Life cycle cost analysis of a built-in guide-type robot for cleaning the facade of high-rise buildings

ABSTRACT

Cleaning the facade of high-rise buildings is a dangerous task that may cause workplace accidents, such as falls and collisions with the façade. Various technologies and devices have been conceived to address this problem, including a façade cleaning robot guided by built-in rails which was developed in South Korea. In this study, a life cycle cost (LCC) analysis was performed to verify the applicability and commercial feasibility of the robot in question. The LCC analysis results showed that the benefit/cost ratio, rate of return, and annual reduction in façade cleaning costs for the automated method were 1.97, 7.19%, and 49.21%, respectively. Thus, the developed robot was confirmed to provide high economic efficiency for high-rise buildings. In addition, a sensitivity analysis of the results to changes in the values of the main input variables was conducted to verify the reliability of the LCC analysis. The results of this study indicated that commercial application of the robot in consideration should improve the safety of façade cleaning work and have very positive economic, industrial, and societal effects.

KEYWORDS:

• Life cycle cost
• building guide
• façade cleaning robot
• high-rise buildings

1. Introduction

Buildings with curtain walls as exterior finishing require them to be regularly cleaned for maintenance (Lee, J.G and Lee, D.J 2012). A survey has shown that such maintenance work is currently performed by workers aboard a gondola or using suspended scaffolding hanging from ropes connected to the roof. These methods may cause workplace accidents, such as falls and collisions with the façade (Seo et al. 2019; Nansai et al. 2017; Kim et al.). Particularly for high-rise buildings, accidents caused by gusts of wind have led to worker deaths at an alarmingly increasing rate (Moon et al. 2015). In recent years, researchers have recognized the risks involved with cleaning the façade of high-rise buildings and have conceived various technologies and devices to mitigate such risks (Nansai and Mohan 2016). In South Korea, a façade cleaning robot guided by built-in rails was developed and is being field-tested to reduce the risks and improve work productivity and quality (Lee et al. 2018; Moon et al. 2015, 2012). To ensure the commercial feasibility and applicability of the developed robot, a life cycle cost (LCC) analysis is required that considers actual working conditions (Zhao, Wu, and Liu 2021; Hu et al. 2021). In particular, a methodology is needed that allows major decision-makers, including the building owner, to analyze the convenience of including the developed robot from the planning stage. Several studies have conducted LCC analyses to assess the practical and sustainable use of different automation technologies in the construction industry (Zhao, Wu, and Liu 2021; Hu et al. 2021; Weng et al. 2020; Han et al. 2020; Yeom et al. 2017; Zwicker et al. 2016). Although the LCC analysis methodologies used in these studies do not differ significantly from one another, they are not readily applicable to the LCC analysis of the developed robot. Therefore, an LCC analysis model that conforms to the specific features of the robot, its operation procedures and the characteristics of the target working environment, needs to be devised.

In this study, an LCC analysis model was proposed for evaluating the economic feasibility and applicability of the developed robot for high-rise buildings. In the model, the economic efficiency of automation is compared with that of conventional methods through case application and sensitivity analysis. The proposed analysis model is expected to serve as a reliable evaluation tool and a basic framework for objectively testing the feasibility of incorporating the developed robot into a building. Applying the developed robot to cleaning the exterior walls of high-rise buildings is expected to have very positive economic, industrial, and societal effects.

2. Theoretical background

2.1. Conventional façade cleaning method

For general business facilities, building owners regularly clean the façade for the comfort of the building occupants and the aesthetical improvement of the residential environment. Interviews with building owners, building facility management companies, and companies specializing in exterior cleaning indicated that exterior surfaces need to be cleaned once or twice a year, and more frequent cleaning is performed for important buildings such as corporate and major government offices. As shown in Figure 1, building exteriors are conventionally cleaned by workers aboard a gondola or using suspended scaffolding while hanging on ropes.

Figure 1. Conventional methods for high-rise building exterior cleaning.

While gondolas tend to be safer than suspended scaffolding, both pose a high risk of accidents, such as falls or collisions with the outer wall owing to gusts of wind. Moreover, there is a high risk of safety accidents, such as falling objects hitting pedestrians passing by below. In particular, the severity of an accident would be very high if it occurs when exterior cleaning work is performed after the safety structures (safety net, flared shield in, etc.) have been removed (Yeom et al. 2017). Figure 2 shows the representative disaster cases related to work on exterior walls as suggested by the Korea Occupational Safety & Health Agency (KOSHA), which has been continuously making efforts to promote safety awareness by publishing educational material to prevent such cases. More effective measures to prevent safety accidents are urgently required.

Figure 2. Representative disaster cases related to work on exterior walls suggested by KOSHA (Korea Occupational Safety & Health Agency 2019).

2.2. Cases of façade cleaning robots

Some automated exterior wall cleaning robots are being developed to solve the safety problems of the conventional method described in Section 2.1. The automated robots have the advantage that they solve these safety problems by eliminating the need of manual labor, while simultaneously ensuring better work productivity and economy than the conventional method. However, automated robots have a high initial cost, and some of them have a limitation that they must be incorporated from the beginning of the building plan. In addition, automated robots are only compatible with certain building shapes, and their cleaning quality is slightly lower than that of the conventional method.

