“Is Energy That Different from Labor?” Similarity in Determinants of Intensity for Auto Assembly Plants

Abstract

This paper addresses the question “Is energy that different from labor?” from the perspective of efficiency. It presents a novel statistical analysis for the auto assembly industry in North America to examine the determinants of relative energy intensity, and contrasts this with a similar analysis of the determinants of another important factor of production, labor intensity. The data used combine two non-public sources of data previously used to separately study key performance indicators (KPIs) for energy and labor intensity. The study found these two KPIs are statistically correlated (the correlation coefficient is 0.67) and the relationship is one-to-one. The paper identifies 11 factors that may influence both energy and labor intensity KPIs. The study then contrasts which of the empirical factors the two KPIs’ share and how they differ. Two novel statistical methods, Huber estimators and Multiple M-estimators, combined with regularized algorithms, are identified as the preferred methods for robust statistical models to estimate energy intensity. Based on our analysis, the underlying determinants of energy efficiency and labor productivity are quite similar. This implies that strategies to improve energy may have spillover benefits to labor, and vice versa. The study shows vehicle variety, car model types, and launch of a new vehicle penalize both energy and labor intensity, while flexible manufacturing, production volume, and year of production improve both energy and labor intensity. In addition, the study found that the plants that produce small cars are more energy-efficient and productive compared to plants that produce large vehicles. Moreover, in a given functional unit, i.e., on a per-unit basis, Japanese plants are more energy-efficient and productive compared to American plants. Plant managers can use the proposed data-driven approach to make the right decisions about the energy efficiency targets and improve plants’ energy efficiency up to 38% using hybrid regression methods, mathematical modeling, plants’ resources, and constraints.

1. Introduction

The climate crisis and its consequence for life on the planet require a global awareness about green manufacturing, particularly energy efficiency. In recent years, many governments, the general public, and manufacturing companies have focused on efficiency as a primary way to both save money and reduce emissions. Nowadays, companies are not only concerned about their financial business performance but also about the impact of their manufacturing operations on the environment [1,2,3,4].

In 2013, industrial companies’ energy consumption was 22% of total U.S. energy consumption and ranked second after transportation [5]. It was estimated that the U.S. automotive sector’s energy use was over 800 trillion BTU per year [6]. However, if the contribution of the substantial supply chain is included, the total energy consumption related to the car manufacturing industry will be considerably higher. A typical car manufacturing facility consumes different sources of energy, of which electricity and natural gas are the two most predominant ones. Electricity cost is higher between the two and represents 62% of the total energy costs in a car manufacturing facility [1,2].

The automotive industry has witnessed several challenges that pressure this sector to change its business model and reprioritize its long-term strategy. Some of those include cost pressure, lower sales volume, electric vehicles (EVs), autonomous vehicles (AVs), and carbon footprint reductions that are forced by national and international regulators [7,8]. During the last few decades, many governments and industrial sectors have shown steady progress in improving energy efficiency; however, the question of how the industrial sectors can accelerate this journey remain controversial [9]. Some automakers have already started to reduce their carbon footprint by heavily investing in the renewable energy resources. They want to hedge against possible future energy price rise and also meet their social responsibility commitment. Some have invested as much as USD 1 billion to build farms that can use wind, solar panels, landfill gas, or biogas to produce electricity and have plants with zero CO₂ emission by 2040 [10,11].

Although considerable research has been devoted to aggregate manufacturing energy efficiency, less attention has been paid to the factors that reduce energy consumption at a plant level. This paper employs a non-public plant-level dataset along with robust statistical models to estimate plant-level energy efficiency and labor productivity. The first contribution of this paper is the merging of two non-public datasets, previously used to study energy and labor separately. The second contribution is using a systematic approach to identify the factors that enhance both plant’s energy efficiency and labor productivity (The terms “efficiency” and “productivity” are used interchangeably in this paper. The notions of efficiency and productivity are simply “two sides of the same coin” but arise from the different approaches in the literature on energy efficiency and labor productivity.) Using the unique dataset and novel statistical methods, the paper examines synergies between energy intensity and labor intensity, as well as differences.

The remainder of the paper is organized as follows. Related studies, research gaps, and industrial needs are reviewed and discussed in Section 2. Research methodology is presented in Section 3. Data preparation and empirical analysis are examined in Section 4. The conclusion and implications of this study are discussed in Section 5.

2. Literature Review

This section provides an overview of the recent studies on productivity and energy efficiency and attempts to identify the most common productivity KPI, energy efficiency KPI, and their underlying determinants. It categorizes the current research into two main categories, empirical and theoretical research, and builds upon their limitations. The empirical research includes engineering assessments and case studies, and theoretical research includes surveys and analytical and review papers. Section 2 is organized in three subsections: productivity studies, energy efficiency studies, and the link between the two.

2.1. Productivity KPI in This Study

The most expensive element in an OEM (Original Equipment Manufacturer) is the supply chain, while the second is labor cost [12]. Labor contributes 12 to 15 percent of the total production costs for a car manufacturer [13]. Nearly all major automakers are collaborating with the Oliver Wyman Institute to help in assessing their manufacturing plants’ labor productivity. Hours per vehicle (HPV) is the most commonly utilized labor productivity KPI. HPV measures the amount of all direct and indirect labor hours (salaried and hourly employees) needed to assemble a vehicle in body, paint, and trim shops; for more details, readers are referred to Harbour reports [14]. This study uses HPV as the most common productivity KPI to measure the labor intensity and investigates its relationship with the energy efficiency KPI, energy intensity.

2.2. Studies That Influence Energy Efficiency

The authors found that there are two main categories of energy efficiency in the literature, empirical research and theoretical research [15]. The authors summarize the existing studies and review their limitations in the coming subsections.

2.2.1. Empirical Research

Energy Efficiency through Assessments and Exergy Analysis

Engineering assessment studies are mostly of saving energy through developing smart systems or improving the current technology at a manufacturing plant. Galitsky et al. (2008) conducted a comprehensive study about different energy-saving opportunities within U.S. automakers. The authors categorized energy efficiency opportunities either in the area of utility systems or process systems. These utility systems include heat and steam distribution, motors, lighting, material handling, heating ventilation and air conditioning (HVAC), and general. Process-related systems include stamping, welding, and painting [16]. These studies provide recommendations to improve energy efficiency based on technical reports and case studies, including energy efficiency experiences of Asian and European, as well as American car makers. They found paint processes, HVAC, and lighting were the top three consumers of energy, respectively. Kluczek (2019) examined 12 U.S. manufacturing facilities and showed energy intensity could be improved through life cycle assessments (LCAs) and slacks-based measure (SBM). He proposed a comprehensive and sustainable methodology to improve energy intensity in the production systems [17]. Another common traditional practice is exergy analysis, which improves energy efficiency through the second law of thermodynamics [18]. The exergy analysis is a practical method that focus on energy conservation and energy distribution process systems.

The purpose of this research is different and complementary to the studies reported above. This research aims to define the factors to enhance energy intensity via an advanced statistical approach, without focusing on utility systems and process energy efficiency recommendations.

Enhancing Energy Efficiency through Case Studies and Focus Groups

The most common types of qualitative research are case studies and focus groups. Feng and Mears (2016) studied the energy consumption in a car manufacturing plant that utilized electricity and natural and landfill gases. The authors calculated the energy consumption percentages for different departments such as body, paint, and assembly. Additionally, they estimated the monthly energy consumption of the studied plant based on heating and cooling degree days [19]. May et al. (2015, 2016) carried out semi-structured interviews of six European companies. They proposed a tailored and adapted seven-step method to develop energy key performance indicators (e-KPIs) [20,21]. The authors proposed some conceptual frameworks to measure the e-KPIs but were not able to analytically examine and validate the model.

Generally, case studies and focus groups study one or few manufacturing facilities, which potentially limits their generalizability. The current study uses additional variables to measure energy efficiency within a plant.

2.2.2. Theoretical Research

There are several theoretical research approaches such as survey, simulation, and analytical, which will be discussed in the next subsections.

Enhancing Energy Efficiency through Survey

Damert and Baumgartner (2018) studied a sample of 116 global car companies in America, Europe, Japan, and South Korea. Damert and Baumgartner found that OEMs’ climate strategies are significantly different from suppliers and OEMs had stringent climate policies. Moreover, they found that the main contributors of an organization’s climate policy were regional affiliations, its home country’s institutional environment, and the size of the company [22]. Hence, the current study considers plants’ ownership as a factor that may capture various OEMs’ policy or organizations’ culture and leadership style, which may directly/indirectly affect energy efficiency.

Enhancing Energy Efficiency through Analytical Approach

Boyd (2014, 2017) developed an energy performance indicator (EPI) to enable identification of the “best in class” energy performance for an industry. The EPI assigns a specific energy performance score on a 1–100 scale to a plant [23,24]. The author used energy usage, annual production, plant utilization rate, HDD and CDD for the plant location, and the wheelbase of the largest vehicle produced in that plant. Oh and Hildreth (2014) carried out a study using stochastic frontier and data envelopment analysis methods to measure GM plants’ effectiveness of energy-saving initiatives. They used Spearman’s rank-order coefficient and log likelihood tests to check the stochastic frontier analysis model. They proposed a benchmarking process to estimate the energy intensity per vehicle by using variables such as HDD and CDD, plant utilization, and the wheelbase of the largest vehicle produced in the plant [25]. Jeon et al. (2015) estimated the combined energy consumption of both natural gas and electricity of US SMEs in the metal sector. They estimated the annual energy consumption of a manufacturing facility by using various variables such as number of employees, annual production level and hours, and plant area [26]. Alsaleh and Abdul-Rahim (2018, 2019) used the generalized method of moments (GMM) in multiple studies to review the impact of numerous factors on bioenergy intensity in European Countries [27,28,29]. They found that the biggest contributors to bioenergy intensity were growth of gross domestic product and government investment. The intent of our research is different, and the focus of this study is on manufacturing facilities’ energy efficiency rather than improving the energy efficiency of countries and governmental policies. Williams et al. (2020) utilized a network analysis to design a green supply chain. They considered a network of customers and store locations as a supply chain where the customers could drive to or from stores, and retailers supplied the materials to stores from a central warehouse [30]. They identified the number of stores in the supply chain by minimizing the greenhouse gas (GHG) emission. They found doubling the fuel efficiency of customers’ vehicles reduced the supply chain emissions by 46% compared to the baseline scenario.

The research presented in this paper considers additional variables to current studies in the literature. Moreover, several robust methods, including shrinkage and hybrid methods, are utilized to develop robust statistical models that are not sensitive to unusual data points. Furthermore, this study compares the underlying determinants of energy efficiency and labor productivity. The variables and analytical approach are thoroughly discussed in Section 3 and Section 4.

Enhancing Energy Efficiency through Review Papers

Artificial intelligence, digital twins, and digital technology can be used throughout the vehicles lifecycle management to enhance sustainability and quality of the products [31]. Schulze et al. (2016) reviewed 44 scientific papers to define the major elements of energy management. The authors proposed a conceptual framework that has five major key elements: strategy, implementation, controlling, organization, and culture [32]. May et al. (2017) also reviewed 365 articles to examine the main lines of the energy management. They proposed a framework with six essential areas: strategic paradigms, Information and Communication Technologies (ICTs), drivers and barriers, supporting tools and methods, production–performance trade-off, and production process paradigms [33].

