitoring their actual productivity [28,40].

The third step consists of applying a comparative analysis of methodologies from prominent books, such as that of Peurifoy et al. [41], Nunnally [42], Nichols and Day [43], and manuals from global machine manufacturers, such as Komatsu’s specifications and application handbook [44] and Caterpillar’s performance handbook [45], for evaluating the productivity of excavators and tipper trucks. The methodologies should be corrected with actual data from the construction site to improve the accuracy of the actual productivity assessment of excavators and tipper trucks for the observed construction site. Applying the mentioned methodologies, to a greater or lesser extent, will result in different values for the productivity estimates. The methodologies must be ranked according to the criteria of precision (the compliance of the actual productivity assessment of excavators and tipper trucks with the realistic/feasible number of tipper truck daily laps to the unloading place) and practicality (a subjective evaluation of simplicity and unambiguity when choosing coefficient values for assessing the productivity of excavators and tipper trucks). Figure 2 presents the components of the protocol proposal [38] and the model for machine cost-effectiveness in earthworks.

3.1. First Step: Early Warning System

Applying an Early warning system should provide reliable information on the operation of excavators and tipper trucks. Data on the productivity assessment of machines, together with the costs of the machines working hour, the contracted unit prices for the machine work, the amount of work performed, the time spent, and the cost per unit of performed earthworks, constitute the input data of the Early warning system.

The output data of the Early warning system should provide the early detection of the cost-effectiveness and profitability threshold of the operation of excavators and tipper trucks. They also include an assessment of the minimum required daily laps per tipper truck. These output data should ensure that potential negative cost effects are identified and addressed as soon as possible. The following section will describe in more detail the application of the Early warning system.

Cost-effectiveness can be expressed as a ratio of total revenues and total costs, which gives an indicator of cost-effectiveness [17]:

$${\mathrm{E}}_{\mathrm{K}}={\displaystyle \frac{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{u}\mathrm{e}}{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{s}}}$$

(1)

where the indicator of cost-effectiveness must be greater than 1 for positive financial effects. In addition, the cost-effectiveness of machines can be calculated using the following formula [17,46]:

$${\mathrm{E}}_{\mathrm{K}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{T}}\times \mathrm{c}}{{\mathrm{U}}_{\mathrm{V}}\times \mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}}$$

(2)

where

E_K—machine cost-effectiveness [0, ∞)

Q_T—performed amount of work per unit of time [bank cubic meters, BCM];

pcss—the cost of the machine’s working hour [EUR/h];

c—unit price contract [EUR/ BCM];

U_v—time spent [h].

At the same time, if the indicator of cost-effectiveness has a value:

-

E_K > 1, machine utilization is cost-effective;

-

E_K = 1, machine utilization is at the marginal cost-effectiveness;

-

E < 1, machine utilization is not cost-effective.

The cost of earthworks depends on the type of soil and rock, the use of machines, and the organization of machine work [41]. The operation of the machines must also be expressed through the unit cost per unit of material removed [45]. The goal is to choose the machine or combination of machines with the lowest cost per unit of material removed [43]. The cost per unit of performed earthworks, i.e., the proportional cost, can be calculated as follows [42]:

$$\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t} [\mathrm{E}\mathrm{U}\mathrm{R}/\mathrm{B}\mathrm{C}\mathrm{M}]={\displaystyle \frac{\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{a}\mathrm{c}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{e}’\mathrm{s} \mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r} [\mathrm{E}\mathrm{U}\mathrm{R}/\mathrm{h}]}{\mathrm{A}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{m}\mathrm{a}\mathrm{c}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{e} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y} [\mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}]}}$$

(3)

The profitability threshold (i.e., the break-even point) is defined as the level of capacity utilization below which a business entity must not operate because it would operate at a loss [17]. By operating at the profitability threshold, there is no gain or loss; that is, the financial result of the business is zero. The profitability threshold of the machine can be calculated using the following formula [17,46]:

$${\mathrm{Q}}_{\mathrm{K}}={\displaystyle \frac{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}{\mathrm{c}-\mathrm{v}}}$$

(4)

where

Q_K—product quantity at the profitability threshold [BCM/h];

pcss—the cost of the machine’s working hour [EUR/h];

c—unit price contract [EUR/BCM];

v—proportional cost [EUR/BCM].

The product quantity at the profitability threshold represents the minimum required hourly amount of work necessary for cost-effective operation. The minimum required daily amount of work can be calculated using the following formula:

$${{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{m}\mathrm{i}\mathrm{n}}={\mathrm{Q}}_{\mathrm{K}}\times {\mathrm{T}}^{\mathrm{D}\mathrm{A}\mathrm{Y}}$$

(5)

where

Q_T^min—minimum required daily amount of work [BCM/day];

Q_K—product quantity at the profitability threshold (i.e., minimum-required hourly amount of work) [BCM/h];

T^DAY—number of working hours in a day [h].