Table 1 presents a list of automated façade cleaning robots that are currently being used or have recently been developed. These automated robots can be mainly divided into two types, depending on the support mechanism used: wire-suspended (Akinfiev, Armada, and Nabulsi 2009; Balaguer and Abderrahim 2008; Qian et al. 2006; Hamburg University 2001; Fraunhofer 2021; Manntech 2021; IPC Eagle 2021; Gambao and Hernando 2006; Yoo et al. 2019; Kim et al. 2017) and rail-guided (Sugiyama 1998; Yokota, Nishiyama, and Takasaki 1987).

Table 1. Cleaning robots developed worldwide.

Manufacturer	Name of robot	Appearance	Support device	Direction of movement	Field application
Ratioforem (Akinfiev, Armada, and Nabulsi 2009)	Tito 500		Wires	Vertical	×
Disam (Balaguer and Abderrahim 2008)	CAFE		Wires	Vertical	Δ
Shanghai Jiao Tong University (Qian et al. 2006)	Wall cleaning robot with dual-suction cups		Wires	Vertical	×
Hamburg University (Hamburg University 2001)	Sky cleaner 1, 2, 3		Wires	Vertical	Δ
Fraunhofer-Institut IFF (Fraunhofer IFF 2021)	SIRIUSc(sz)		Wires, Suction cups	Vertical	Δ
Manntech (Manntech 2021)	Manntech		Wires	Vertical	Δ
IPC Eagle (IPC Eagle 2021)	High rise		Wires	Vertical	Δ
Newcastle University (Gambao and Hernando 2006)	Arcow		Wires	Vertical	×
Nichon Bisoh (Sugiyama 1998)	Horizontal cleaning system		Guide rails	Horizontal	Δ
Nichon Bisoh (Yokota, Nishiyama, andTakasaki 1987)	Window cleaning system using horizontal moving mechanism		Guide rails	Horizontal	Δ
Hanyang University (Yoo et al. 2019)	Unmanned high-rise façade cleaning robot		Wires	Vertical	Δ
Singapore University (Tun et al. 2018)	vSlider		Suction cups	Vertical and horizontal	×
Seoul National University (Kim et al. 2017)	Wall-climbing platform with modularized wall-cleaning units		Wires	Vertical	×

Wire suspended automated robots are economical, relatively easy to set up, and can be applied to various building types. However, this type of devices is more prone to safety accidents, such as collisions with exterior walls, due to high wind pressure and gusts generated by high-rise buildings. Meanwhile, rail-guided type automated robots have the advantage of being more stable and less affected by the environment under the expected working conditions. Nonetheless, they involve higher initial investment costs for the installation of the guide rails and require high technology owing to the compatibility of two vertical/horizontal robots.

○: possible, Δ: partially possible, ×: impossible

2.3. Development of façade cleaning robot guided by built-in rails

The robot considered in this study can be installed in high-rise buildings during construction or reconstruction (remodeling). As shown in Figure 3, the major components of the robot include a winch-system vertical moving robot (VMR), a horizontal moving robot (HMR), a handheld operator (HHO), and a user-interface-based local commander (LC). The detailed descriptions of the components are presented below.

Figure 3. Components of the evaluated robot.

2.3.1. Vertical moving robot

The VMR utilizes a winch installed in the upper part of a building that enables the developed robot to move vertically along a rail. Another important function of the VMR is serving as a gateway for communication and control. The highest-level controller, which is responsible for communication, control, and sensing (Figure 4), is installed here to control and monitor the robot. Like many other exterior wall maintenance robots, the VMR uses a conventional wire system, but enhanced with a wheel system that comprises auxiliary and main wheels to maintain contact with the building. In addition, a vibration reduction control algorithm is applied to the wire winch system of the VMR to maintain driving stability even at a reference movement speed of 3.6 m/min (Han 2015).

Figure 4. Components of the VMR (Han 2015).

2.3.2. Horizontal moving robot

The HMR is responsible for the actual cleaning of the building exterior. It is equipped with a cleaning tool and various sensors, and it cleans the façade while moving horizontally along guide rails. Figure 5 shows the major components of the HMR. Apart from cleaning the façade, the system’s functions also include providing the horizontal movement to the robot, serving as a sensor gateway for monitoring the cleaning tool and work environment, cleaning the guide rail interior, and monitoring the guide rail and curtain wall. The driving mechanism of the HMR consists of a wheel system comprising auxiliary and main wheels, waterproof motors, and encoders directly connected to the wheels. The wheel system is designed to prevent the robot from deviating from the building guide rail while supporting the loads. The motors that rotate the upper main wheels can respond to changes in the external environment because they meet the IP 68 waterproof rating. The positional information of the HMR is measured with encoders connected to the lower main wheels. As shown in Figure 6, the HMR can travel at a reference speed of 6 m/min in a straight section and 4.2 m/min in a curved section. Its excellent driving stability has been verified in several experiments (Han 2015).

Figure 5. Components of the HMR (Han 2015).

Figure 6. Driving performance of the HMR (Han 2015).

2.3.3. Handheld operator

As shown in Figure 7, the HHO is a device that allows wired and wireless (RF type) remote control of the robot in the event of wireless communication failure. The HHO was designed to prevent safety accidents in the case of a system error by allowing emergency remote manipulation and control.

Figure 7. HHO of the HMR (Han 2015).

2.3.4. Local commander

As shown in Figure 8, the LC is a system that allows workers to remotely control the robot and ensure active fail-safe response by finding abnormal conditions during operation.