Various researchers conducted review studies to define implemented energy efficiency methods in high-energy-consuming industries. Moreover, the authors reviewed four energy efficiency evaluation methods such as stochastic frontier, DEA, benchmarking comparison, and exergy analysis [18,34,35,36]. The intent of this research is different compared to the stated review studies, and it examines a longitudinal study at the plant level. Additionally, the current study proposes a structured methodology that could measure and estimate the plants’ energy efficiency.

2.2.3. Association between Energy Efficiency and Labor Productivity KPIs

Different types of studies like surveys, case studies, and statistical analysis have examined the correlation between the plants’ energy efficiency and productivity. Some researchers studied the correlation between green manufacturing and lean manufacturing, which is almost equivalent to energy efficiency and productivity. This subsection reviews the literature related to productivity and energy efficiency association.

King and Lenox (2001) conducted a comprehensive study on 17,499 U.S. manufacturing facilities over five years, 1991–1996. The authors used a Probit model and two-stage least squares methods in their analysis. They found that organizations who implemented the quality management system standard, ISO 9001, were more likely to also adopt the environmental management standard, ISO 14000 [37].

Boyd and Pang (2000) carried out a research study on 171 U.S. glass manufacturing facilities to consider the correlation between energy efficiency and productivity. Productivity was measured by using a frontier production function approach to define the gap between a hypothetical plant and a benchmark of best practice. They found that a 1% productivity improvement resulted in more than 1% energy enhancement for the flat glass manufacturers; however, the result was not significant for the container glass manufacturers [4].

Worrell et al. (2003) examined the association between energy efficiency and productivity enhancement measures over 70 industrial plants in the U.S. They discovered that energy efficiency investments could boost the overall productivity in the industry [38].

Bergmiller and McCright (2009) surveyed 47 American companies to study the synergy between lean and green programs. They found green manufacturing drivers could result in significant achievements in lean practices, specifically cost performance enhancement. Moreover, the number of people dedicated to waste projects could be reduced because of implementing the projects that benefit both green and lean projects [3]. Inman and Green (2018) carried out a similar study on 182 manufacturing managers in the U.S. and found similar results [39].

Sobral et al. (2013) conducted an in-depth case study utilizing in-person interviews and direct observations in a multinational car maker. They interviewed different people like the plant’s environmental technicians, lean initiators, and managers in both production and environmental departments. They found lean manufacturing practices can create sustainable environmental benefits [1]. In a similar study, Cherrafi et al. (2017) showed companies could save 20–40% of their energy consumption by implementing lean and green manufacturing simultaneously [40]

Diaz-Elsayed et al. (2013) developed an approach to incorporate the lean and green strategies in a production system. They carried out a discrete event simulation study on a part supplier in the automotive industry. They noticed that implementing the combination of lean and green practices reduced the production lead time and production cost by 10.8% [41].

Chiarini (2014) conducted a case study on five European automotive suppliers to investigate the relation between a few specific lean practices and green manufacturing. He used cellular manufacturing, value stream mapping, single minute exchange of die, total productive maintenance, and 5S as lean practices. He found all studied variables, except for the single minute exchange of die, can improve energy efficiency and create sustainable manufacturing processes [42].

Herrmann et al. (2008) conducted a simulation study at a European organization to investigate the synergy between lean and green manufacturing. They used five lean practices as a representative of lean manufacturing. The lean practices used were pull-system standardization, total quality management, Andon line, and continuous flow practices [43]. The scholars found that standardization practices resulted in lower energy consumption, but other lean practices increased energy consumption per product unit.

Boyd and Curtis (2014) studied the linkages between management practices and both energy efficiency and workforce productivity in the U.S. [44]. Unlike Bloom’s study in the UK, they found no link between good management and energy efficiency [45].

Several studies found green supply chain management practices could lead to a better organizational performance in different areas such as environmental, economic, performance, and social [46,47,48].

Wei and Liu (2017) studied the global rebound outcomes on energy use and emissions resulting from energy efficiency improvement. The scholars used a Computable General Equilibrium (CGE) model to evaluate the energy efficiency improvement compared to a business-as-usual scenario. They estimated a very large rebound outcome on energy use and related emissions (70% and 90%, respectively) in 2040 at the global level. Capital and labor supply are the most important factors that can play a critical role in developing an effective energy supply in the long term. Rath et al. (2019) examined the relation of energy consumption and total factor productivity (TFP) for 36 countries. They found that the use of fossil fuels reduces the growth of TFP, whereas the use of renewable energy increases the growth of TFP [49,50]. The study examined by Chen et al. found that the relation between total labor costs and energy intensity was negative for 22 emerging economies [51].

Many successful case studies have been carried out to explore the productivity and energy efficiency association. However, case studies may potentially limit the generalizability. Additionally, survey questions are usually designed so that a variety of respondents can answer them. Therefore, survey studies may not be as substantial as studies utilizing empirical studies and secondary analysis. Furthermore, there are some contradictions between various researchers about the relation between productivity and energy efficiency, or lean manufacturing and green manufacturing. Hence, the authors of the research presented here decided to examine the relation between energy efficiency and labor productivity using a secondary analysis which is more generalizable compared to case studies and surveys.

Table 1. Existing literature research methods and limitations.

Research Areas	Research Approach	Research Methods	References	Limitations
Enhancing energy efficiency	Empirical	Engineering assessment	Hildreth (2014), [25] Thollander et al. (2007), [32] Galitsky et al. (2008), [16] Li and Tao (2017), [18]	They were concentrated on the energy assessment only, and no mathematical or statistical modeling that could assist other manufacturing plants were provided.
		Focus group and case study	Feng & Mears (2016), [19] May et al. (2016), [21] May et al. (2015), [20]	In general, a case study potentially limits its generalizability.
	Technical	Survey	Damert and Baumgartner (2018), [22]	The study only considered the effect of ownership on energy efficiency.
		Analytical	Boyd (2014, 2017). [23,44] Jeon et al. (2015), [26] Oh and Hildreth (2014), [25] Alsaleh and Abdul-Rahim (2018, 2019), [27,28,29]	These studies used very few variables to evaluate the energy efficiency. This paper includes several new variables to measure the energy efficiency.
		Review papers	Li and Tao (2017), [18] May et al. (2017), [33] Mardani et al. (2017), [34] Schulze et al. (2016), [32] Prabhu et al. (2015), [35] Bhattacharya et al. (2015), [36]	They presented a very high level of information and developed a conceptual framework which may not be practical at the plants’ operational level.
Energy efficiency and productivity association	Empirical	Case study (Interview, simulation, value stream mapping)	Cherrafi et al. (2017), [40] Chiarini (2014), [42] Sobral et al. (2013), [1] Diaz-Elsayed et al. (2013), [41] Herrmann et al. (2008), [43]	Since they were case studies, they potentially limit their generalizability.
	Technical	Survey	Bergmiller and McCright (2009), [3] King and Lenox (2001), [37] Inman and Green (2018), [39]	In general, a survey’s validity in scientific research could be an issue.
		Statistical	Boyd and Curtis (2014), [44] Bloom et al. (2010), [45] Boyd and Pang (2000), [4]	There are contrary results regarding the energy efficiency and productivity association.

presents a summary of available research and the existing research limitations.

This study is built upon several research gaps identified in

Table 2. The research gaps and industrial needs.

Research Gaps/Objectives	Research Questions	Industry Needs	Areas of Focus	Degree of Contribution
Gap 1 There are contrary results in the literature regarding the association between energy efficiency and productivity KPIs	RQ1. Is there a significant correlation between energy efficiency and productivity?	The plant managers may have better insight into the association between productivity and energy efficiency KPIs	Energy efficiency and productivity association	Modest contribution
Gap 2 There are few studies with statistical analysis approach defining the impact of important variables and factors on energy efficiency KPI	RQ2. What are the most important factors that can improve the energy efficiency?	The auto plants can use the developed analytical method to improve the energy efficiency	Energy efficiency	Decisive contribution
Gap 3 No study has compared the underlying determinants of energy efficiency and productivity KPIs	RQ3. What are the common determinants that can improve both productivity and energy efficiency KPIs at the same time?	The plant managers may have a better comprehension of the factors that can improve productivity and energy efficiency	Energy efficiency and productivity association	Decisive contribution

that have been found during the literature review. These gaps and research questions can be addressed by investigating the relationship between energy efficiency and productivity, defining the underlying determinants of energy efficiency, and comparing those energy efficiency determinants to the productivity determinants. Table 2 highlights the research gaps and questions, industry needs, areas of focus, and degree of contribution.

The research gaps and questions are discussed in detail in the following sections.

3. Research Methodology

This paper uses the Unit Energy Intensity (UEI) to represent the energy efficiency KPI. The UEI is the plant’s annual energy consumption divided by the total number of vehicles produced in a year. The plant’s location may have a significant contribution to the amount of annual energy consumption. Therefore, the effect of HDD and CDD must be considered and UEI needs to be adjusted accordingly. Galitsky et al. (2008) found that 11–20% of the energy consumption might be contributed to comfort heating and cooling. In this study, it was assumed that at most 14% of electricity consumption is used for comfort cooling if a plant is cooled, and at most 17% of natural gas consumption is used for comfort heating. The adjusted UEIs for electricity and natural gas consumption could be defined using adjusted HDD and CDD as follows:

$${\mathrm{UEI}}_{\mathrm{Elec}-\mathrm{adj}}=\frac{\mathrm{Annual}\mathrm{electricity}\mathrm{usage}}{\mathrm{Annual}\mathrm{production}\mathrm{volume}}\times (1-0.14\times \mathrm{CDDadj})$$

$${\mathrm{UEI}}_{\mathrm{NG}-\mathrm{adj}}=\frac{\mathrm{Annual}\mathrm{natural}\mathrm{gas}\mathrm{usage}}{\mathrm{Annual}\mathrm{production}\mathrm{volume}}\times (1-0.17\times \mathrm{HDDadj})$$

where

$${\mathrm{CDD}}_{\mathrm{adj}}=\frac{\mathrm{CDD}-\mathrm{Min}\left(\mathrm{CDD}\right)}{\mathrm{Max}\left(\mathrm{CDD}\right)-\mathrm{Min}\left(\mathrm{CDD}\right)}$$

If a plant is not cooled, the CDD_adj = 0. Min(CDD) and Max(CDD) are calculated from all the plants’ locations during the study period.

$${\mathrm{HDD}}_{\mathrm{adj}}=\frac{\mathrm{HDD}-\mathrm{Min}\left(\mathrm{HDD}\right)}{\mathrm{Max}\left(\mathrm{HDD}\right)-\mathrm{Min}\left(\mathrm{HDD}\right)}$$

Min(HDD) and Max(HDD) are calculated from all the plants’ location during the study period. All the participants’ plants are heated during the winter months.