After calculating the minimum required daily amount of work, the minimum required tipper truck daily laps can be calculated using the following formula:

$${\mathrm{n}}^{\mathrm{d}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{y} \mathrm{l}\mathrm{a}\mathrm{p}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{i}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{r}\mathrm{u}\mathrm{c}\mathrm{k}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{n}}^{\mathrm{T}\mathrm{T}}\times {\mathrm{Q}}^{\mathrm{T}\mathrm{T}}\times \mathrm{s}\mathrm{w}\mathrm{e}\mathrm{l}\mathrm{l} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}}}$$

(6)

where

Q_T^min—minimum required daily amount of work [BCM/day];

n^TT—number of tipper trucks on the construction site;

Q^TT—volume of material loaded into the tipper truck per lap [loose cubic meters, LCM].

Figure 3 shows the flow of activities when applying the Early warning system. As previously emphasized, significant information for applying the Early warning system is the actual productivity of construction machines (achieved during earthworks at the observed construction site). The protocol proposal by Šopić et al. [38] is used to assess the actual productivity of excavators and tipper trucks. Data collection should be conducted within a few days (about 3 to 7 days during the entire working time).

Based on the actual productivity assessment, cost-effectiveness, and profitability threshold for excavators, tipper trucks, and machine groups (consisting of excavators and tipper trucks), it can be determined whether the contracted unit prices for earthworks (excavation and removal of materials) are favorably for the contractor.

Moreover, based on the profitability threshold, the value of the minimum required daily amount of work that an excavator, a tipper truck, or a machine group (consisting of excavator and tipper trucks) must perform can be obtained. In addition, the value of the minimum required daily laps per tipper truck can be calculated. Clearly, the goal is to have a higher number of tipper truck daily laps than the minimum and, consequently, a higher amount of completed work than the minimum required.

In a situation where the use of construction machines turns out to be non-cost-effective, it is imperative to reorganize the work of machines on the construction site according to the available possibilities to prevent further losses (for the contractor).

3.2. Second Step: Status of the Previous Work Period

The application of the Early warning system at the selected construction site must be compared with the data from the (time-depended) temporary reports to obtain a final assessment (i.e., Status) of the cost-effectiveness of excavators and tipper trucks for the previous work period (i.e., for the past month or a longer period, following the issuance of a temporary report). In addition, it is important to compare the actual time spent on excavation and removal of materials with the optimal and maximum permitted duration. The following section will describe in more detail the application of the Status of the previous work period.

Temporary reports are usually issued monthly or after a longer time. They must contain data on the actual volume of excavated material of the construction site. The actual volume of excavated material, for this research, needs to be achieved by a precise geodetic survey and measurement on the construction site. From the construction site diary, the number of days of the previous work period when excavation and removal of materials were carried out can be obtained (i.e., the actual time spent). On the other hand, the duration of work can be calculated by applying the following formula [47]:

$$\mathrm{T}={\displaystyle \frac{\mathrm{Q}}{\mathrm{P}}}$$

(7)

where

T—duration of work [h];

Q—amount of work [BCM];

P—machine productivity [BCM/h].

An estimate of the optimal duration of work can be obtained based on the actual (optimal/desired) productivity of machine group (consisting of excavator and tipper trucks). Furthermore, an estimate of the maximum permitted duration can be obtained based on the profitability threshold of machine group. However, the goal is to have a shorter duration than the maximum permitted to achieve positive financial benefits.

Suppose the use of excavators and tipper trucks was satisfactorily cost-effective in the previous work period, and the work was carried out within the desired duration. In that case, it is necessary to continue with the same intensity, while considering potential additional improvements.

On the other hand, suppose using excavators and tipper trucks was not cost-effective in the previous work period (despite the Early warning system indicating otherwise at the time of use). In that case, it is crucial to investigate the causes of such a situation. Figure 4 shows the flow of activities for assessing the Status of excavator and tipper trucks used during the previous work period.

4. Application of the Model for Machine Cost-Effectiveness in Earthworks

The construction site where the research model was applied was one of the construction site routes of the infrastructure project. The infrastructure project included constructing a new section of the state road in Rijeka (Croatia). The measurements and data processing for assessing the actual productivity of machines and applying the Early warning system were accomplished in September 2021. The excavation and loading were carried out with a Caterpillar excavator, model 320B LN. Four Mercedes-Benz 4144 8 × 4 tipper trucks with four axles and a maximum permissible weight of 40,000 kg (40 t) were used to transport the material. The material from the excavation was transported locally; that is, it was used as fill material on another route within the infrastructure project construction site. The material was loaded into tipper trucks and leveled to the top of the box. The road distance between the two construction site routes in both directions was about 6 km.