Figure 8. LC of the HMR (Han 2015).

2.3.5. Robot operation

Figure 9 shows the different steps involved in the operation of the robot. The robot is operated by a building manager. Once its operation is started, it automatically cleans along the predefined path without additional manipulation.

Figure 9. Automated operation of the robot.

3. Formulation of the Life Cycle Cost Analysis Model for the façade cleaning robot guided by built-in rails

As a first step for the LCC analysis of the automated high-rise building exterior cleaning system herein considered (Yeom and Kim 2014), direct and phone interviews were conducted with five companies specializing in exterior wall cleaning and facility management (FM) to determine the annual frequency, required personnel, and cost of the conventional cleaning methods. The interview results showed that building owners determine the cleaning cycles of their buildings. Exterior walls are generally cleaned twice a year in the case of public institutions and conglomerate headquarters and once a year in the case of other private high-rise buildings. The daily labor cost for exterior cleaning is 150–500 USD per worker, with actual wages depending on the worker’s skill level. In this study, the LCC analysis of the robot was performed under the conservative assumption of one cleaning per year, and an analysis of the sensitivity of the results to the number of cleanings per year was then conducted.

3.1. Setting the scope of the life cycle cost analysis

3.1.1. Specifications and initial investment cost of the façade cleaning robot guided by built-in rails

The hardware of the robot consists of a vertical moving module, a horizontal moving module, a wire winch system, and a cleaning tool, in addition to the guide rails. The performance and specifications of the robot are presented in Table 2. According to the manufacturer, one robot costs 106,250 USD.

Table 2. Performance and specifications of the hardware of the developed robot.

Module	Parameter	Details
Horizontal moving module	Weight	300 kg
	Driving motor	ANIMATICS SM34165MT-IP (2 SET)
	Gear head	NEMA 34 series 22:1
	Auxiliary encoder	Autonics E50S8-2000-4-L-5-CS (2 SET)
	Power source	DC 48 V 20 Ah/24 V 60 Ah
	Number of batteries	2
	Water storage	74.5 L
	Docking method	Semiautomatic (insertion: automatic, detachment: manual)
	Central link method	Two-link structure
	Central damper capacity	800 N
	Suspension tolerance	40 mm
	Dimensions	400 mm (545 mm including wheels) × 1600 mm × 1970 mm
	Main Body Frame	Aluminum (AL6061), SUS304
Vertical moving module	Weight	200 kg
	Brake motor	Concerns CON35-71-50 Hall type (4 SET)
	Rail installation motor	Concerns CON35-19-50 Hall type (2 SET)
	Water storage	10 L
	Rail installation length	<50 mm
	Brake device capacity	2000 N
	Driving method	Wire movement
	Dimensions	518 × 1600 × 2300 (1350 when folded)
	Main body frame	Aluminum (AL6061), SUS304
Wire winch system	Capacity weight	1000 kg
	Velocity	13–18 m/min
	Wire specifications	10 mm × 60 m
	Horsepower	5.0 × 6 hp
	Weight	220 kg
Cleaning tool	Weight	60 kg
	Linear actuator	Maxon EC-4pole 30 brushless Motor
	Rotating actuator	Maxon EC-4pole 22 brushless Motor
	Injection nozzle	Spraying system B10000AUH-01
	Squeeze module allowable stroke	100 mm

3.1.2. Annual cost of the conventional cleaning method

An order for cleaning the exterior walls of a high-rise building is placed after the owner or facility management (FM) requests quotes from companies specializing in exterior cleaning. In South Korea, the cost is calculated per unit labor or unit area. The survey results showed that lump-sum contracts are mainly used to pay the cleaning costs of high-rise buildings because extra charges owing to height and complexity differ by company, and there is no standardized quotation method. The economic efficiencies of conventional and automated methods were compared for the target building (see Section 4) based on the actual quotes from companies specializing in exterior wall cleaning.

3.1.3. Costs of the installation of guide rails for the operation of the cleaning robot

In this study, the guide rail installation cost for operating the robot was calculated based on the actual quote from a company that manufactures and installs the guide rails(Tables 3 and 4). According to this manufacturer, installing the guide rail to the target building increases the cost of one curtain wall unit (1.5 m × 3.5 m) by approximately 25.6%. Therefore, the cost difference between the curtain wall with the guide rail and the conventional curtain wall was used in the LCC analysis model as the guide rail installation cost for the target building.

Table 3. Costs of main components of a conventional curtain wall.

Item	Product	Specifications	Cost	Final cost per unit
Raw material	Al Bar	1.5 m × 3.5 m	3.83 USD/kg	392.89 USD/unit
	Painting cost	PVDF three coats	0.79 USD/kg
Processing cost	Processing assembly cost	-	1.04 USD/kg
	Assembly caulking cost	-	0.50 USD/m
Main materials	Sealant for assembly	-	2.33 USD/CT
	Weather sealant	15 × 10 × 8 m	2.50 USD/CT
	Structural sealant	15 × 8 × 10 m	3.80 USD/CT
	Norton tape (structural tape)	15 × 8 × L(m)	1.08 USD/m
	Assembly gasket (EPDM material)	9.5 × 12 × L(m)	0.01 USD/m
General materials	General materials	-	0.25 USD/kg
	Protection materials	-	0.83 USD/m
Construction materials	Embed anchor	1 ea/unit	6.67 USD/ea
	Primary fastener	1 ea/unit	4.17 USD/ea
	Secondary fastener (bracket)	2 ea/unit	2.17 USD/ea

Table 4. Costs of main components of a curtain wall with guide rails.