Hence, the UEI_Elec-adj and UEI_NG-adj could be calculated as described (This assumes that the average energy share is linear in the range of HDD and CDD. Further investigation confirmed that UEI_Elec-adj and UEI_NG-adj are linear in the range of HDD and CDD). After a literature review, interviewing experts who had considerable expertise in industry practice and academia, and practical consideration, 11 factors have been identified for analysis and their impact on UEIs. Some factors have never been utilized in the context of UEIs and some variables’ definitions have been changed by authors. These factors are: vehicle segment, launching a new vehicle, year, car assembly and capacity (CAC) utilization, flexible manufacturing (FM), total number of chassis configurations and body styles (vehicle variety), number of annual working days (AWD), number of models produced, annual production volume (APV), whether or not the plant is cooled (AC), and plant ownership. The summary of these factors, including their references, are shown in

Table 3. The important factors/variables that might impact on UEIs.

Factor/Variable	Comments/References	Definition	Research Hypotheses
Productivity KPI	[14]	HPV represents the productivity KPI. HPV is calculated by dividing the total working hours of certain hourly and salaried employees by the total number of vehicles produced in a calendar year. These working hours are measured during all stages of vehicle production and processing including body, painting, and final assembly.	NA
Energy efficiency KPI	Not used in the literature	In our study, UEI is the energy efficiency KPI and calculated as plant’s annual energy consumption divided by the total number of vehicles produced in a year.	NA
Vehicle segment	Not used in the literature to estimate UEIs	Vehicle segment is defined as cars’ class. The authors used the same vehicle segment categories which were developed to measure HPV [52]	H1. Vehicle segment has a significant impact on the UEIs
CAC Utilization	[14,23,24,25,33]	CAC utilization is the total number of cars manufactured per design capacity line in December of the data year. CAC can be calculated as: Annual capacity = 235 days per year × 16 h per day × Capacity line rate (except where otherwise stated, capacity line rate is based on December) CAC = (Total number of cars manufactured / Annual Capacity) × 100	H2. UEIs are correlated with CAC Utilization
Vehicle variety	Not used in the literature to estimate UEIs	It considers the total number of car body types and chassis configurations. - Number of car body types: It describes the number of variations in body types such as convertible, passenger, cargo van, wagon, 2-door, 3-door, 4-door, and 5-door [14]. - Number of chassis: It describes the number of variations in chassis configuration such as rear or front wheel drive [14].	H3. UEIs are correlated with the vehicle variety
Number of models	Not used in the literature to estimate UEIs	It describes how many various car nameplates are manufactured in a plant.	H4. UEIs are correlated with the number of models
APV	[23,24,25,26]	APV represents the total number of cars manufactured by the end of the year (i.e., in December), except where otherwise stated.	H5. UEIs are correlated with APV
Plant ownership	[20,22] Not used in the literature to estimate UEIs	Plant ownership may drive differences in terms of plants’ working culture, management style, technologies, work regime, and regulations. Damert and Baumgartner (2018) and May et al. (2015) indirectly considered plant ownership as a factor that might impact UEIs.	H6. UEI variation for American and Japanese is significantly different
Flexible manufacturing (FM)	Not used in the literature to estimate UEIs	Flexible manufacturing involves using standard procedures, common locator points, shared skid systems, etc. It assists manufacturers in producing better cars at cheaper price while preserving quality. FM used in this study incorporates the flexibility of the equipment, volume, mix, and utilization, which reflect the effects of market variations and economies of scale. The FM utilized in this study can be determined as follows: FM = Ln (FEq × FV × FM × FU) where FEq = The equipment flexibility, described as: $\frac{\mathrm{No}.\mathrm{of}\mathrm{body}\mathrm{styles}}{\mathrm{No}.\mathrm{of}\mathrm{body}\mathrm{lines}}\times \frac{\mathrm{No}.\mathrm{of}\mathrm{body}\mathrm{styles}}{\mathrm{No}.\mathrm{of}\mathrm{paint}\mathrm{lines}}\times \frac{\mathrm{Vehicle}\mathrm{variety}}{\mathrm{No}.\mathrm{of}\mathrm{assembly}\mathrm{lines}}$ FV = The production volume, referred to as volume flexibility FM = The various number of nameplates that are produced in a factory, referred to as mix flexibility FU = The CAC, referred to as utilization flexibility	H7. UEIs are correlated with flexible manufacturing
Air conditioning (AC)	Not used in the literature to estimate UEIs	AC is a binary variable and set equal to one when a plant is cooled during the summer months, otherwise it is set to zero. This variable is used for the energy source of electricity only.	H8. UEIs are correlated with AC
Vehicle launch	Not used in the literature to estimate UEIs	A great amount of effort is put forth by engineering, supply chain, production, logistics, and quality teams to overcome the challenges of a new product launch. The study shows that the plants encountered some difficulties keeping their UEIs while introducing new vehicles.	H9. UEIs are correlated with launching a new vehicle
AWD	Not used in the literature to estimate UEIs	AWD describes the number of scheduled working days for the data year. The AWD does not account for planned holidays and vacations (such as summer and New Year shutdowns). Throughout the study period, the AWD for all brand names was essentially uniform and fell between 230 and 245 days.	H10. UEIs are correlated with AWD
Year of production	Not used in the literature to estimate UEIs	Year is the fiscal year that the data are provided for	H11. UEIs are correlated with year of production

. Moreover, 11 hypotheses were posed in Table 3 for further investigation.

Table 3 indicates that, prior to this research, eight factors/variables have not been utilized in the literature to estimate the energy efficiency KPI, UEIs. In this study, the factors that are used to estimate the UEIs include: year of UEI measurement, vehicle segment, CAC utilization, new vehicle launch, vehicle variety, number of car models produced, APV, FM, AWD, whether or not the plant is cooled, and plant ownership.

The research steps, data preparation, and empirical analysis conducted in this research are shown in Figure 1. Figure 1a summarizes the research steps and Figure 1b summarizes the data preparation and analysis. The research questions and hypotheses are discussed in detail in Section 4.

4. Data Preparation and Empirical Analysis

Data collection and preparation, the association between UEIs and HPV, the empirical approach to statistical analysis, model specification and refinement, and model selection and validation are reviewed in this section.

4.1. Data Collection and Preparation

The data analyzed in this study covered a 6-year period, 1999–2005 (excluding 2002), for the North American Automakers involved in the development of the Energy Star EPI (The Energy Star data were collected in two waves (as described in Boyd 2014). During the first round, two plants provided data for 2001 that caused a data gap in this year.) and Harbour Institute’s assessments. The authors used a secondary analysis on a combined dataset based on the Energy Star and Harbor reports. The combined dataset has been used to identify and develop UEIs and important determinants on UEIs and HPV.

Once the data from Energy Star and the Harbour reports were collected, edit checks were performed, and the UEI_Elec-adj and UEI_NG-adj were plotted versus all variables, other than nominal variables, to discover any typographical error or extreme unusual data points. Some outliers from the original dataset were found, and it was decided not to remove them, but rather to minimize their impact by applying a method to down-weight them. The number of plants of two ownerships (American: Ford and GM, Japanese: Honda, Nummi, and Toyota) used in this research is presented in

Table 4. Frequency of data for different car manufacturers in the study period.

Ownership	1999	2000	2001	2003	2004	2005	Total *
American	25	23	0	20	21	21	110
Japanese	2	2	2	4	4	8	22
Total	27	25	2	24	25	29	132

* One observation that has a huge discrepancy between Energy Star and Harbour reports dataset was deleted from the analysis.

.

The descriptive statistics for UEI_Elec-adj and UEI_NG-adj over the study period are presented in Appendix A,

Table A1. Descriptive statistics for UEI_Elec-adj and UEI_NG-adj.

Yr.	Variable	Ownership	N	Mean	StDev	Min.	Q1	Median	Q3	Max.
1999	UEIElec-adj	American	25	650.9	315.8	370.5	471.5	631.4	859.4	1504.4
		Japanese	2	538.5	29.3	500.8	*	538.5	*	542.3
	UEING-adj	American	25	5.185	2.657	1.935	3.453	5.013	7.104	10.999
		Japanese	2	3.125	0.292	2.644	*	3.125	*	3.057
2000	UEIElec-adj	American	23	675.9	383.4	381.1	529.2	630	881.1	1866.5
		Japanese	2	525.28	3.48	522.26	522.26	525.28	528.29	528.29
	UEING-adj	American	23	5.185	3.178	1.795	3.548	5.036	7.218	16.264
		Japanese	2	3.05	0.286	2.805	2.805	3.05	3.3	3.3
2001	UEIElec-adj	Japanese	2	510.4	32.2	491.6	*	510.4	*	537.2
	UEING-adj	Japanese	2	2.929	0.248	2.454	*	2.929	*	2.805
2003	UEIElec-adj	American	20	749.9	340.5	452.6	547.9	624.8	843.6	1885.3
		Japanese	4	471.43	1.12	403.63	402.105	404.43	406.747	405.22
	UEING-adj	American	20	4.715	2.536	2.422	3.286	4.126	7.248	10.239
		Japanese	4	2.78	0.308	2.16	2.187	2.378	2.573	2.596
2004	UEIElec-adj	American	21	752	448.8	415.3	550.1	659.3	947.1	2380.2
		Japanese	4	463.7	60.1	388.2	428.224	430.7	433.168	473.2
	UEING-adj	American	21	4.712	4.539	2.16	3.566	4.869	6.983	22.832
		Japanese	4	2.752	0.59	2.074	2.292	2.492	2.696	2.909
2005	UEIElec-adj	American	21	760.9	280.4	431.5	566	700.9	849.2	1622.6
		Japanese	8	412.9	28.4	345.5	345.5	370.8	402.3	402.3
	UEING-adj	American	21	4.7	2.359	2.261	3.385	5.321	6.469	12.343
		Japanese	8	2.605	0.242	2.029	2.029	2.406	2.48	2.48

. The UEI_Elec-adj and UEI_NG-adj variation for different ownership categories in the study period is illustrated in Figure 2 and Figure 3. These figures indicate that Japanese ownership had a lower value of UEI_Elec-adj and UEI_NG-adj during the study period. However, the actual comparisons may slightly change because of utilizing the UEIs which were not adjusted for the climate.

Abolhassani and Jaridi (2016) found that vehicle segmentation was an important factor/variable in estimating the HPV. In order to reduce the vehicle segmentation’s variation, they recommended to reduce the number of vehicle segments from 14 to 3 [52]. The same vehicle class grouping is used in this study. It was decided to combine group C with group B to enhance the significance of the statistical analysis for all the groups and create a balanced sample (group C had six records only). As shown in

Table 5. Different vehicle segmentation.

Segment	Used Grouping	Frequency of Data
Subcompact, Midsize, Midsize SUV, Small Pickup	A	64
Compact, Small SUV, Sports Car, Luxury, Large, Minivan, Large Van, Full-Size SUV, Full-Size Pickup, Medium Duty	B	68
Total		132

, two vehicle segments are used in this study.