A Samsung Galaxy S10 smartphone and a Qstarz BL-1000GT Standard GPS receiver (Taiwan) were used to collect data on the operation of the excavator and tipper trucks. Data collection on the operation of the excavator and tipper trucks occurred on days with favorable weather conditions, with good working conditions, and with excellent use of working time. The machinist and drivers had previous experience in operating an excavator, i.e., in driving a tipper truck. Data were collected for three days during the entire working time. No unjustified or lengthy delays were observed during the operation of excavator and tipper trucks (when collecting data from the construction site). The video analysis was performed using MATLAB software version 9.4 (R2018a) [48]. The GPS tracking data processing was performed in Qstarz QRacing software version 3.99.810 [49] and free Google Earth Pro software version 7.3.6.9345 [50]. Statistical data processing was performed using Microsoft Excel 2013 (15.0.5553.1000) spreadsheet software and the Microsoft Excel add-in Real Statistics [51]. Figure 5 shows the excavator and one tipper truck during loading at the observed construction site.

4.1. First Step: Early Warning System (State Road in Rijeka, Croatia)

At the observed construction site, the excavation, loading, and removal of type B soil material was the focus of this research.

Table 1. Data from the construction site.

Data from the Construction Site for Excavator and Tipper Trucks:
Number of working hours in a day	TDAY = 9 h
Excavator actual productivity (aligned with tipper truck productivity)	PE = P4TT = 72.56 BCM/h = 653.04 BCM/day
Actual productivity of 1 tipper truck	PTT = 18.14 BCM/h = 163.26 BCM/day
Actual productivity of 4 tipper trucks	P4TT = 72.56 BCM/h = 653.04 BCM/day
Actual/optimal productivity of machine group	PO = 72.56 BCM/h = 653.04 BCM/day
Volume of material loaded into the tipper truck per lap	QTT = 15.07 LCM
Number of tipper trucks on the construction site	nTT = 4
Optimal number of daily tipper truck laps	13 laps (site → unloading place → site)
Swell factor (established for the observed construction site)	0.8333
Time spent (data for the Early warning system)	UvEWS = 9 h
The amount of work performed for the time spent (1 day)	QTE = 653.04 BCM (excavator)
The amount of work performed for the time spent (1 day)	QTTT = 163.26 BCM (1 truck)
The amount of work performed for the time spent (1 day)	QT4TT = 4 × 163.26 = 653.04 BCM (4 trucks)
Contracted unit price (for excavator work)	cE = 3.15 EUR/BCM
Cost of excavator working hour	pcssE = 63.31 EUR/h
Contracted unit price (for tipper trucks work)	cTT = 5.15 EUR/BCM
Cost of tipper truck working hour	pcssTT = 51.36 EUR/h

shows the data from the observed construction site, including the contracted unit prices for excavator and tipper truck work, costs of excavator and tipper truck working hour, number of working hours per day, optimal (maximum) number of daily tipper truck laps (based on tracking and monitoring of tipper trucks driving during data collection), the established swell factor for the observed construction site, etc. As previously pointed out, the actual productivity of the excavator and tipper trucks was obtained from the research conducted by Šopić et al. [38].

Table 2. Excavator cost-effectiveness and profitability threshold for Type B soil material.

Cost-effectiveness of excavator:
${{\mathrm{E}}_{\mathrm{K}}}^{\mathrm{E}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{E}}\times {\mathrm{c}}^{\mathrm{E}}}{{{\mathrm{U}}_{\mathrm{V}}}^{\mathrm{E}\mathrm{W}\mathrm{S}}\times {\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{E}}}}={\displaystyle \frac{653.04\times 3.15}{9\times 63.31}}=3.61$	3.61 > 1.0
	good, positive effects
The use of excavator is cost-effective!
Profitability threshold of excavator:
${\mathrm{v}}^{\mathrm{E}}={\displaystyle \frac{{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{E}}}{{\mathrm{P}}^{\mathrm{E}}}}={\displaystyle \frac{63.31}{72.56}}=0.87 \mathrm{E}\mathrm{U}\mathrm{R}/\mathrm{B}\mathrm{C}\mathrm{M}$
${{\mathrm{Q}}_{\mathrm{K}}}^{\mathrm{E}}={\displaystyle \frac{{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{E}}}{{\mathrm{c}}^{\mathrm{E}}-{\mathrm{v}}^{\mathrm{E}}}}={\displaystyle \frac{63.31}{3.15-0.87}}=27.77 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}$	$72.56 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}>27.77 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}$
	good, positive effects
The excavator has higher productivity than the minimum required.
Calculation of the minimum required daily amount of work if the excavator operates at the profitability threshold:
${{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{m}\mathrm{i}\mathrm{n}\left(\mathrm{E}\right)}=27.77\times 9=249.93 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}$	$653.04 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}>249.93 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}$
	good, positive effects
Calculation of the minimum required daily laps for one tipper truck (for a total of 4 tipper trucks) if the excavator operates at the profitability threshold:
${\mathrm{n}}^{\mathrm{d}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{y} \mathrm{l}\mathrm{a}\mathrm{p}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{i}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{r}\mathrm{u}\mathrm{c}\mathrm{k}\left(\mathrm{E}\right)}={\displaystyle \frac{249.93}{4\times 15.07\times 0.8333}}=4.98\approx 5 \mathrm{d}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{y} \mathrm{l}\mathrm{a}\mathrm{p}\mathrm{s}$	13 daily laps > 5 daily laps
	good, positive effects

