Examining the Causes of Plastic Bags Usages and Public Perception about its Effects on the Natural Environment

Plastic bags are one of the most commonly used products in our daily life. The current research aims to investigate the common causes of its usage and public perception about its effect on the natural environment, including land, air and water pollution. The researchers collected data from 173 individuals from Islamabad and Rawalpindi cities of Pakistan using a non-probability convenience sampling technique. Empirical results reveal that 53% of participants are extensively using plastic bags. Moreover, to dispose of, 46.82% prefer to openly dump it while 30.63% prefer to burn. Most of the respondents (30.63%) valued the significant role of TV and Radio in communicating the unfavourable effects of plastic bag wastes. Interestingly, an equal number of participants opined increase and decrease trend in the usage of plastic bags however most of them considered cloth bags as an alternative solution for the problem. This study can help to access the severity of the problem, identify the reasons and provide alternative solutions considering public perspective located in the targeted region.

Introduction
For a long time, countries all over the world are using plastic as an accidental innovation in hydrocarbons. Plastic bags were first manufactured in the 1970s (Williamson, 2003) and their use went on increasing day by day (Mahmood et al., 2020). In the last quarter of the 20 th century, an enormous amount of products were created using plastics (Sugii, 2008). At first, it looked as convenient, cheap, flexible and long-lasting resource ranging from the production of electric appliances body to single sheet plastic bags. Most of these bags are being disposed of as waste after single time usage (Moharam & Maqtari, 2014). The United States petrochemical industries first presented and encouraged the production of plastic bags, followed by Western Europe and then to the whole world (Clapp & Swanston, 2009). At the start, it looked like users were unaware of its harmful effects (V & HR, 2011), they continued its use as a comfortable and affordable material (Adane & Muleta, 2011). Plastic production companies might be aware of the harmful environmental effects of plastic but like some of the other technological innovations (Mulder, 2013), nobody told the hazardous effects of this innovation until the substantial consequences were observed by the environmentalists and masses (Imran & Abbas, 2020). People are used to it because of which it has become a challenge to stop the people from its use and provide them with some alternate options (Abbas, 2020a).
The profusion and limited tenure of plastic bags have tremendous harmful effects on the ecosystem of the world (Moharam & Maqtari, 2014). Moreover, these products limited life span usage leads to disposal which take centuries for decomposition. More and more countries are in use of these products without the consideration of environmental impact (Kumar, 2018) as they are more concerned with current development instead of looking at the future consequences. No doubt there are several benefits associated with the use of plastic but the established system of plastic is now known for the severe environmental issues. So far, the concerned matter has been given less attention for its production and consumption patterns (Nielsen et al., 2019). Plastic bags' daily waste is the largest component of environment pollution. Food packs with plastic lining, plastic bottles and other such items' disposal can pollute groundwater and is also harmful to animal life. Because of careless attitude, 85% of plastic grocery bags are dumped in open landfills (Kumar, 2018). Some countries are yet formulating policies while some others have implemented rules and regulations against the use of polythene products. As per the United Nations (UN) 2018 report, it is mentioned that around 127 countries have implemented some kind of policies related to the prohibition for the use of plastic bags Shah, 2019). Researchers, scholars, investigators and worldwide known national and international institutions have published several articles and reports on the harmful impact of plastic bags in different regions but unfortunately in Pakistan, the research related to the issue under consideration is very limited.
In Pakistan's scenario, recently it has been observed that the government has realized the severity of problems associated with the uncontrollable use of plastics. The restriction on the consumption of plastic items has been imposed in multiple cities in Pakistan. Although some of the shopkeepers have been charged heavy penalties for the violation of adopted policy (Baloch, 2019) currently the practice of use of plastic bags could not be stopped because of the negligence and uncontrollability of the concerned governmental authorities. Environment Protection Authority in Federal Capital and Departments in provinces are not playing their due role for effectively checking pollution and maintaining the environment clean and healthy.
The study has been conducted for identification of problems associated with the excessive usage of plastic bags from the public perspective. Public opinion on the issue is necessary to be taken to solve the problems for the protection of existing animals and plant species and their upcoming generations for the sustainability and continuity of the life cycle. In this era, it is necessary to access the severity of the problem, identify the reasons and provide alternative solutions regarding the hazardous and profound impact of plastic bags on our surroundings. The situation is worsening because these bags regular consumption is resulting in unrecoverable loss of productive land, clean water and fresh air that is essential for living beings. The data has been collected from the individuals irrespective of their gender, education, religion, background, caste, colour and profession.