The mean of HPV varies from 20 to 25 and from 25 to 35 for groups A and B, respectively. Subcompact, midsize, midsize SUV, and small pickup served as group A and the remaining segments as group B. Different vehicle segmentations are shown in Table 5.

The minimum sample size for a statistical model must be greater than 2R + 25, where R is the number of regressors [53]. In the following statistical model, 12 regressors, including the intercept, are used to estimate the response. Hence, R = 12 and the sample size must be greater than 49. Therefore, the number of data points used to develop the UEIs’ statistical models is sufficient for both car groups.

4.2. Association of UEIs and HPV and RQ1 Examination

In this subsection, the first research question

RQ1: Is there a significant correlation between energy efficiency and productivity?

is examined and discussed.

A correlation analysis is used to estimate the association between UEIs and HPV. There are several methods of correlation analysis, e.g., Pearson, Spearman’s rank order, and Kendall’s tau. The Pearson correlation is used when the data follow a normal distribution. However, if normality does not hold, the non-parametric Spearman’s rank-order or Kendall’s tau correlations are more appropriate [54].

The Shapiro and Wilk test can be used to check whether the data are normally distributed. If the p-value obtained in this test is less than or equal to a desired α, in this study 0.05, the null hypothesis (normality) is rejected. Failing to reject normality indicates that there is not enough evidence to suggest the null hypothesis is false at the 1-α confidence level [55]. The Shapiro and Wilk test and related p-value are shown in

Table 6. Shapiro and Wilk test for HPV, UEI_Elec-adj, and UEI_NG-adj.

	Shapiro and Wilk Test Statistic	p-Value
HPV	0.82142	2.01 × 10−11
UEIElec-adj	0.78284	9.35 × 10−13
UEING-adj	0.79855	3.106 × 10−12

for HPV, UEI_Elec-adj, and UEI_NG-adj.

Table 6 indicates that HPV, UEI_Elec-adj, and UEI_NG-adj do not follow the normal distribution. Hence, the non-parametric correlation tests, like Spearman or Kendall, must be used. Usually, Kendall is applied when there are tied values of the response variables; however, Spearman is applied for series of data without tied values. Because there are no tied values in this dataset, the authors use Spearman’s correlation test. The Spearman’s correlation test is carried out between HPV and UEIs. The null hypothesis shows that there is no monotonic correlation between HPV and UEIs, versus the alternative hypothesis, which indicates the existence of a monotonic correlation. The Spearman’s correlation test between the HPV and UEIs is given in

Table 7. Spearman’s correlation test statistics for the HPV and UEIs.

	Variables	HPV	UEIElec-adj	UEIElec-adj
All plants (n = 132)	HPV	1.0000
	UEIElec-adj	0.6764 0.0000	1.0000
	UEING-adj	0.6777 0.0000	0.7937 0.0000	1.0000

.

Table 7 indicates that there is a statistically significant positive correlation between HPV and UEIs; hence, RQ1 is addressed. Moreover, the correlation coefficients between HPV and UEI_Elec-adj and UEI_NG-adj are almost the same. The Spearman’s correlation between HPV and UEI_Elec-adj is 0.6764, meaning there is a significantly large and positive relationship between these two variables.

The results of the Spearman’s correlation analysis for different variables and various scenarios are shown in

Table 8. Spearman’s correlations and the corresponding p-values by ownership, American manufacturers, and utilizing air conditioning.

	Variables	HPV	UEIElec-adj	UEIElec-adj
Plants’ ownership
American (n = 110)	HPV	1.0000
	UEIElec-adj	0.6698 0.0000	1.0000
	UEING-adj	0.6810 0.0000	0.7557 0.0000	1.0000
Japanese (n = 22)	HPV	1.0000
	UEIElec-adj	−0.1914 0.3935	1.0000
	UEING-adj	−0.4225 0.0501	0.4654 0.0291	1.0000
Vehicle launch
No vehicle launch (n = 106)	HPV	1.0000
	UEIElec-adj	0.5882 0.0000	1.0000
	UEING-adj	0.5902 0.0000	0.7449 0.0000	1.0000
Vehicle launch (n = 26)	HPV	1.0000
	UEIElec-adj	0.7483 0.0000	1.0000
	UEING-adj	0.8509 0.0000	0.8995 0.0291	1.0000
Air conditioning
AC (n = 48)	HPV	1.0000
	UEIElec-adj	0.6836 0.0000	1.0000
	UEING-adj	0.5659 0.0000	0.7557 0.0000	1.0000
No AC (n = 84)	HPV	1.0000
	UEIElec-adj	0.7544 0.000	1.0000
	UEING-adj	0.7549 0.0000	0.7436 0.0000	1.0000
American plants
GM (n = 63)	HPV	1.0000
	UEIElec-adj	0.5552 0.0000	1.0000
	UEING-adj	0.6145 0.0000	0.6058 0.0000	1.0000
Ford (n = 47)	HPV	1.0000
	UEIElec-adj	0.8000 0.000	1.0000
	UEING-adj	0.7649 0.0000	0.7239 0.0000	1.0000

.

The findings from Table 8 are listed as follows (at the 0.05 significance level), The impacts of plant size on UEIs are provided on

Table A2. Spearman’s correlation test statistics for the UEIs and plant size.

	Variables	Plant	UEIElec-adj	UEIElec-adj
All plants (n = 132)	Plant size	1.0000
	UEIElec-adj	0.3519 0.0000	1.0000
	UEING-adj	0.2298 0.0014	0.7937 0.0000	1.0000

, Appendix A:

• The Spearman’s correlation between HPV and UEIs is statistically significant for American companies; however, it is not significant for Japanese plants. Intuitively, the correlation coefficients between HPV and UEIs are different for plant characteristics/ownership. The authors used Fisher transformation to statistically investigate the difference between the plants’ ownership. The reader should refer to Appendix A and

  Table A3. The correlations comparison for different scenarios.

  Different Group Comparison	UEI	Z
  American vs. Japanese	UEIElec-adj	4.034
  American vs. Japanese	UEING-adj	5.148
  Launch vs. no Launch	UEIElec-adj	−1.276
  Launch vs. no Launch	UEING-adj	−2.521
  AC vs. no AC	UEIElec-adj	−0.792
  AC vs. no AC	UEING-adj	−1.844
  GM vs. Ford	UEIElec-adj	−2.382
  GM vs. Ford	UEING-adj	−1.470

  for a detailed methodology. However, it must be emphasized that the Fisher transformation on the rank transformation, Spearman rank, is an approximation and the reader must be cautious in their interpretation. Furthermore, the reader must be cautious about multiple testing issues (i.e., the Bonferroni corrections must be used to compensate for the multiple group effects).
• The Spearman’s correlations between HPV and UEIs while launching a new vehicle are higher when there is no new vehicle launch.
• The Spearman’s correlations between HPV and UEIs for the plants that are not cooled are higher compared to plants that are cooled.
• The Spearman’s correlations between HPV and UEIs for Ford are higher than GM.

4.3. Empirical Approach to the Statistical Analysis

A multiple linear regression model, MLRM, is selected where UEIs are considered as the response, with 11 and 10 regressors for electricity and natural gas, respectively. Multiple transformations of each original continuous regressor, including cube, square, inverse cube, square root, logarithm, and reciprocal, were examined to determine the most appropriate transformation for each continuous regressor. Initially, 11 regressors (or their transformed regressors) were selected for more in-depth analysis.

The UEI statistical model formulation is as follows:

$${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}/\mathrm{NG}-\mathrm{adj}}=\widehat{{\mathsf{\beta }}_0}+{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{P}}\widehat{{\mathsf{\beta }}_{\mathrm{i}}}\mathrm{F}\left({\mathrm{x}}_{\mathrm{i}}\right)$$

(1)

where

${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}/\mathrm{NG}-\mathrm{adj}}$ = The estimated value of adjusted unit energy intensity; the units are kWh or MMBtu (1 MMBtu ≈ 1055 MJ) for electricity and natural gas, respectively;

P = 11 (the number of regressors);

F(x) = Identity function or indicator of nominal variable or real transformation (real transformation can include cube, square, inverse cube, square root, logarithm, and reciprocal of any of the genuine continuous variables);

X₁ = APV, no units;

X₂ = FM, no units;

X₃ = AWD, days;

X₄ = Year, no units;

X₅ = CAC utilization, no units;

X₆ = Vehicle variety, no units;

X₇ = Number of car models, no units;

X₈ = New vehicle launch, no units;

X₉ = Vehicle segment (A and B), no units;

X₁₀ = AC (Air conditioning status; it is used when the energy source is electricity), no units;

X₁₁ = Plant ownership (American and Japanese), no units.

4.4. Model Specification

The Akaike Information Criteria (AIC) are commonly used with the goal of identifying the most appropriate combination of regressors to adequately describe the interrelationship between the regressors and the response, UEIs. Furthermore, AIC can be used for the statistical modeling and variable selection [56].

To enhance the predictive power of the statistical model, some transformations were performed. The preliminary statistical model was developed using stepwise regression with AIC for all 11 independent variables (there would be 10 variables when the energy source is natural gas), in which CAC and APV are transformed. The significant regressors (at the 10% significance level) and resulting coefficient estimates are demonstrated in

Table 9. Initial multiple linear regression for the UEI_Elec-adj.

Regressor/Variable	Coefficient Estimates	Std. Error	t Value	Pr(>|t|)
Intercept	47,839.52	14,327.59	3.339	0.001118	**
AWD	3.0655	0.8523	3.597	0.000468	***
Vehicle Variety	11.128	4.5255	2.459	0.015348	*
No. of Models	68.2555	15.1413	4.508	1.52 × 10−5	***
Year	−20.533	7.1228	−2.883	0.004667	**
ln(APV)	−461.527	61.8735	−7.459	1.45 × 10−11	***
ln(CAC)	−308.371	81.6402	−3.777	0.000247	***
Plant Ownership (Japanese *)	−99.0017	52.0287	−1.903	0.059439	.
Vehicle Launch	78.9496	41.6989	1.893	0.060703	.
Segment B **	99.2191	36.0382	2.753	0.006812	**
AC	121.8007	36.5979	3.328	0.001159	**
Significance Level Codes: ‘***’ 0.001, ‘**’ 0.01, ‘*’ 0.05, ‘.’ 0.1, ‘ ’ 1
Residual standard error: 176.2 on 121 degrees of freedom
Multiple R-squared: 0.7931, Adjusted R-squared: 0.776
F-statistic: 46.39 on 10 and 121 DF, p-value: <2.2 × 10−16
AIC = 1375.82

* Japanese plants are contrasted with American plants. ** Segment B is contrasted with segment A.

and

Table 10. Initial multiple linear regression for the UEI_NG-adj.