shows the calculation of the cost-effectiveness and profitability threshold of using an excavator during the excavation and loading of Type B soil material. Furthermore,

Table 3. Tipper trucks’ cost-effectiveness and profitability threshold for Type B soil material.

Cost-effectiveness of 1 tipper truck:
${{\mathrm{E}}_{\mathrm{K}}}^{\mathrm{T}\mathrm{T}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{T}\mathrm{T}}\times {\mathrm{c}}^{\mathrm{T}\mathrm{T}}}{{{\mathrm{U}}_{\mathrm{V}}}^{\mathrm{E}\mathrm{W}\mathrm{S}}\times {\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{T}\mathrm{T}}}}={\displaystyle \frac{163.26\times 5.15}{9\times 51.36}}=1.82$	1.82 > 1.0
	limited positive effects
Cost-effectiveness of 4 tipper trucks:
${{\mathrm{E}}_{\mathrm{K}}}^{4\mathrm{T}\mathrm{T}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{4\mathrm{T}\mathrm{T}}\times {\mathrm{c}}^{\mathrm{T}\mathrm{T}}}{{{\mathrm{U}}_{\mathrm{V}}}^{\mathrm{E}\mathrm{W}\mathrm{S}}\times {\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{4\mathrm{T}\mathrm{T}}}}={\displaystyle \frac{\left(4\times 163.26\right)\times 5.15}{9\times \left(4\times 51.36\right)}}=1.82$	1.82 > 1.0
	limited positive effects
The use of tipper trucks is approaching the marginal cost-effectiveness!
Profitability threshold of 1 tipper truck:
${\mathrm{v}}^{\mathrm{T}\mathrm{T}}={\displaystyle \frac{{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{T}\mathrm{T}}}{{\mathrm{P}}^{\mathrm{T}\mathrm{T}}}}={\displaystyle \frac{51.36}{18.14}}=2.83 \mathrm{E}\mathrm{U}\mathrm{R}/\mathrm{B}\mathrm{C}\mathrm{M}$
${{\mathrm{Q}}_{\mathrm{K}}}^{\mathrm{T}\mathrm{T}}={\displaystyle \frac{{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{T}\mathrm{T}}}{{\mathrm{c}}^{\mathrm{T}\mathrm{T}}-{\mathrm{v}}^{\mathrm{T}\mathrm{T}}}}={\displaystyle \frac{51.36}{5.15-2.83}}=22.14 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}$	$18.14 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}<22.14 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}$
	negative effects
Profitability threshold of 4 tipper trucks:
${\mathrm{v}}^{\mathrm{T}\mathrm{T}}={\displaystyle \frac{{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{4\mathrm{T}\mathrm{T}}}{{\mathrm{P}}^{4\mathrm{T}\mathrm{T}}}}={\displaystyle \frac{\left(4\times 51.36\right)}{72.56}}=2.83 \mathrm{E}\mathrm{U}\mathrm{R}/\mathrm{B}\mathrm{C}\mathrm{M}$
${{\mathrm{Q}}_{\mathrm{K}}}^{4\mathrm{T}\mathrm{T}}={\displaystyle \frac{{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{4\mathrm{T}\mathrm{T}}}{{\mathrm{c}}^{\mathrm{T}\mathrm{T}}-{\mathrm{v}}^{\mathrm{T}\mathrm{T}}}}={\displaystyle \frac{\left(4\times 51.36\right)}{5.15-2.83}}=88.55 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}$	$72.56 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}<88.55 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}$
	negative effects
The tipper trucks have lower productivity than the minimum required!
Calculation of the minimum required daily amount of work if 1 tipper truck operates at the profitability threshold:
${{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{m}\mathrm{i}\mathrm{n}\left(\mathrm{T}\mathrm{T}\right)}=22.14\times 9=199.26 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}$	$163.26 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}<199.26 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}$
	negative effects
Calculation of the minimum required daily amount of work if 4 tipper trucks operate at the profitability threshold:
${{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{m}\mathrm{i}\mathrm{n}\left(4\mathrm{T}\mathrm{T}\right)}=88.55\times 9=796.95 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}$	$653.04 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}<796.95 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}$
	negative effects
Calculation of the minimum required daily laps per tipper truck if tipper trucks operate at the profitability threshold:
${\mathrm{n}}^{\mathrm{d}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{y} \mathrm{l}\mathrm{a}\mathrm{p}\mathrm{s} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{i}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{r}\mathrm{u}\mathrm{c}\mathrm{k}\left(4\mathrm{T}\mathrm{T}\right)}={\displaystyle \frac{796.95}{4\times 15.07\times 0.8333}}=15.87\approx 16$	13 daily laps < 16 daily laps
	negative effects