Item	Product	Specifications	Cost	Final cost per unit
Raw material	Al Bar	1.5 m × 3.5 m	3.83 USD/kg	493.37 USD/unit
	Painting cost	PVDF three coat	0.79 USD/kg
Processing cost	Processing assembly cost	-	1.04 USD/kg
	Assembly caulking cost	-	0.50 USD/m
Main materials	Sealant for assembly	-	2.33 USD/CT
	Weather sealant	15 × 10 × 8 m	2.50 USD/CT
	Structural sealant	15 × 8 × 10 m	3.80 USD/CT
	Norton tape (structural tape)	15 × 8 × L(m)	1.08 USD/m
	Assembly gasket (EPDM material)	9.5 × 12 × L(m)	0.01 USD/m
	ST’L for section reinforcement	□-78 × 58 × 7 T (Hotdip)	2.08 USD/kg
General materials	General materials	-	0.25 USD/kg
	Protection materials	-	0.83 USD/m
Construction materials	Embed anchor	1 ea/unit	6.67 USD/ea
	Primary fastener	1 ea/unit	4.17 USD/ea
	Secondary fastener (bracket)	2 ea/unit	2.17 USD/ea

3.1.4. Service life and maintenance cost of the cleaning robot

The service life of the target building and guide rail system was set to 40 years based on the Enforcement Decree of the Corporate Tax Act in South Korea. The service life of the robot should also reach 40 years with regular maintenance and replacement of main components, but it was set to 20 years for a conservative analysis. Thus, the robot was assumed to be replaced once within the service life of the building. For the LCC analysis model, the maintenance cost of the robot was calculated according to the replacement and inspection costs of components with a service life of less than 10 years.

3.2. Development of the life cycle cost analysis model for the façade cleaning robot guided by built-in rails

The LCC analysis of the robot herein considered was performed in the following order: analysis of the target building settings and restrictions, analysis of the cash flows (i.e., net present value and equivalent annual worth methods), and sensitivity analysis. Figure 10 shows the detailed components of each process in the LCC analysis model.

Figure 10. LCC analysis model for the robot.

4. Case study application of the life cycle cost analysis method formulated for the façade cleaning robot guided by built-in rails

4.1. Overview of the target building

The LCC analysis of the automated method was based on the assumption that the owner of the high-rise building operates the developed robot for 40 years. As presented in Table 6, a 66-story high-rise mixed-use building with curtain walls located in Seoul, South Korea, was selected as the target building. The actual quote for a once-per-year exterior wall cleaning of the target building received from a company specializing in the subject was 64,500 USD, which was used for the LCC analysis of the conventional method. For the automated method, the LCC analysis was performed using the difference in installation costs between a conventional curtain wall and a curtain wall with guide rails (695,371.48 USD), the initial cost of purchasing the cleaning robot (106,250 USD), and the maintenance cost of the robot (see Table 5).

Table 5. Maintenance cost of the robot.

Replacement cycle	Component	Replacement cost/one time
1 year	Precision inspection	458.33 USD
3 years	Sensor for alignment	875.00 USD
	Sensor for cell detection
	Sensor for obstacle detection
5 years	HMR battery	1,666.67 USD
	Sub-controller
	Power module 2
	Main controller
	Power module 1
	Linear actuator controller module
	Wire-winch controller
	HHO
8 years	Blower module	133.33 USD

Table 6. Target building used in the LCC analysis.

Building name		Tower Palace-I building B
Size	Width	42.6 m
	Depth	35.1 m
	Height	234 m
	Number of floors	66
Structure type		Steel-frame reinforced-concrete structure
Exterior wall curtain wall area		36,000 m^2
Curtain wall module dimension		1.5 m (width) × 3.5 m (height)

4.2. Discount rate for the life cycle cost analysis

Financial data from the last 10 years, including inflation rate, time deposit interest rate, and social discount rate (Economic Statistics System 2019a, 2019b; National Law Information Center 2019), was incorporated to improve the reliability of the LCC analysis results for the cleaning robot (Figure 11). . A social discount rate is generally applied in LCC analysis, but an average inflation rate of 1.96% was applied as a discount rate in this study aiming for a more conservative analysis. Considering the ranges of the time deposit interest rate and social discount rate for the last 10 years, a sensitivity analysis was also performed on the discount rate in the range of 0–5.5%.

Figure 11. Changes in financial data over the last 10 years.

4.3. Results of the cycle cost analysis of the cleaning robot

4.3.1. Cash flow diagram for the life cycle

As explained in Section 3, prior to the LCC analysis of the cleaning robot, the annual labor cost of the conventional method, the guide rail installation cost for the operation of the automated method, and the robot purchase and maintenance costs were calculated considering the variables and restrictions set above. Figure 12 shows the resulting cash flow diagram.

Figure 12. Cash flow diagram for the conventional and automated methods.