Regressor/Variable	Coefficient Estimates	Std. Error	t Value	Pr(>|t|)
(Intercept)	578.5916	139.2828	4.154	6.03 × 10−5	***
Vehicle Variety	0.36758	0.07104	5.174	8.93 × 10−7	***
FM	−0.32597	0.15538	−2.098	0.037941	*
Year	−0.25658	0.06932	−3.701	0.000321	***
ln(APV)	−4.1223	0.61132	−6.743	5.24 × 10−10	***
ln(CAC)	−2.33311	0.78209	−2.983	0.003436	**
Plant Ownership (Japanese *)	−0.80878	0.46742	−1.73	0.086064	.
Segment.B **	0.56456	0.3485	1.62	0.107781
Significance Level Codes: ‘***’ 0.001, ‘**’ 0.01, ‘*’ 0.05, ‘.’ 0.1, ‘ ’ 1
Residual standard error: 1.761 on 124 degrees of freedom
Multiple R-squared: 0.7272, Adjusted R-squared: 0.7118
F-statistic: 47.23 on 8 and 124 DF, p-value: <2.20 × 10−16
AIC = 157.2

* Japanese plants are contrasted with American plants. ** Segment B is contrasted with segment A.

for UEI_Elec-adj and UEI_NG-adj, respectively.

Here are the results of the UEI_Elec-adj statistical model:

• The F-test (p-value < 2.20 × 10⁻¹⁶) determines that the null hypothesis could not be statistically rejected and the UEI_Elec-adj can be estimated based on a set of regressors or their transformation.
• Out of 11 regressors, ten variables, including AWD, air conditioning, vehicle variety, vehicle segment, number of models, plant ownership, year of survey, APV, and CAC, are statistically significant at the 10% significance level.
• The adjusted r-squared indicates that the set of ten selected regressors explains 77% of the variation in UEI_Elec-adj.

Here are the results of the UEI_NG-adj statistical model:

• The F-test (p-value < 2.20 × 10⁻¹⁶) determines that the null hypothesis could not be statistically rejected and the UEI_NG-adj can be estimated based on a set of regressors or their transformation.
• Out of 10 (AC was excluded because the energy source is natural gas) regressors, six including vehicle variety, FM, year of survey, APV, CAC, and plant ownership are statistically significant at the 10% significance level.
• The adjusted R-squared indicates that the set of six selected regressors explains 71% of the variation in UEI_Ng-adj.

A thorough examination of the residuals shows that all underlying assumptions of the regression analysis are met. In order to explore the possible endogeneity and simultaneity issues, the authors performed the serial correlation for the dependent variables (UEIs) over the study period. For the white noise series, it is expected that each autocorrelation be close to zero. Furthermore, 95% of the spikes in the autocorrelation function, ACF, lies within ±$\frac{2}{\sqrt{T}}$, where T is the length of the time series. It is common to plot the control bands on a graph of the ACF. If there are one or more large spikes outside these control bands, or if more than 5% of spikes are outside these control bands, then the series is possibly not white noise [57]. The result of the serial correlation for the UEIs and different combination of Japanese/American, vehicle segment A/B, and whether or not the plant was launching a new vehicle indicate that there is no serial correlation over the study period and the autocorrelation plots show independent white noise. In addition, the authors use four control variables (plant ownership, vehicle segment, launching a new vehicle, and plant air conditioning status) to avoid any possible endogeneity [58].

4.5. Model Enhancement

Some unusual and high-leverage data points are identified when building the multiple linear regression model in the previous subsection. These data points were not data entry errors, nor did they come from a different population than most of the data. There was therefore no compelling reason to exclude these plants from the analysis. It was decided not to exclude these plants from the analysis and to include all of them; subsequently, robust regression is used as a good way to down-weight unusual data points [59,60].

There are several statistical modeling techniques to improve the performance of a statistical model. These methods include all robust methods (M-Estimation, MM-Estimation, SMDM-estimators), shrinkage methods (lasso, ridge, and elastic net), and the combination of robust and shrinkage methods. Here is the list of statistical methods used and developed:

• M-Estimation: M-estimators are a broad class of robust regression methods that also include the maximum likelihood estimators [61]. Huber and Tukey bisquare weight functions are the most common M-estimators [62].
• MM-Estimation: MM estimator (or Multiple M-estimator) is a special form of M-estimation. It is a combination of high breakdown-point and efficient estimation, S estimation [61,63].
• SMDM-Estimation: The scholars suggested additional steps to enhance the MM-estimation. They used an adaptive method to re-estimate the regression parameters and utilize them for the initial estimate in multiple M-estimation [64,65].
• Shrinkage and Regularized Regression: Shrinkage and regularized methods are typically used to optimize the bias–variance trade-off. The three most popular shrinkage estimators include ridge, lasso, and elastic net regressions and are determined as follows:

$$\mathrm{Ridge}\mathrm{regression}:{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathsf{\beta }}_0-{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}{\mathsf{\beta }}_{\mathrm{j}}{\mathrm{x}}_{\mathrm{ij}}\right)}^2+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}{\mathsf{\beta }}_{\mathrm{j}}{}^2=\mathrm{RSS}+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}{\mathsf{\beta }}_{\mathrm{j}}{}^2$$

(2)

$$\mathrm{Lasso}\mathrm{regression}:{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathsf{\beta }}_0-{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}{\mathsf{\beta }}_{\mathrm{j}}{\mathrm{x}}_{\mathrm{ij}}\right)}^2+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}\left|{\mathsf{\beta }}_{\mathrm{j}}\right|=\mathrm{RSS}+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}\left|{\mathsf{\beta }}_{\mathrm{j}}\right|$$

(3)

$$\begin{array}{c}\mathrm{Elastic}\mathrm{net}:{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathsf{\beta }}_0-{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}{\mathsf{\beta }}_{\mathrm{j}}{\mathrm{x}}_{\mathrm{ij}}\right)}^2+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}(\left(1-\mathsf{\alpha }\right){\mathsf{\beta }}_{\mathrm{j}}{}^2+\mathsf{\alpha }\left|{\mathsf{\beta }}_{\mathrm{j}}\right|)\\ =\mathrm{RSS}+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}(\left(1-\mathsf{\alpha }\right){\mathsf{\beta }}_{\mathrm{j}}{}^2+\mathsf{\alpha }\left|{\mathsf{\beta }}_{\mathrm{j}}\right|)\end{array}$$

(4)

The tuning parameter, λ, is identified via an iterative process and minimizing the cross-validation mean squared prediction error. Then, the shrinkage and regularized regression coefficient estimates are determined using the obtained tuning parameter and refitting the regression model. The regularized methods usually do not hold any assumptions and converge faster than ordinary least squares [66]. Hence, there is no need to perform any further residual analysis, and the coefficient estimates could be considered as a proper value of the actual coefficients.

Elastic net regression is a hybrid method that combines both ridge and lasso. The term $\left(1-\mathsf{\alpha }\right){\mathsf{\beta }}_{\mathrm{j}}{}^2$ coerces the correlated coefficient estimates to be averaged, whereas the term $\mathsf{\alpha }\left|{\mathsf{\beta }}_{\mathrm{j}}\right|$ promotes a sparse solution in the coefficients of the averaged features [67]. The $\mathsf{\alpha }$, hyper-parameter, varies between 0 and 1 and controls the ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ penalization (0 is ridge and 1 is lasso).

The authors did not optimize the objective function, Equation (4), in two-dimensional space, for both α and λ. They optimized it in one dimension, λ only, and used equal spaces of α ($\mathsf{\alpha }=0, 0.25, 0.5, 0.75, 1)$to check if there are significant differences on the model’s performance when α varies.

5.

Hybrid Regression Methods: There are some outliers in the pooled dataset; therefore, robust methods can be used to down-weight these unusual observations. Furthermore, shrinkage methods can be used to shrink the coefficient estimates and take care of any possible collinearity. Therefore, the combination of the robust and shrinkage methods was used. Consequently, the weight of each observation (i.e., each plant) was calculated, and a matrix of weights was formed in which the diagonal is the weights of plants for a particular robust method and the off-diagonal matrix is zero. The matrix of weights is then used in the shrinkage methods to reduce any possible collinearity. Utilizing the weights of each plant and considering the shrinkage methods, Equations (2)–(4) may be rewritten as:

$$\mathrm{Ridge}\mathrm{regression}:{\min }_{\mathsf{\beta }}{\left(\mathrm{Y}-\mathrm{X}\mathsf{\beta }\right)}^{\mathrm{T}}{\mathrm{W}}_{\mathrm{m}}\left(\mathrm{Y}-\mathrm{X}\mathsf{\beta }\right)+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}{\mathsf{\beta }}_{\mathrm{j}}{}^2$$

(5)

$$\mathrm{Lasso}\mathrm{regression}:{\min }_{\mathsf{\beta }}{\left(\mathrm{Y}-\mathrm{X}\mathsf{\beta }\right)}^{\mathrm{T}}{\mathrm{W}}_{\mathrm{m}}\left(\mathrm{Y}-\mathrm{X}\mathsf{\beta }\right)+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}\left|{\mathsf{\beta }}_{\mathrm{j}}\right|$$

(6)

$$\mathrm{Elastic}\mathrm{net}:{\min }_{\mathsf{\beta }}{\left(\mathrm{Y}-\mathrm{X}\mathsf{\beta }\right)}^{\mathrm{T}}{\mathrm{W}}_{\mathrm{m}}\left(\mathrm{Y}-\mathrm{X}\mathsf{\beta }\right)+\mathsf{\lambda }{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{p}}(\left(1-\mathsf{\alpha }\right){\mathsf{\beta }}_{\mathrm{j}}{}^2+\mathsf{\alpha }\left|{\mathsf{\beta }}_{\mathrm{j}}\right|)$$

(7)

where

$\mathrm{W}$_m is an n x n matrix where n = 132 (n is the sample size and equals the number of data points). ${\mathrm{W}}_{\mathrm{m}}$ is a diagonal matrix where the elements off the main diagonal are all zero, and the diagonal is the data points’ weights (i.e., W_im, i = 1, 2, …, n). The weights also depend on m, which indexes the robust method type (i.e., M-estimators (Huber and Tukey bisquare), MM-estimator, and SMDM-estimator).

The W_m matrix for the Huber method (m = 1) can be represented as follows:

$${\mathrm{W}}_{\mathrm{m}}=\left[\begin{array}{ccc}{\mathrm{w}}_{1,1}& 0\cdots & 0\\ ⋮& \ddots & ⋮\\ 0& \cdots & {\mathrm{w}}_{132,1}\end{array}\right]$$

Model selection and validation are discussed in the next subsection.

4.6. Model Selection and Validation

Researchers commonly use cross-validation as an important step to validate the final model. There are two main objectives which cross-validation can help: addressing any possible overfitting and calculating the mean squared error, MSE.

In K-fold cross-validation, the dataset is divided into K samples with equal sizes known as K folds. Among K equal folds, K − 1 folds are utilized to train the model and the model performance is evaluated on the last fold. The leave-one-out cross-validation, LOOCV, is another common approach that can be used in model validation. In LOOCV, the dataset is split into K folds where K equals the number of data points (K = n). However, LOOCV can be computationally expensive to use if the sample size is large [68].

According to Kohavi (1995), ten equal folds (K = 10) produces better results than other numbers of folds such as LOOCV, five, or twenty folds. With the goal of achieving the highest level of accuracy, ten folds were applied to evaluate the model performance.