shows the calculation of the cost-effectiveness and profitability threshold of using tipper trucks during the removal of Type B soil material. Finally,

Table 4. Machine group cost-effectiveness and profitability threshold for Type B soil material.

Cost-effectiveness of machine group (excavator and tipper trucks):
${{\mathrm{E}}_{\mathrm{K}}}^{\mathrm{M}\mathrm{G}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{M}\mathrm{G}}\times {\mathrm{c}}^{\mathrm{M}\mathrm{G}}}{{{\mathrm{U}}_{\mathrm{V}}}^{\mathrm{E}\mathrm{W}\mathrm{S}}\times {\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{M}\mathrm{G}}}}={\displaystyle \frac{653.04\times (3.15+5.15)}{9\times \left(63.31+4\times 51.36\right)}}=2.24$	2.24 > 1.0
	good, positive effects
The use of machine group (excavator and tipper trucks) is cost-effective!
Profitability threshold of machine group (excavator and tipper trucks):
${\mathrm{v}}^{\mathrm{M}\mathrm{G}}={\displaystyle \frac{{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{M}\mathrm{G}}}{{\mathrm{P}}^{\mathrm{M}\mathrm{G}}}}={\displaystyle \frac{\left(63.31+4\times 51.36\right)}{72.56}}=3.70 \mathrm{E}\mathrm{U}\mathrm{R}/\mathrm{B}\mathrm{C}\mathrm{M}$
${{\mathrm{Q}}_{\mathrm{K}}}^{\mathrm{M}\mathrm{G}}={\displaystyle \frac{{\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{M}\mathrm{G}}}{{\mathrm{c}}^{\mathrm{M}\mathrm{G}}-{\mathrm{v}}^{\mathrm{M}\mathrm{G}}}}={\displaystyle \frac{\left(63.31+4\times 51.36\right)}{\left(3.15+5.15\right)-3.70}}=58.42 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}$	$72.56 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}>58.42 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{h}$
	good, positive effects
The machine group (excavator and tipper trucks) has a higher productivity than the minimum required.
Calculation of the minimum required daily amount of work if the machine group operates at the profitability threshold:
${{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{m}\mathrm{i}\mathrm{n}\left(\mathrm{M}\mathrm{G}\right)}=58.42\times 9=525.78 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}$	$653.04 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}>525.78 \mathrm{B}\mathrm{C}\mathrm{M}/\mathrm{d}\mathrm{a}\mathrm{y}$
	good positive effects
Calculation of the minimum required daily laps per tipper truck (for a total of 4 tipper trucks) if the machine group operates at the profitability threshold:
${\mathrm{n}}^{\mathrm{d}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{y} \mathrm{l}\mathrm{a}\mathrm{p}\mathrm{s} \left(\mathrm{M}\mathrm{G}\right)}={\displaystyle \frac{525.78}{4\times 15.07\times 0.8333}}=10.47\approx 11 \mathrm{d}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{y} \mathrm{l}\mathrm{a}\mathrm{p}\mathrm{s}$	13 daily laps > 11 daily laps
	good, positive effects

shows the calculation of the cost-effectiveness and profitability threshold of using a machine group (excavator and tipper trucks) during excavation, loading, and removal of Type B soil material.

The results indicate that using an excavator for excavation and loading of Type B soil material is cost-effective and that the excavator has higher productivity than the minimum required. On the other hand, the use of tipper trucks for the removal of Type B soil material approaches marginal cost-effectiveness, and tipper trucks have lower productivity than the minimum required. However, the contracted unit price for the excavation of Type B soil material was high enough to cover possible losses due to the unfavorable contracted unit price for the removal of Type B soil material.

The results indicate that the excavator and tipper trucks are cost-effective and sufficiently profitable for Type B soil material. Still, the recommendation was to follow the optimal (maximum possible), or appropriate enough (higher than the minimum required), number of daily tipper truck laps (because it is easily measurable data) in the following days to maintain the machines’ cost-effectiveness.