4.3.2. Present value, benefit/cost ratio, rate of return, and breakeven point

(1) Net present value

The net present value (NPV) method compares the cash flows of the conventional and automated methods by summing the involved benefits and costs discounted at their present value, as presented in equation (1)(1) $\begin{array}{rl}& \mathrm{N}\mathrm{e}\mathrm{t}\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\\ & =\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}-\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\\ & =\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}\times \left(\mathrm{P}/\mathrm{A},\mathrm{i},\mathrm{n}\text{break}\right)-\left(\begin{array}{c}\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{p}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\\ +\mathrm{g}\mathrm{u}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}+\\ \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\\ \mathrm{o}\mathrm{f}\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\end{array}\right)\\ & =\mathrm{\$}64,500\left(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},40\right)-\mathrm{\$}106,250\left[1+\left(\mathrm{P}/\mathrm{F},1.96\mathrm{\%},20\right)\right]\\ & +\mathrm{\$}695,371.48+\mathrm{\$}458.33\left(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},40\right)\\ & +\mathrm{\$}875\left(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},3\right)\left(P/A,1.96\mathrm{\%},39\right)\\ & +\mathrm{\$}\mathrm{1.666.67}\left(\mathrm{A}\mathrm{F},1.96\mathrm{\%},5\right)\\ & \left(P/A,1.96\mathrm{\%},35\right)+\mathrm{\$}133.33\left(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},8\right)\left(P/A,1.96\mathrm{\%},32\right)\\ & =\mathrm{\$}1,776,869.68-\left(\begin{array}{c}\mathrm{\$}178,316.33+\mathrm{\$}695,371.48\\ +\mathrm{\$}28,804.52\end{array}\right)=\mathrm{\$}874,377.35\end{array}$(1) . The present value of the net profit derived from the incorporation of the cleaning robot was analyzed for 40 years of operation, i.e., the service life of the target building. The results indicated that the robot produced a benefit of 874,377.35 USD in present value. This confirmed the excellent economic efficiency of the automated method compared to the conventional method.

(1) $\begin{array}{rl}& \mathrm{N}\mathrm{e}\mathrm{t}\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\\ & =\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}-\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\\ & =\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}\times \left(\mathrm{P}/\mathrm{A},\mathrm{i},\mathrm{n}\text{break}\right)-\left(\begin{array}{c}\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{p}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\\ +\mathrm{g}\mathrm{u}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}+\\ \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\\ \mathrm{o}\mathrm{f}\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\end{array}\right)\\ & =\mathrm{\$}64,500\left(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},40\right)-\mathrm{\$}106,250\left[1+\left(\mathrm{P}/\mathrm{F},1.96\mathrm{\%},20\right)\right]\\ & +\mathrm{\$}695,371.48+\mathrm{\$}458.33\left(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},40\right)\\ & +\mathrm{\$}875\left(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},3\right)\left(P/A,1.96\mathrm{\%},39\right)\\ & +\mathrm{\$}\mathrm{1.666.67}\left(\mathrm{A}\mathrm{F},1.96\mathrm{\%},5\right)\\ & \left(P/A,1.96\mathrm{\%},35\right)+\mathrm{\$}133.33\left(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},8\right)\left(P/A,1.96\mathrm{\%},32\right)\\ & =\mathrm{\$}1,776,869.68-\left(\begin{array}{c}\mathrm{\$}178,316.33+\mathrm{\$}695,371.48\\ +\mathrm{\$}28,804.52\end{array}\right)=\mathrm{\$}874,377.35\end{array}$(1)

(2) Benefit/cost ratio

The B/C ratio determines economic profitability by comparing the present value of the generated benefit to that of the generated cost. A B/C ratio greater than 1 means that the generated benefit is greater than the generated cost. As presented in equation (2)(2) $\begin{array}{rl}& B/Cratioanalysis\\ & =\left(\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}\right)/\left(\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{v}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\right)\\ & =\left[\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}\times \left(\mathrm{P}/\mathrm{A},\mathrm{i},\mathrm{n}\right)\right]/\left(\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\text{break}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{p}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}+\mathrm{g}\mathrm{u}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}+\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{f}\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\right)\\ & =\mathrm{\$}64,500\left(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},40\right)/\left(\mathrm{\$}178,316.33\text{break}+\mathrm{\$}695,371.48+\mathrm{\$}28,804.52\right)\\ & =\mathrm{\$}1,776,869.68/\mathrm{\$}902,492.33\\ & =1.97\end{array}$(2) , the B/C ratio of the developed robot was found to be 1.97, which demonstrates its economic efficiency.

(2) $\begin{array}{rl}& B/Cratioanalysis\\ & =\left(\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}\right)/\left(\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{v}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\right)\\ & =\left[\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}\times \left(\mathrm{P}/\mathrm{A},\mathrm{i},\mathrm{n}\right)\right]/\left(\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\text{break}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{p}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}+\mathrm{g}\mathrm{u}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}+\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{f}\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\right)\\ & =\mathrm{\$}64,500\left(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},40\right)/\left(\mathrm{\$}178,316.33\text{break}+\mathrm{\$}695,371.48+\mathrm{\$}28,804.52\right)\\ & =\mathrm{\$}1,776,869.68/\mathrm{\$}902,492.33\\ & =1.97\end{array}$(2)