The developed statistical model can be used to estimate $\widehat{{\mathrm{Y}}_{\mathrm{ij}}},$where i represents the observation and j represents the fold. The error can be calculated by determining the difference between the response and its estimated value, as ${\mathrm{Y}}_{\mathrm{ij}}-\widehat{{\mathrm{Y}}_{\mathrm{ij}}}$, for all the K folds. Therefore, the cross-validation error, CV_(k), can be calculated as,

$${\mathrm{CV}}_{\left(\mathrm{k}\right)}={{\displaystyle \sum }}_{\mathrm{i}=1}^k\frac{n_i\times {\mathrm{MSE}}_i}{n}$$

(n_i is the number of data points in fold i).

Where

$${\mathrm{MSE}}_{\mathrm{i}}={{\displaystyle \sum }}_{\mathrm{i}\in {\mathrm{k}}^{\mathrm{th}}\mathrm{fold}}\frac{{\left({\mathrm{Y}}_{\mathrm{i}}-{\mathrm{Y}^}_{\mathrm{i}}\right)}^2}{{\mathrm{n}}_{\mathrm{i}}}$$

Table 11. Performance comparison of the developed statistical models for electricity (using 10-fold cross-validation).

Energy Source	Regression Method	Estimation Type	Adjusted R-Squared	Residual Standard Error (RSD)	Cross-Validation with 10 Folds (MSE)
${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}-\mathrm{adj}}$	MLRM	MLRM with transformation	0.77	176.2	188.50
	Robust Regression	M-estimator (Huber)	0.79	121	186
		M-estimator (Tukey bisquare)	0.62	86.4	221
		MM-estimator	0.78	101	222
		SMDM-estimator	0.79	152	236
	Shrinkage Methods	Ridge Regression, α = 0	0.79		187.22
		Lasso regression, α = 1	0.80		188.47
		Elastic net, α = 0.50	0.79		187.22
	Hybrid (Robust and Shrinkage) Methods	Lasso with M-estimator (Huber)	0.83		153
		Lasso with M-estimator (Tukey bisquare)	0.80		88.85
		Lasso with MM-estimator	0.81		103.51

and

Table 12. Performance comparison of the developed statistical models for natural gas (using 10-fold cross-validation).

Energy Source	Regression Method	Estimation Type	Adjusted R-Squared	Residual Standard Error (RSD)	Cross-Validation with 10 Folds (MSE)
${\widehat{\mathrm{UEI}}}_{\mathrm{NG}-\mathrm{adj}}$	MLRM	MLRM with transformation	0.71	1.76	1.93
	Robust Regression	M-estimator (Huber)	0.72	1.58	2.03
		M-estimator (Tukey bisquare)	0.70	1.51	2.09
		MM-estimator	0.67	1.40	2.05
		SMDM-estimator	0.65	1.60	2.22
	Shrinkage Methods	Ridge Regression, α = 0	0.72		1.94
		Lasso regression, α = 1	0.73		1.93
		Elastic net, α = 0.50	0.73		1.94
	Hybrid (Robust and Shrinkage) Methods	Lasso with M-estimator (Huber)	0.73		1.63
		Lasso with M-estimator (Tukey bisquare)	0.70		1.56
		Lasso with MM-estimator	0.73		1.39
		SMDM-estimator	0.73		1.54

summarize all developed regression models for electricity and natural gas. These include the base model (MLRM with data transformation) and improved models: all robust regressions, shrinkage and regularized regressions, and the combination of robust and shrinkage techniques.

Here are the findings from Table 11 and Table 12.

• Multiple linear regression has higher residual standard error (RSD) compared with robust regressions.
• Multiple linear regression has lower adjusted R-squared compared with regularized regressions and robust regressions.
• The hybrid methods (combination of regularization and robust) have almost the highest adjusted R-squared and lowest cross-validation errors compared with other methods.

Table 11 shows that the adjusted R-squared improved from 0.77 (base Elec model) to 0.83 (Huber lasso) and from 0.71 (base NG model) to 0.73 (MM lasso); however, the cross-validation errors were reduced from 188.49 to 153 and from 1.93 to 1.39 for electricity and natural gas, respectively. Moreover, a careful examination of Table 11 and Table 12 confirms the existence of some unusual observations in our study, lower residual standard error for robust regressions compared to MLRM, and the rationale that hybrid methods have better regression fitting performance.

On top of the statistical models’ performance, the regressors’ coefficient signs were carefully examined for different statistical models that were presented in Table 11 and Table 12. Almost all the estimated coefficients in different statistical models had the same sign except for the vehicle launch variable. For electricity energy source, the sign of this variable was positive when multiple linear regression or lasso with M-estimator (Huber) was used. It means that while launching a new vehicle the electricity consumption per vehicle increases. The authors investigated this fact through data visualization and conducting a paired sample t-test. The results showed that while launching a new vehicle, ${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}-\mathrm{adj}}$ increased. Therefore, the authors decided to use the lasso with M-estimator (Huber) and lasso with MM-estimator, which show better statistical performance compared to MLRM for electricity and natural gas, respectively.

4.7. UEI Model Discussion and RQ2 Examination

In this subsection, the second research question

RQ2: What are the most important factors that can improve the energy efficiency?

and 11 hypotheses are examined and discussed.

The final developed statistical models including the coefficient estimates for ${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}-\mathrm{adj}}$ and ${\widehat{\mathrm{UEI}}}_{\mathrm{NG}-\mathrm{adj}}$ are depicted in

Table 13. The final models’ coefficient estimates.

Regressor/Variable	Coefficient Estimates $({\widehat{\mathbf{U}\mathbf{E}\mathbf{I}}}_{\mathbf{E}\mathbf{l}\mathbf{e}\mathbf{c}-\mathbf{a}\mathbf{d}\mathbf{j})}$	Coefficient Estimates $\left({\widehat{\mathbf{U}\mathbf{E}\mathbf{I}}}_{\mathbf{N}\mathbf{G}-\mathbf{a}\mathbf{d}\mathbf{j}}\right)$	Both Energy Resources
Intercept	5,1182.4	571.394
AWD	2.6	−0.00688	***
Vehicle Variety	17	0.35536	+
FM	−16	−0.33441	−
Number of Models	69.7	0.26753	+
Year	−22.3	−0.25666	−
Ln (APV)	−429.5	−4.08135	−
Ln (CAC)	−340.9	−0.65277	−
Plant Ownership (Japanese *)	−80	−0.47642	−
Vehicle Launch	45.1	.	***
Segment B **	112.4	0.82821	+
AC	112.4	NA
Adjusted R-squared	0.83	0.73
Cross-Validation—10 folds	153	1.39

* Japanese ownership is contrasted with American plants. ** Segment B is contrasted with segment A. *** The impact of all regressors on ${\widehat{\mathrm{UEI}}}_{\mathrm{NG}-\mathrm{adj}}$ and ${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}-\mathrm{adj}}$ is similar other than these two variables.

.

Table 13 indicates that four regressors directly reduce UEIs and two regressors elevate them. Regressors that directly reduce UEIs include flexibility, APV, CAC, and production year. Observation year does not reduce UEIs per se; however, there are some latent factors such as technological improvement or work regime that might be confounding and occurring during the same period that may improve the estimated UEIs. On the contrary, vehicle variety and model types increase the UEIs. The study shows that while launching a new vehicle, the UEI_Elec-adj increases; conversely, the UEI_NG-adj remains unchanged during the launch. The paint line’s ovens have the highest natural gas consumption in a plant. They are always running, except for the weekends or when the plants are down for the long holidays or maintenance activity. That could be considered as a probable reason that UEI_NG-adj remains unchanged while launching a new product. In addition, another possible reason might be the low number of plants that had a new vehicle launch during the study period (n = 26).

The developed UEI equations are:

$$\begin{array}{c}{\mathrm{UEI}}_{\mathrm{Elec}\_\mathrm{adj}}=(51182.4+2.6\mathrm{AWD}+17\mathrm{Vehicle}\mathrm{Variety}-16\mathrm{Flexibility}+69.7\mathrm{Model}-22.3\mathrm{Year}-429.5\ln \left(\mathrm{APV}\right)\\ -340.9\ln \left(\mathrm{CAC}\right)+45.1\mathrm{Vehicle}.\mathrm{launch}-80\mathrm{Japanese}+112.4\mathrm{Segment}.\mathrm{B}+112.4\mathrm{AC})\end{array}$$

(8)

$$\begin{array}{c}{\mathrm{UEI}}_{\mathrm{NG}\_\mathrm{adj}}=(571.394-0.00688\mathrm{AWD}+0.3553\mathrm{Vehicle}\mathrm{Variety}-0.3344\mathrm{Flexibility}+0.2675\mathrm{Model}\\ -0.2675\mathrm{Year}-4.08135\ln \left(\mathrm{APV}\right)-0.6527\ln \left(\mathrm{CAC}\right)-0.4764\mathrm{Japanese}+0.8282\mathrm{Segment}.\mathrm{B})\end{array}$$

(9)

The main findings from Table 13 and Equations (8) and (9) can be summarized for electricity and natural gas as follows:

Electricity:

• The regression model output indicates that 83% of the variation in UEI_Elec-adj is explained by the group of 11 significant regressors.
• Cross-validation error is 153 kWh/vehicle.
• The UEI_Elec-adj increases by 17 kWh or 2.26% (calculated based on using the mean of UEI_Elec-adj = 752.96 kWh) for each unit increase in vehicle variety when all other regressors are fixed.
• When a new vehicle is launched, the UEI_Elec-adj may increase by 45.1 kWh or 5.99%.
• The average UEI_Elec-adj difference between vehicle segments A and B is 112.4 kWh or 14.93%.
• Japanese plants are more energy-efficient by consuming 80 kWh (10.62%) less electricity compared to American plants.
• The UEI_Elec-adj is higher for plants that are cooled by 112.4 kWh or 14.93%.
• Natural gas:
• The regression model output indicates that 73% of the variation in UEI_NG-adj is explained by the group of nine significant regressors; vehicle launch is not significant. However, the AWD variable impact is minimal and negligible.
• Cross-validation error is 1.39 MMBtu/vehicle (1 MMBtu ≈ 1055 MJ).
• The UEI_NGc-adj increases by 0.356 MMBtu, 6.38% (calculated based on using the mean of UEI_NG-adj = 5.58 MMBtu) for each unit increase in vehicle variety when all other regressors are fixed (1 MMBtu ≈ 1055 MJ).
• The average UEI_NG-adj difference between vehicle segments A and B is 0.828 MMBtu or 14.84% (1 MMBtu ≈ 1055 MJ).
• Japanese plants are more energy-efficient by consuming 0.476 MMBtu (8.53%) less natural gas compared to American plants (1 MMBtu ≈ 1055 MJ).

Table 13 shows the impact of the developed/defined regressors on UEIs; hence, RQ2 is addressed. Moreover, the MRLM and hybrid models’ coefficient estimates for both electricity and natural gas are compared in

Table A4. MRLM and hybrid method coefficients’ estimate comparison for UEI_Elec-adj.