4.2. Second Step: Status for Previous Work Period (State Road in Rijeka, Croatia, September 2021)

Issuing a temporary monthly report (including geodetic measurement data of the volume of the material removed) for September 2021 and based on the number of working days/hours (data from the construction site diary) for the excavation and removal of Type B soil material, together with the contracted unit prices, costs of excavator and tipper truck working hour, and the excavator idle cost, allows for a final assessment (i.e., Status) of the cost-effectiveness of using excavator and tipper trucks (for September 2021).

Table 5. Data from the construction site for previous work period (September 2021).

Data from the Construction Site for Previous Work Period:
Actual time spent (previous work period)	UvPWP = 77 h
Idleness of excavator (percentage)	30%
Excavator idle cost	47.48 EUR/h
Amount of work for the previous work period (excavator)	QTEPWP = 1785.40 BCM
Amount of work for the previous work period (one tipper truck)	QTTTPWP = 446.35 BCM
Amount of work for the previous work period (four tipper trucks)	QT4TTPWP = 4 × 446.35 = 1785.40 BCM
Amount of work for the previous work period (machine group)	QTMGPWP = 1785.40 BCM

shows the data from the observed construction site for previous work period (September 2021). The working and idle hours of the excavator are automatically recorded by a machine device. The number of working hours for excavators usually refers to the engine’s operational hours. Idle hours are not counted for tipper trucks.

Table 6. Excavator cost-effectiveness for previous work period (September 2021).

Cost-effectiveness of excavator for previous work period:
${{\mathrm{E}}_{\mathrm{K}}}^{\mathrm{E}\mathrm{P}\mathrm{W}\mathrm{P}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{E}\mathrm{P}\mathrm{W}\mathrm{P}}\times {\mathrm{c}}^{\mathrm{E}}}{{{\mathrm{U}}_{\mathrm{V}}}^{\mathrm{P}\mathrm{W}\mathrm{P}}\times {\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{E}\mathrm{P}\mathrm{W}\mathrm{P}}}}=$ $={\displaystyle \frac{1785.40\times 3.15}{77\times \left[\left(0.7\times 63.31\right)+\left(0.3\times 47.48\right)\right]}}=1.25$
	1.25 > 1.0
	minimum positive effects
The use of an excavator has approached the marginal cost-effectiveness for the previous work period!

shows the calculation of the cost-effectiveness of using an excavator for the previous work period. It can be observed that the use of an excavator approached marginal cost-effectiveness. In other words, although the price for the excavation and loading of Type B soil material was favorably negotiated for the contractor, delays that occurred during the work performance caused a lower outcome in the use of the excavator. Furthermore,

Table 7. Tipper trucks cost-effectiveness for previous work period (September 2021).

Cost-effectiveness of 1 tipper truck for previous work period:
${{\mathrm{E}}_{\mathrm{K}}}^{\mathrm{T}\mathrm{T}\mathrm{P}\mathrm{W}\mathrm{P}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{T}\mathrm{T}\mathrm{P}\mathrm{W}\mathrm{P}}\times {\mathrm{c}}^{\mathrm{T}\mathrm{T}}}{{{\mathrm{U}}_{\mathrm{V}}}^{\mathrm{P}\mathrm{W}\mathrm{P}}\times {\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{T}\mathrm{T}}}}={\displaystyle \frac{446.35\times 5.15}{77\times 51.36}}=0.58$	0.58 < 1.0
	negative effects
Cost-effectiveness of 4 tipper trucks for previous work period:
${{\mathrm{E}}_{\mathrm{K}}}^{4\mathrm{T}\mathrm{T}\mathrm{P}\mathrm{W}\mathrm{P}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{4\mathrm{T}\mathrm{T}\mathrm{P}\mathrm{W}\mathrm{P}}\times {\mathrm{c}}^{\mathrm{T}\mathrm{T}}}{{{\mathrm{U}}_{\mathrm{V}}}^{\mathrm{P}\mathrm{W}\mathrm{P}}\times {\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{4\mathrm{T}\mathrm{T}}}}={\displaystyle \frac{\left(4\times 446.35\right)\times 5.15}{77\times \left(4\times 51.36\right)}}=0.58$	0.58 < 1.0
	negative effects
The use of tipper trucks was not cost-effective for the previous work period!

shows the calculation of the cost-effectiveness of using tipper trucks for the previous work period. It can be observed that the use of tipper trucks was not cost-effective. Again, as previously mentioned, delays that occurred during work performance caused an unfavorable outcome in the use of tipper trucks. Finally,

Table 8. Machine group cost-effectiveness for previous work period (September 2021).