(3) Rate of return

The rate of return (return on investment) analyzes economic efficiency by computing the rate of return that makes the NPV of an investment equal to zero. As presented in equation (3)(3) $\begin{array}{rl}& \mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{R}\mathrm{e}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{n}\\ & \mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}-\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}=0\\ & \mathrm{\$}64,500\left(\mathrm{P}/\mathrm{A},\mathrm{i},40\right)-\{\mathrm{\$}106,250\left[1+\left(\mathrm{P}/\mathrm{F},\mathrm{i},20\right)\right]\text{break}+\mathrm{\$}695,371.48+\mathrm{\$}458.33\left(\mathrm{P}/\mathrm{A},\mathrm{i},40\right)+\mathrm{\$}875\left(\mathrm{A}/\mathrm{F},\mathrm{i},3\right)\left(\mathrm{P}/\mathrm{A},\mathrm{i},39\right)+\mathrm{\$}\mathrm{1.666.67}\left(\mathrm{A}/\mathrm{F},\mathrm{i},5\right)\left(\mathrm{P}/\mathrm{A},\mathrm{i},35\right)+\mathrm{\$}133.33\left(\mathrm{A}/\mathrm{F},\mathrm{i},8\right)\left(\mathrm{P}/\mathrm{A},\mathrm{i},32\right))\}=\\ & i\approx 7.19\mathrm{\%}\end{array}$(3) and Figure 13, the rate of return of the automated method compared to the conventional method was found to be 7.19%, which indicates very high profitability for the developed robot.

(3) $\begin{array}{rl}& \mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{R}\mathrm{e}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{n}\\ & \mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}-\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}=0\\ & \mathrm{\$}64,500\left(\mathrm{P}/\mathrm{A},\mathrm{i},40\right)-\{\mathrm{\$}106,250\left[1+\left(\mathrm{P}/\mathrm{F},\mathrm{i},20\right)\right]\text{break}+\mathrm{\$}695,371.48+\mathrm{\$}458.33\left(\mathrm{P}/\mathrm{A},\mathrm{i},40\right)+\mathrm{\$}875\left(\mathrm{A}/\mathrm{F},\mathrm{i},3\right)\left(\mathrm{P}/\mathrm{A},\mathrm{i},39\right)+\mathrm{\$}\mathrm{1.666.67}\left(\mathrm{A}/\mathrm{F},\mathrm{i},5\right)\left(\mathrm{P}/\mathrm{A},\mathrm{i},35\right)+\mathrm{\$}133.33\left(\mathrm{A}/\mathrm{F},\mathrm{i},8\right)\left(\mathrm{P}/\mathrm{A},\mathrm{i},32\right))\}=\\ & i\approx 7.19\mathrm{\%}\end{array}$(3)

Figure 13. Rate of return analysis results.

(4) Breakeven point analysis

The breakeven point is time at which the present value of the generated benefit is equal to that of the generated cost. The profit owing to utilization of the cleaning robot occurs after the breakeven point. As presented in equation (4)(4) $\begin{array}{c}\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}=\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\\ \mathrm{\$}64,500(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},\mathrm{n})\\ =\mathrm{\$}106,250[1+(\mathrm{P}/\mathrm{F},1.96\mathrm{\%},20)]+\mathrm{\$}695,371.48\text{break}+\mathrm{\$}458.33(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},40)\\ +\mathrm{\$}875(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},3)(\mathrm{P}/\mathrm{A},1\text{break}.96\mathrm{\%},39)\\ +\mathrm{\$}1.666.67(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},5)(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},35)\\ \text{break}+\mathrm{\$}133.33(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},8)(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},32)\end{array}$(4) and Figure 14, the breakeven point of the automated method was found to be 16.52 years.

(4) $\begin{array}{c}\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}=\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\\ \mathrm{\$}64,500(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},\mathrm{n})\\ =\mathrm{\$}106,250[1+(\mathrm{P}/\mathrm{F},1.96\mathrm{\%},20)]+\mathrm{\$}695,371.48\text{break}+\mathrm{\$}458.33(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},40)\\ +\mathrm{\$}875(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},3)(\mathrm{P}/\mathrm{A},1\text{break}.96\mathrm{\%},39)\\ +\mathrm{\$}1.666.67(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},5)(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},35)\\ \text{break}+\mathrm{\$}133.33(\mathrm{A}/\mathrm{F},1.96\mathrm{\%},8)(\mathrm{P}/\mathrm{A},1.96\mathrm{\%},32)\end{array}$(4)

Figure 14. Breakeven point analysis results.

4.3.3. Reduction in annual cleaning costs with the equivalent annual worth method

The equivalent annual worth method compares the cash flow of an investment under the assumption that the benefits and costs are evenly generated each year during the analysis period. Equation (5)(5) $\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}=\left(\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}-\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\text{break}\mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\right)/\left(\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\right)=\left(\mathrm{\$}64,500-\mathrm{\$}902,492.33\left(\mathrm{A}/\mathrm{P},1.96\mathrm{\%},40\right)\right)\text{break}/\mathrm{\$}902,492.33\left(\mathrm{A}/\mathrm{P},1.96\mathrm{\%},40\right)\hspace{0.17em}=\left(\mathrm{\$}64,500-\mathrm{\$}32,760.28\right)/\mathrm{\$}32,760.28=49.21\mathrm{\%}$(5) and Figure 15 present the annual reduction in the cost of exterior wall cleaning achieved with the automated method compared to the conventional method. The automated method saves 31,739.72 USD per year during the service life of the target building (40 years), which is a cost reduction of 49.21%.