	MLRM		Hybrid Method
Variable	Estimate	Pr(>|t|)	Estimate	% Change *
Intercept	47,839.52	0.00	51,182.40	−6.99
AWD	3.07	0.00	2.60	15.19
Variety.bodyandchassis	11.13	0.02	17.00	−52.77
Model.types	68.26	0.00	69.70	−2.12
Year	−20.53	0.00	−22.30	−8.61
ln(APV)	−461.53	0.00	−429.50	6.94
ln(CAC)	−308.37	0.00	−340.90	−10.55
Ownership.Japanese **	−99.00	0.06	−80.00	19.19
Vehicle.Launch	78.95	0.06	45.10	42.87
Segment.B ***	99.22	0.01	112.40	−13.28
AC	121.80	0.00	112.40	7.72
Flexibility	NA	NA	−16	-

* MRLM is the base. ** Japanese ownership is contrasted with American plants. *** Segment B is contrasted with segment A.

and

Table A5. MRLM and hybrid method coefficients’ estimate for UEI_NG-adj.

	MLRM		Hybrid Method
Variable	Estimate	Pr(>|t|)	Estimate	% Change *
(Intercept)	578.5916	6.03 × 10−5	571.394	1.24
Variety.bodyandchassis	0.36758	8.93 × 10−7	0.35536	3.32
Flexibility	−0.32597	0.037941	−0.33441	−2.59
Year	−0.25658	0.000321	−0.25666	−0.03
ln(APV)	−4.1223	5.24 × 10−10	−4.08135	0.99
ln(CAC)	−2.33311	0.003436	−0.65277	72.02
Ownership.Japanese **	−0.80878	0.086064	−0.47642	41.09
Segment.B ***	0.56456	0.107781	0.82821	46.70
Model.types	NA	NA	0.26753	−
AWD	NA	NA	−0.00688	−
Vehicle.Launch	NA	NA		-

* MRLM is the base. ** Japanese ownership is contrasted with American plants. *** Segment B is contrasted with segment A.

, Appendix A, to understand what can be learned from the hybrid models. Table A4 and Table A5 show:

○

Electricity: flexibility, vehicle launch, and plant ownership (Japanese) regressors are not significant at the 5% significance level in the MLRM; however, they are significant for the hybrid model, lasso with M-estimator (Huber). Moreover, the difference between the MLRM and hybrid methods’ coefficient estimates for vehicle variety, plant ownership (Japanese), and vehicle launch variables is more than 20%.

○

sup>∙ Natural gas: AWD, vehicle segment, plant ownership, and number of models variables are not significant at the 5% significance level in the MLRM; however, they are significant for the hybrid model, lasso with MM-estimator. Moreover, the difference between the MLRM and hybrid methods’ coefficient estimates for ln(CAC), plant ownership (Japanese), and Segment B variables is more than 20%.

The constructed hypotheses in Table 3 can be examined through the following test and considering Table 13 [64],

$$\{\begin{array}{c}{\mathrm{H}}_0: {\mathsf{\beta }}_i=0 \mathrm{where} \mathrm{i}=1, 2, \dots \mathrm{P} \left(\mathrm{P} \mathrm{is} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{regressors}, \mathrm{in} \mathrm{this} \mathrm{study} 11\right)\\ {\mathrm{H}}_{\mathrm{A}}: {\mathsf{\beta }}_i \ne 0\end{array}$$

The null hypothesis in a regression model is represented by t₀ = $\hat{\mathsf{\beta }}$_j/$\widehat{\mathrm{se}}$ ($\hat{\mathsf{\beta }}$ j) ~ t(n − p − 1). The H₀ is rejected in favor of H_A if |t₀| > t(n – p − 1, 1 − α/2).

Table 14. Hypothesis testing results.

Research Hypotheses	$({\widehat{\mathbf{U}\mathbf{E}\mathbf{I}}}_{\mathbf{E}\mathbf{l}\mathbf{e}\mathbf{c}-\mathbf{a}\mathbf{d}\mathbf{j}})$ Hypotheses Testing Result (Y/N)	$\left({\widehat{\mathbf{U}\mathbf{E}\mathbf{I}}}_{\mathbf{N}\mathbf{G}-\mathbf{a}\mathbf{d}\mathbf{j}}\right)$ Hypotheses Testing Result (Y/N)
H1. Vehicle segment has a significant impact on the UEIs	Y—Segment A has the lower UEI	Y—Segment A has the lower UEI
H2. UEIs are correlated with CAC Utilization	Y	Y
H3. UEIs are correlated with the vehicle variety	Y	Y
H4. UEIs are correlated with the number of models	Y	Y
H5. UEIs are correlated with APV	Y	Y
H6. UEI variation for American and Japanese is significantly different	Y—Japanese has the lower UEI	Y—Japanese has the lower UEI
H7. UEIs are correlated with flexible manufacturing	Y	Y
H8. UEIs are correlated with AC	Y	NA
H9. UEIs are correlated with launching a new vehicle	Y	Y
H10. UEIs are correlated with AWD	Y	Y
H11. UEIs are correlated with year of production	Y	Y

summarizes the constructed hypotheses in Table 3 and illustrates their testing results.

Table 14 shows that all 11 research hypotheses were accepted for both ${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}-\mathrm{adj}}$and ${\widehat{\mathrm{UEI}}}_{\mathrm{NG}-\mathrm{adj}}$other than H9 for ${\widehat{\mathrm{UEI}}}_{\mathrm{NG}-\mathrm{adj}}$ (the potential reason for not accepting this hypothesis was discussed in Table 13 findings).

5. Conclusions and Implications

This section discusses the comparison of UEI and HPV determinants, policy implications, conclusions and study limitations, and future research.

5.1. UEI and HPV Determinant Comparison and RQ3 Examination

In this subsection, the third research question

RQ3: What are the common determinants that can improve both productivity and energy efficiency KPIs at the same time?

is examined and discussed.

The paper outlines the underlying determinants of unit energy intensity, UEIs, and labor intensity, HPV. However, the study finds that these two KPIs are correlated, but the relationship is not one-to-one and the underlying determinants of these two KPIs can be different.

Table 15. Comparing HPV and UEI statistical models.

	HPV *—(Coef. Sign)	UEIElec-adj	UEING-adj
Intercept	+	51,182.40	571.39
AWD	+	2.60	−0.01
Vehicle Variety	+	17.00	0.36
Number of Models	NA **	69.70	0.27
Year	-	−22.30	−0.26
ln(APV)	-	−429.50	−4.08
ln(CAC)	+	−340.90	−0.65
Plant Ownership (Japanese)	NA **	−80.00	−0.48
Vehicle Launch	+	45.10	.
Segment B	+	112.40	0.83
Segment C **	+	NA **	NA **
FM	-	−16.00	−0.33
AC	NA **	112.4	NA **

* Adapted from Abolhassani and Jaridi (2016) [53]. ** NA: Not Applicable/Available.

compares these two KPIs’ (HPV and UEIs) coefficient estimates and addresses RQ3.

There are some factors that have similar effects on both HPV and UEIs. The AWD, FM, APV, and year of manufacturing enhance HPV and UEIs at the same time. On the contrary, vehicle variety, number of models, and launching a new vehicle penalize HPV and UEIs at the same time. Additionally, segment B is less productive and energy-efficient compared to segment A. The study shows Japanese manufacturers are more energy-efficient and productive compared to American OEMs. CAC is the only determinant that has an opposite sign when comparing HPV and UEIs.

The authors did not find any compelling reasons indicating that platform sharing and percentage of hourly employees can impact energy intensity, and consequently UEIs. Therefore, the authors decided not to include them in the UEI models.

The current study proposes a systematic and comprehensive approach to strengthen the automakers’ energy efficiency. On one hand, it determines the correlation between labor intensity and energy intensity, HPV and UEIs, and studies whether or not car ownership, launching a new vehicle, and cooling a plant impact this correlation coefficient. On the other hand, it demonstrates several steps, including building base regression models involving various transformations, utilizing robust and regularized methods, and developing hybrid statistical models to estimate the UEIs. Our novel and hybrid statistical models outperform conventional multivariate regression models (the adjusted R-squared and mean squared cross-validation error for electricity improved from 0.77 to 0.83 and 188.5 to 153, respectively).

5.2. Practical and Policy Implications

Any plant operational manager could use the developed regression models, Equations (8) and (9), to obtain the preferred target values for UEIs. They can define the optimal values for each strategy by using Mixed Integer Programming (MIP) optimization and considering the plant’s constraints. A metaheuristic optimization method or the branch and bound (BB) method can be utilized to obtain the optimal value for each strategy. The developed hybrid regression models represent the objective function and each regressor’s limitation can be used as a constraint (lower or upper bound). For instance, for vehicle segment A, which was the most energy-efficient segment during the study period, with 568.24 kWh, the following MIP mathematical modeling can be used to attain a target UEI_Elec-adj of 350 kWh (350 kWh is 38% energy efficiency enhancement compared to the most energy-efficient benchmark plant). Z is the distance from the specified target value for UEI_Elec-adj, 350 kWh in the example below.

$$\begin{array}{c}Min\left(z\right)=(51182.4+2.6\mathrm{AWD}+17\mathrm{Vehicle}\mathrm{Variety}-16\mathrm{Flexibility}+69.7\mathrm{Model}-22.3\mathrm{Year}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-429.5\ln \left(\mathrm{APV}\right)-340.9\ln \left(\mathrm{CAC}\right)+45.1\mathrm{Vehicle}.\mathrm{launch}-80\mathrm{Japanese}+112.4\mathrm{Segment}.\mathrm{B}\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+112.4\mathrm{AC}-350{)}^2\hfill \end{array}$$

(10)

Subject to:

 234 ≤ AWD, integer ≤ 283;

 2 ≤ Vehicle variety, integer ≤ 12;

 13.8 ≤ FM ≤ 25.8;

 1 ≤ Number of car models, integer ≤ 5;

 10.25 ≤ ln(APV) ≤ 13.03;

 2.56 ≤ Ln(CAC) ≤ 4.91;

 1999 ≤ Year, integer ≤ 2005.

Z is the expected value of the Taguchi loss function and includes both the variance of the estimator and its deviation from the sample mean. Z can be determined as,

$$\mathrm{Z}={\left({\overline{\mathrm{X}}}^{}-\mathrm{T}\right)}^2+S^2$$

where

Z = Taguchi loss function;

$\overline{\mathrm{X}}$ = The sample mean;

T = The given target, in our research 350 kWh;

S² = The sample variance (since we are hitting the target in each iteration, the variance will be zero).

A nonlinear optimization model known as Mixed Integer Distributed Ant Colony Optimization, MIDACO, was utilized to overcome some common challenges such as convexity, flat spots, stochastic noise, and non-differentiability [69].

Table 16. Optimal regressors’ values for UEI_Elec-adj of 350 kWh—MIDACO Algorithm.