Cost-effectiveness of machine group (excavator and tipper trucks) for previous work period:
${{\mathrm{E}}_{\mathrm{K}}}^{\mathrm{M}\mathrm{G}\mathrm{P}\mathrm{W}\mathrm{P}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{M}\mathrm{G}\mathrm{P}\mathrm{W}\mathrm{P}}\times {\mathrm{c}}^{\mathrm{M}\mathrm{G}}}{{{\mathrm{U}}_{\mathrm{V}}}^{\mathrm{P}\mathrm{W}\mathrm{P}}\times {\mathrm{p}\mathrm{c}\mathrm{s}\mathrm{s}}^{\mathrm{M}\mathrm{G}\mathrm{P}\mathrm{W}\mathrm{P}}}}=$ $={\displaystyle \frac{1785.40\times \left(3.15+5.15\right)}{77\times \left[\left(0.7\times 63.31\right)+\left(0.3\times 47.48\right)+\left(4\times 51.36\right)\right]}}=0.73$
	0.73 < 1.0 negative effects
The use of a machine group (excavator and tipper trucks) was not cost-effective for the previous work period!

shows the calculation of the cost-effectiveness of using a machine group (excavator and tipper trucks) for the previous work period. It can be observed that using a machine group was also not cost-effective for the same reasons.

The causes for the delays on the construction site were caused by several factors: the areas with gas installations, which are of significant importance for the city of Rijeka, were insufficiently accounted for in the existing drafts used for the preparation of the excavation; and the failure of the excavator, which slowed down the work for a few days until it was repaired. It is important to note that the first-mentioned reason was inevitable.

The obtained cost-effectiveness estimates obtained for September 2021 pertain only to the operation of the excavator and tipper trucks, as specified in the contracted items that are the subject of study of this paper.

Based on the machine group’s actual (optimal) productivity, which showed the cost-effective use of the machines (indicated by applying the Early warning system), it is possible to obtain an optimal duration of work. Furthermore, based on the machine group’s profitability threshold, it is possible to get the maximum permitted duration.

Table 9. Comparison of the actual time spent with the optimal and maximum permitted duration.

Optimal duration of work (based on the actual/optimal productivity of machine group and without work stoppage):
${\mathrm{T}}_{\mathrm{O}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{M}\mathrm{G}\mathrm{P}\mathrm{W}\mathrm{P}}}{{\mathrm{P}}^{\mathrm{O}}}}={\displaystyle \frac{1785.40}{72.56}}=24.61\approx 25 \mathrm{h}$	77 h > 25 h
	Exceeding the desired deadline
The actual time spent for excavating and removing of Type B soil material is 52 h longer than the optimal duration of work!
Maximum permitted duration of work (based on the profitability threshold of machine group):
${\mathrm{T}}_{\mathrm{M}\mathrm{A}\mathrm{X}}={\displaystyle \frac{{{\mathrm{Q}}_{\mathrm{T}}}^{\mathrm{M}\mathrm{G}\mathrm{P}\mathrm{W}\mathrm{P}}}{{{\mathrm{Q}}_{\mathrm{K}}}^{\mathrm{M}\mathrm{G}}}}={\displaystyle \frac{1785.40}{58.42}}=30.56\approx 31 \mathrm{h}$	77 h > 31 h
	Exceeding the desired deadline
The actual time spent for excavating and removing of Type B soil material is 46 h longer than the maximum permitted duration of work!

compares the actual time spent for the excavation and removal of Type B soil material with the optimal and maximum permitted duration. It can be observed that the actual time spent is 52 hours longer than the optimal duration and 46 hours longer than the maximum permitted duration. Figure 6 shows a graphic representation of the actual duration of excavation and removal of Type B soil material, compared to the optimal duration and the maximum permitted duration. In addition, in Figure 6, three areas of machine productivity can be observed: one refers to the case when the machine group has lower productivity than the minimum required (hatched in red), the second refers to when the machine group has higher productivity than the minimum required (hatched in green), and the third refers to hard-to-achieve machine productivity (hatched in grey). The mentioned areas are divided by the maximum permitted duration and optimal durations. The preferred area is the one that refers to the case when the machine group has higher productivity than the minimum required (hatched in green). However, on the observed construction site, due to delays during work, the use of excavator and tipper trucks for the previous work period was not cost-effective or profitable (the use of machines is in the red area).

5. Discussion

The operation of machines during earthworks needs to be continuously monitored to ensure careful resource management and to encourage practices that improve resource productivity, aligning with sustainability principles. The literature review and contractors have both indicated a significant need to prove the cost-effectiveness of the unit price contract, which includes the operation of machines. The problem is further increased by the established rough subjective assessments when contracting machine work and the questionable accuracy of the internal work norms of machines (based on the expected machine productivity). Therefore, the cost-effectiveness of the unit price contract, which includes the operation of machines, may remain unknown or be discovered too late.

The Early warning system can provide timely and reliable detection of cost-effectiveness and profitability thresholds for excavators and tipper trucks during the excavation and material removal. A final assessment (i.e., Status) of the cost-effectiveness of excavators and tipper trucks for the previous work period (usually for the past month or a more extended time following the issuance of a temporary report) can be obtained with the precise geodetic measurement data of the material removed from the construction site.