(5) $\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}=\left(\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{B}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}-\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\text{break}\mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\right)/\left(\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{U}\mathrm{n}\mathrm{i}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\right)=\left(\mathrm{\$}64,500-\mathrm{\$}902,492.33\left(\mathrm{A}/\mathrm{P},1.96\mathrm{\%},40\right)\right)\text{break}/\mathrm{\$}902,492.33\left(\mathrm{A}/\mathrm{P},1.96\mathrm{\%},40\right)\hspace{0.17em}=\left(\mathrm{\$}64,500-\mathrm{\$}32,760.28\right)/\mathrm{\$}32,760.28=49.21\mathrm{\%}$(5)

Figure 15. Cost reduction with the equivalent annual worth method.

4.3.4. Sensitivity analysis

A sensitivity analysis is needed to evaluate the variability of the LCC analysis results because the input variables or assumptions may change depending on the environment and conditions. Therefore, a sensitivity analysis was performed on 1) the number of exterior wall cleanings per year, 2) the discount rate and annual maintenance cost, and 3) the robot and guide rail installation costs.

(1) Sensitivity analysis on the number of exterior wall cleanings per year

Although the number of exterior wall cleanings per year was set to one in the LCC analysis previously discussed, a sensitivity analysis was performed on the number of cleanings per year because public institutions and conglomerate headquarters are generally cleaned twice a year, and the number of times the cleaning is undertaken may also change at the discretion of the building owner. Table 7 indicates that the economic efficiency of the cleaning robot compared to the conventional method significantly improved as the number of times cleaning was undertaken per year increased.

(2) Sensitivity analysis on the discount rate and maintenance cost

Table 7. Sensitivity analysis on the number of times cleaning is undertaken per year.

Number of cleanings per year	Present value (USD)	Benefit/cost ratio	Breakeven point (years)	Rate of return	Reduction in annual cleaning costs
1	874,377.35	1.97	16.52	7.19%	49.21%
2	2,651,247.03	3.94	7.60	15.82%	74.60%
4 (quarterly cleaning)	6,204,986.38	7.88	3.66	32.06%	87.30%

Changes in discount rates such as the inflation rate and time deposit interest rate, as well as the robot maintenance cost, are the primary assumptions and variables that affect future commercial application and marketing of the automated cleaning technology. Tables 8 and 9 present the sensitivity analysis on the discount rate and maintenance cost, respectively. The developed robot was found to be economically efficient in the analyzed ranges of the discount rate and maintenance cost. Therefore, the robot demonstrated high economic efficiency under all economic conditions and working environments.

(3) Sensitivity analysis on the robot and guide rail installation costs

Table 8. Sensitivity analysis on the discount rate.

Discount rate	Present value (USD)	Benefit/cost ratio	Breakeven point (years)	Rate of return	Reduction in annual cleaning costs
0.00%	1,630,220.19	2.72	14.73	7.19%	63.19%
0.71% (minimum inflation rate)	1,308,911.91	2.41	15.27		58.46%
1.51% (minimum time deposit interest rate)	1,014,451.43	2.11	16.02		52.67%
1.96% (average inflation rate)	874,377.35	1.97	16.52		49.21%
2.52% (average time deposit interest rate)	721,354.89	1.81	17.23		44.70%
3.69% (maximum time deposit interest rate)	463,038.94	1.53	19.15		34.61%
4.03% (maximum inflation rate)	400,651.36	1.46	19.87		31.52%
4.5% (minimum social discount rate)	322,147.93	1.37	21.01		27.14%
5.5% (maximum social discount rate)	180,384.23	1.21	24.37		17.43%

Table 9. Sensitivity analysis on the maintenance cost.

Maintenance cost	Present value (USD)	Benefit/cost ratio	Breakeven point (years)	Rate of return	Reduction in annual cleaning costs
Reduction (−50%)	888,779.61	2.00	16.21	7.26%	50.02%
Current analysis values applied	874,377.35	1.97	16.52	7.19%	49.21%
Increase (+50%)	859,975.10	1.94	16.83	7.11%	48.40%

A sensitivity analysis was conducted considering the cost of the manufacturing of the robot components and the cost of the changes required in the curtain wall design to incorporate the guide rails. The results presented in Tables 10 and 11 showed that the automated method is not economically viable if the cost derived from installing the guide rails exceeded 57.74% of that of a conventional curtain wall. This indicates that the manufacturing cost of the guide rail curtain wall should be reduced. Eventually, a commercialization model should be developed that focuses on reducing the installation costs of the guide rails to improve the economic efficiency.

Table 10. Sensitivity analysis on the robot cost.

Robot cost (USD)	Present value (USD)	Benefit/cost ratio	Breakeven point (years)	Rate of return	Reduction in annual cleaning costs
40,800	982,765.71	2.24	14.23	8.14%	55.31%
61,200	947,801.73	2.14	14.95	7.82%	53.34%
81,600	912,837.74	2.06	15.69	7.51%	51.37%
105,000 (current analysis values applied)	874,377.35	1.97	16.52	7.19%	49.21%
122,400	842,909.77	1.90	17.20	6.93%	47.44%

Table 11. Sensitivity analysis on the guide rail installation cost.