Decision Variables	Decision Variables’ Bounds **	Optimum Attained Setting ***	Practical Insight
UEIElec-adj	(345.55, 2380.17)
AWD *	(234, 283)	240	“AWD” is fixed at 240
Vehicle variety	(2, 12)	2	Since “Vehicle variety” affects UEIElec-adj negatively (its coefficient estimate has a positive sign), the attained optimum value is almost at the lower end of the spectrum, which means that the factory has to manufacture less vehicle variety
FM	(17.26, 24.26)	21.58	Since “FM” has a positive influence on UEIElec-adj (FM coefficient estimate has a negative sign), the attained optimum value is almost inclined to the higher end of the spectrum, which means that the factory has to be more flexible
Number of Models	(1, 5)	1	Since “Model types” affects UEIElec-adj negatively, the attained optimum value is at the lower end of the spectrum, which means that the factory has to manufacture fewer models
LN(APV)	(10.25, 13.03)	12.03	Since “APV” has a positive influence on UEIElec-adj, the attained optimum value is almost at the higher end of the spectrum, which means that the factory has to manufacture at the greatest possible volume
LN(CAC)	(2.56, 4.91)	4.01	Since “CAC” has a positive influence on UEIElec-adj, the attained optimum value is almost at the higher end of the spectrum, which means that the factory has to manufacture at the greatest possible car assembly and capacity utilization (CAC) level
Year *	(1999, 2005)	2005	The “year” was fixed at 2005
Vehicle launch	1	1	The “vehicle launch” was fixed at one, defining the optimal value when launching a new vehicle
Ownership	(American, Japanese)	Japanese	Since Japanese factories were more energy-efficient, Japanese ownership was selected (however, in reality, Japanese plants might possess a better management style, production system, technology, etc.)
Segment	A	A	Segment A was selected for the illustration in the optimization model
AC	1	1	It was assumed that the plant was cooled
Optimization model result
KPI Measure	Target	Z
UEIElec-adj	350	1.45 × 10−18

* The AWD and year were fixed at 240 and 2005, respectively. ** Each variable’s bounds are shown in Table A6 in Appendix A (for segments A and B). *** The optimization solver was run for 100 iterations. Note: the reader should consider that some of the variables cannot be controlled by a plant manager.

depicts decision variables, decision variables’ range, obtained optimum values, practical insight, and the mean squared error, Z, for segment A.

The bio-inspired optimization method usually introduces stochastic noise, but the content of this research differs from the other optimization problems. The Z is calculated as 1.45 × 10⁻¹⁸, which means that the deviations from target (350 kWh) are too small and negligible. Hence, the authors decided to accept the obtained regressors’ values as optimal that were achieved through 100 iterations and did not perform a large number of iterations.

The authors used the final statistical model (Equation (8)) along with the regressors’ range,

Table A6. Ranges for UEI_Elec-adj, UEI_NG-adj, and predictors.

Variable	Values Range
Segment	A	B
UEIElec-adj	(345.55, 2380.17)	(370.52, 1952.2)
UEING-adj	(1.77,23.85)	(2.49, 17.33)
AWD	(234, 283)	(183, 336)
Vehicle Variety	(2, 12)	(2, 20)
FM	(17.26, 24.26)	(16.77, 25.8)
Model types	(1, 5)	(1, 7)
APV	(28,356, 456,169)	(67,364, 426,499)
CAC	(13, 137)	(29, 150)
Year	(1999, 2005)	(1999, 2005)
AC	0, 1	0, 1
Launch of a new vehicle	0, 1	0, 1
Plant ownership	American, Japanese	American, Japanese

, and examined a Monte Carlo simulation to explore if 350 kWh/vehicle is an appropriate target for UEI_Elec-adj. The histogram of 10,000 simulated UEI_Elec-adj along with the 95% confidence interval are illustrated in Figure 4 (the 95% confidence interval ranges from 56.75 to 1745.26 kWh/vehicle). It was found that 10% of the simulated UEI_Elec-adj were less than 350 kWh/vehicle; hence, 350 kWh was a reasonable target for UEI_Elec-adj.

The developed statistical model can be used to obtain the optimal settings for natural gas as well. Therefore, the OEMs can use the developed and implemented hybrid regression models along with mathematical modeling to improve their UEIs. While this approach can generally be applied to a manufacturing plant, it is essential to emphasize that the constraints and the regressors’ range are specific to the companies being studied and could greatly impact the results for new plants.

5.3. Conclusions

The strategies to enhance energy intensity have become an important area of interest by many industries and researchers. In the literature, there are two common approaches for energy improvement: changing the industry frontier using the available best practices or implementing energy efficiency practices, such as replacing or upgrading the current equipment at a manufacturing plant [54]. The purpose of this research is different and complementary to the studies reported in the literature. There is little awareness of the group of regressors/variables that impact energy intensity, UEIs, at the theoretical and empirical levels in auto industry, increasing which is one of the key objectives of this study. Based on our analysis, the underlying determinants of energy efficiency and labor productivity are quite similar. This implies that strategies to improve energy may have spillover benefits to labor, and vice versa. The only underlying determinant that differs in sign is for capacity utilization. This may be due to the fact that labor is more flexible vis-à-vis utilization and energy has a larger fixed component.

In this study, we first investigated the association between energy intensity, UEIs, and labor intensity, HPV. The authors found that there was a statistically significant correlation between energy intensity and labor intensity for both electricity and natural gas (RQ1).

In the next step, the effect of 11 regressors on UEIs was examined, and the combination of M-estimator (Huber) or Multiple M-estimator and lasso regression was utilized to build robust statistical models to determine the impact of these regressors on UEIs. The regressors were chosen and developed based on a comprehensive literature review and practical purposes (RQ2).

It was found that launching a new vehicle and adding new car models were often seen as the primary reasons that would result in increased energy intensity. For instance, a one-unit increment in a new model adds a raise of 69.7 kWh, 9.26%, and 0.267 MMBtu, 4.78l%, for UEIs (1 MMBtu ≈ 1055 MJ). Adoption of some complementary strategies in a manufacturing plant, such as increasing the CAC, FM, and production volume, was shown to reduce the UEIs.

Table 17. Vehicle variety strategy effect on ${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}-\mathrm{adj}}$.

	Vehicle Variety Coeff. per Table 13	Number of Body Styles	Number of Chassis	Vehicle Variety	Effect on ${\widehat{\mathbf{UEI}}}_{\mathbf{Elec}-\mathbf{adj}}$ (kWh)
S1	17	3	5	8	136
S2	17	1	2	3	51

depicts an example for two different scenarios, and it indicates how vehicle variety could increase the ${\widehat{\mathrm{UEI}}}_{\mathrm{Elec}-\mathrm{adj}}$. In scenario 1, S1, assembling eight vehicle varieties would cost an extra 85 kWh per vehicle (=136 − 51 kWh) compared to scenario 2, S2, where a plant assembles three vehicle varieties.

The study shows flexibility is a crucial best practice that helps companies improve productivity and energy efficiency. Businesses should be flexible enough to respond effectively to various changes in today’s competitive environment. Such flexibility can be achieved by creating a sustainable technology competency, improving employees’ skills, and building an appropriate organizational culture that cultivates efficiency and effectiveness. One of the great examples of the flexible business model was when the COVID-19 pandemic hit the world. The impact on the companies which had a flexible business model was minimal and they were able to quickly adapt themselves during the Coronavirus shutdowns and reopening.

The authors also show that there is a strong alignment between energy efficiency and productivity determinants. They found that flexible manufacturing, production volume, and year of production can improve productivity and energy efficiency. On the contrary, vehicle variety, number of models, and launching a new vehicle penalized both productivity and energy efficiency (RQ3).

Japanese plants are more energy-efficient compared to American plants, for both electricity and natural gas energy resources. There might be some fundamental differences between Japanese and American car manufacturers that are worthwhile to consider. For example, American companies may produce less subcompact cars and produce more midsize SUVs, which consume more energy to produce. In addition, Japanese companies’ subcompact cars may be smaller than American companies’ subcompact cars, although they belong to the same vehicle segment. In addition, there may be some differences between Japanese and American OEMs’ supply chain. For instance, the level of outsourcing might be different between Japanese and American plants. Furthermore, Japanese plants may intend to produce small parts inside and outsource large or semi-finished parts, which may not be the case for American plants.

It is worth noting that improvements in energy efficiency can often offset a car maker’s profitability. For example, customers seem to prefer having more vehicle varieties or segment B vehicles (pickup, trucks, sport, luxury, and van) that may increase OEMs’ production costs; however, it might be completely aligned with OEMs’ profitability targets. Particularly in recent years, the variety of available vehicles to clients has significantly increased and customers prefer to have trucks or pickup cars (segment B) instead of small cars (segment A). Consequently, OEMs may intend to produce a greater number of car body types and chassis configurations specifically for segment B to increase their profitability at the expense of extra energy consumption. OEMs could use the proposed approach to define the optimal value of each strategy in order to simultaneously improve profitability and energy efficiency.

5.4. Study Limitations and Recommendations for Future Research

Similar to any research, there are limitations and data deficiencies in this study. For the plants that produced multiple vehicle segments, data were considered for the segment with highest volume. As this research was examined using the available data from 1999–2005, extrapolation to the current situation is not recommended, and the results must be viewed in the context of the available data. However, the principles behind the models and methodology will not change and can be replicated with a more recent dataset. The assumptions made for this research include:

• A total of 14% of UEI_Elec was used for comfort cooling. It was assumed and found that the average energy share is linear in the range of CDD. The amount of 14% is only achieved when CDD is at the maximum, and CDD_adj ranges from 0 to 1, which indicates that UEI_Elec-adj ranges from 0.86 to 1. It means if plants A and B have the same UEI, but plant A is located in a hot climate (high CDD) and consequently cooled more, the UEI for plant A is lower than plant B, and plant A is more energy-efficient. On the other hand, if plant C has the lowest CDD and there is no electricity usage to cool the plant, all the electricity consumption was used to assemble vehicles.
• A total of 17% of UEI_NG was used for comfort heating. It was found that the average energy share is almost linear in the range of HDD, and 17% is only achieved when HDD is at its maximum.
• The base temperature used to calculate CDD and HDD was 65 °F (≈18.3 °C).
• All plants were heated 24 h a day during the heating months.
• The plants were cooled 24 h a day during the cooling months, if cooled.
• The plants did not use on-site renewable energy sources or cogeneration and they purchased all their electrical energy.
• The authors were not able to exclude internal logistics, transportation, and supply energy consumption; hence, they were included in the study as plants’ energy consumption.

Recommendations for possible future work include:

• Identifying new regressors that can be added to the UEI models. For example, the level of automation in a plant, plant’s building size, and lean manufacturing may be included in the UEI models.
• The use of Group Lasso for the nominal variables (plant ownership and vehicle segmentation).
• In contrast to American plants, which failed to reduce UEIs over the study period, Japanese plants were able to reduce it. It might be worthwhile to study the reasons of increasing the UEIs for American plants during the study period. For instance, exploring the underlying determinants between Japanese and American management style might be of interest.
• Exploring the possible relationship between energy efficiency, productivity, sustainable smart manufacturing, sustainable industry 4.0, cyber-physical production network, and profitability [70,71].