Applying the Early warning system at the observed construction site of the infrastructure project indicated that using an excavator for the excavation and loading of Type B soil material is cost-effective, and that the excavator has higher productivity than the minimum required. However, the Early warning system further indicated that the use of tipper trucks for removing Type B soil material approaches marginal cost-effectiveness and that tipper trucks have lower productivity than the minimum required. Therefore, the contracted price for removing Type B soil material should have been higher because such a situation would be significantly more favorable for the contractor. As previously mentioned, the contracted unit price for the excavation of Type B soil material was high enough to cover possible losses due to the unfavorable contracted unit price for the removal of Type B soil material. The recommendation was to follow the optimal (maximum possible) number of tipper truck daily laps or an appropriate number higher than the minimum required, as these data are easily measurable, to maintain the machines’ cost-effectiveness. Issuing a temporary monthly report (including the geodetic measurement data of the volume of material removed) showed that using an excavator for the excavation and loading of Type B soil material approached the marginal cost-effectiveness. Furthermore, the use of a tipper truck, as well as a machine group, was not cost-effective. The previously mentioned delays worsened work performance and caused an undesirable outcome in the use of excavator and tipper trucks.

Applying the proposed model at the observed construction site demonstrated its practicality and purpose. The model for machine cost-effectiveness in earthworks requires consistent conditions on the construction site. Consistency of conditions refers to the need to use the same excavator and tipper trucks, hauling materials to the same landfill, and the sufficient experience of the operator when operating the excavator and of the drivers when driving the tipper trucks. Early detection of the cost-effectiveness and the profitability threshold must be carried out before the temporary monthly report is issued. In addition, accurate data are expected to be used in all the documentation and calculations.

The disadvantages of the model include the time it takes to collect and process the data and the problems associated with it, such as the replacement of a machine that does not have the same characteristics as the machine being recorded or tracked, machine failure, tipper trucks with different characteristics, material removal to several different unloading places, and long distances between unloading places, which implies a longer duration for data collection.

Therefore, an important direction of further research is modifying the presented model when the loaded material is taken to several unloading places, when tipper trucks with different specifications are used, as well as different excavators on the same construction site, and when machines are often changed. Other improvements to the model include greater automation, improved accuracy, the use of portable truck scales, and the application of other audio-visual and/or sensing technology for estimating the box volume of tipper trucks (as a substitute for expensive load scanners).

Furthermore, testing the model on a larger and more diverse set of construction projects or earthworks scenarios would be beneficial. In addition, the model could be enhanced by considering a wider range of factors that can impact the cost-effectiveness and duration of earthworks operations, such as weather conditions, site-specific constraints, and the availability of other equipment or resources. Incorporating optimization algorithms or decision-making frameworks within the model could enhance its practical utility by providing recommendations or strategies to improve the cost-effectiveness of earthworks operations. Expanding the model’s scope to consider a more comprehensive set of cost drivers, both for performance preparation and performance itself, could lead to a more all-embracing approach to estimating and managing earthworks costs. By addressing these potential limitations and disadvantages, the contribution and practical relevance of the model could be further strengthened, making it extra attractive to construction industry practitioners and researchers in the field of earthworks cost management.

6. Conclusions

This paper presents a model for machine cost-effectiveness in earthworks that consists of an Early warning system and the Status of the previous work period. The model represents an innovative, unique, and practical approach for tracking and monitoring the progress of earthworks.

The purpose of the Early warning system is to reliably detect the cost-effectiveness and profitability threshold of excavators and tipper trucks. In case the Early warning system indicates that the use of excavators and/or tipper trucks is approaching marginal cost-effectiveness or is not cost-effective, it is very important to reorganize the operation of the machines on the construction site as soon as possible. The Status of the previous work period is time-dependent and gives the final assessment of the cost-effectiveness of excavators and tipper trucks (for the past month or a longer period). Depending on the final assessment of the cost-effectiveness of using excavators and tipper trucks, it is advisable to consider the possibilities of additional improvement or the application of corrective measures.

Having insight into the actual productivity of construction machines, their cost-effectiveness, and profitability threshold, it is possible to detect deviations between planned and actual productivity, create projections of costs and required time, monitor the earthworks dynamics and progress, and timely detect risky, unfavorable or unacceptable performance. The proposed model for machine cost-effectiveness in earthworks implies the application of the protocol proposal [38] for data collection and processing in the productivity assessment of earthworks using audio-visual and location-sensing technology. By applying the proposed model, correct decisions can be made, and corrective measures can be applied to the construction site in a timely manner. The model should significantly benefit contractors by improving profitability and supporting their interests.