Cost increase (rate) compared to the conventional curtain wall (USD)	Present value (USD)	Benefit/cost ratio	Breakeven point (years)	Rate of return	Reduction in annual cleaning costs
71,873.49 (10% increase)	1,297,879.50	3.71	8.10	16.55%	73.04%
407,810.24 (15% increase)	1,161,938.59	2.89	10.66	11.96%	65.39%
543,746.98 (20% increase)	1,026,001.85	2.37	13.35	9.22%	57.74%
695,371.48 (25.6% increase) (current analysis values applied)	874,377.35	1.97	16.52	7.19%	49.21%
815,620.47 (30% increase)	754,128.36	1.74	19.18	6.00%	42.44%
1,569,748.83 (57.74% increase)	0	1.00	40.00	1.96%	0.00%

(4) Synthesis of results

As a result of the sensitivity analysis, the economic feasibility of the cleaning robot was found to be most sensitive to the installation costs of the guide rails, making the automated method unviable if the price of the guide rail increased by 57.74% compared to a conventional curtain wall. Furthermore, it was confirmed that the possible profit is sensitive to the number of exterior wall cleanings per year, with the economic feasibility significantly improving as the number of times cleaning was undertaken increased. Conversely, it was concluded that the sensitivity was lower to other variables, such as the discount rate, maintenance cost, and cost of the cleaning robot, .

In addition to the above LCC analysis results, introducing a cutting-edge and landmark element to the exterior of newly constructed high-rise buildings such as the developed robot should provide significant intangible benefits, such as an increase in real estate value. This is because the introduction of new technologies such as information and communications technology affects the value of real estate (Dixon 2005).

5. Conclusions

The conclusions of this study are as follows:

1. The annual cleaning cost of the conventional cleaning method, specifications and initial investment cost of the considered robot, guide rail installation cost, and service life and maintenance cost of the robot were specified to develop the LCC analysis model of the automated cleaning method (Figure 10).

2. For the exterior wall cleaning of the target building, the conventional method incurred a cost of 64,500 USD, while the automated method required the installation of guide rails at a cost of 695,371.48 USD, excluding the initial investment and maintenance costs of the robot. The cleaning robot had an NPV of 874,377.35 USD, B/C ratio of 1.97, rate of return of 7.19%, breakeven point of 16.52 years, and annual cost reduction of 31,739.72 USD/year (49.21%). This indicates that the automated method has significantly higher economic efficiency than conventional methods for the case study herein discussed.

3. The sensitivity analysis showed that the economic efficiency of the automated method improved with the number of exterior wall cleanings per year. The sensitivity analysis on the discount rate and maintenance cost revealed that the robot demonstrated excellent economic efficiency under all possible economic conditions and working environments. The sensitivity analysis on the robot and guide rail installation costs showed that the economic efficiency significantly improved as the robot cost decreased and that the automated method lost the economic efficiency if the installation of the guide rails requires an investment of more than 57.74% of the cost of a conventional curtain wall. Therefore, the manufacturing cost of the guide rail curtain wall should be reduced for future marketing and distribution of the developed robot.

The developed LCC analysis model has high utilization value because it not only provides the results for the robot in its current state but can also be applied to future developments of the robot. In addition, the LCC analysis model is not limited to the robot model herein considered but can also be applied to various robots for automating construction.

However, the developed robot has a limitation that it can be used only when the exterior of the building is simple. As a result, depending on the building shape, the suspended scaffold might be partially needed for complete cleaning, and economic feasibility may be questionable. A plan to overcome these limitations should be discussed through future research. Long-term data from building testbeds in which the developed robot is applied should be analyzed to further verify the reliability of the results of this study. In addition, the analysis model formulated in this study will enable an LCC analysis of cases in which various building facades and green walls are included.

Nomenclature

LCC	=	Life Cycle Cost
VMR	=	Vertical Moving Robot
HMR	=	Horizontal Moving Robot
HHO	=	Handheld Operator
LC	=	Local Commander
FM	=	Facility Management

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by INHA UNIVERSITY Research Grant.

Notes on contributors

Dong-Jun Yeom

Dong-Jun Yeom, who earned his Ph.D. in Construction Management in Department of Architectural Engineering in 2018 from Inha University. He worked for the Industrial Science and Technology Research Institute at Inha University for 2 years. He has given a series of lectures on computer aided design, computer programming for engineering application, construction information technologies and etc. at Inha University since 2015. He currently serves as a postdoctoral research engineer in the Korea Institute of Civil Engineering and Building Technology.

Ju-Hak Kim

Ju-Hak Kim, who earned his Ph.D. in Construction Management in Department of Architectural Engineering in 2020 from Inha University. He currently serves as a President/CEO in Taebo Industries, Ltd.

Jun-Sang Kim

Jun-Sang Kim, who earned his matser in Construction Management in Department of Architectural Engineering in 2020 from Inha University. He is a Ph.D. student majoring in Construction Management at Inha University.

Young Suk Kim

Dr. Young Suk Kim, who earned his Ph.D. in Construction Engineering and Project Management in 1997 from the University of Texas at Austin. He has given a series of lectures on an execution of building work, construction management, time management, cost management, contract management, construction information technology, and automation in construction and etc. at Inha University since 1999. He currently serves as a professor in Department of Architectural Engineering at Inha University and a chairman of University Development Commission at Korea Institute of Construction Engineering and Management. His research interests are in the areas of sustainable construction, cost and time management, engineering education, and automation in construction. He has conducted various research projects in terms of automation in construction: an Automated Pavement Crack Sealing Machine, Tele-operated Concrete Pipe Laying Manipulator in the Trenches, Automated Controller for Checking Verticality and Automated, an Intelligent Excavating System, and etc.