In the process of plastic production, various harmful materials are produced to impact the environment. These materials contribute to acid rain which is the real threat to the natural and artificial environment especially in the regions which were historically highly dependent on coal, such as Eastern Europe. On the other hand, smog is also responsible for human health issues. Furthermore, two plastic shopping bags manufacturing produces 0.1kg of waterborne waste that is capable of disrupting associated environment such as water channels and the life therein exist. The problem of air and water pollution is more intensified when it is found that most of the plastic shopping bags are manufactured in the countries having few eco-friendly regulations like China that comes up with adverse effect on the environment and human health (Ellis et al., 2005). These bags are not only causing air and water pollution but they have also made a negative impact on agriculture lands. Many individuals do not know reuse of plastic waste that pollutes the agriculture land and mixes with other decomposable materials. As plastics are nonbiodegradable, they remain in the soil and block the supply of minerals and water to the agriculture land, necessary for the growth of plants. Even though plastic bags have the characteristic of thin in size, it resists roots of crops to penetrate through the bags and move around the soil to find the nutrients. In this way, plastic bags are responsible for the immense harm to the agriculture land for the growth of agriculture plants and fields (M. A. J. Jalil & Mian, 2011).
Plastic bags obstruct the sewerage system in populated areas and towns. Such a situation creates bad smells and becomes a source of various bacteria that could increase a large number of diseases (Adane & Muleta, 2011). Still, in urban areas, where wildlife is relatively limited, plastic bags cause significant environmental harm. Runoff water collects and carries useless plastic bags and finally collects them into storm sewers. Once in these sewers, the bag often forms clumps with other types of wastes and ultimately block the flow of water (Abbas, 2020b). This prevents the run of water from properly draining, which often cause inconvenience to those living or working in the area. For example, roads often flood when storm sewers become blocked, which forces them to be closed until the water drains. This excess water can damage roads, buildings and other property. It also collects pollutants and spreads them far and wide, where they cause extra damage. Blocked storm sewers can also disrupt the water flow throughout local watersheds. Blocked gutter pipes can starve local wetlands, creeks and streams of the water they require, which can lead to massive die-offs and in some cases, total downfall. (Greener Ideal Staff, 2018).
Such problems are developed due to non-seriousness of peoples for disposing of litter including plastics and other items in open places. Some people burn plastic bags at roads or grounds that produce very harmful smoke fatal for health and increase environment temperature. It has been learnt that in Malaysia, the temperature is gradually but slowly increasing due to which sea level may rise and result in flash floods. To control such untoward situation, Malaysia restricted the use of plastics . Singapore, the neighbour of Malaysia has already banned the use of plastic bags to avoid the harmful effects of plastics on agriculture production and environment (Md. A. Jalil et al., 2013). In this regard, a study was carried out to find out the effects of the decrease in plastic bag usage in big markets (Ohtomo & Ohnuma, 2014). The study was carried out by adopting a dual motivation model about the usage of plastic bags and it was evaluated that how environment-friendly behaviour affects actual behaviour of the individual (Abbas et al., 2015;. In the first week, the shop keeper gave free plastic bags to purchasers in routine. In the second week, the intervening week, of study, customers were asked if they wanted to get plastic bags or otherwise. It was analysed that during the pre-intervention week (first week), 78% of the customers accepted to receive plastic bags and 22% did not accept. In the post-intervention week (second week), 73% of the customers refused to accept plastic bags and only 27% accepted to receive plastic bags. A significant difference in acceptance of plastic bags was observed in pre and post-intervention week. This shows that the question asked by the shopkeeper helped in reducing the use of plastic bags. Therefore, it indicates that planned human efforts always help to achieve objectives. In this case, the objective was to reduce the usage of plastic bags because of their harmful effects.
Based on the above discussion, this research proposes the following hypotheses; H1: Plastic bags are the most commonly used products. H2: Characteristics of plastic bags are the reason behind its wide usage. H3: There is no environment-friendly option for plastic bags disposal. H4: Plastic bags are causing various environmental issues. H5: Media has an important role in creating awareness about plastic bags harmful effects. H6: There is an increasing trend in the usage of plastic bags. H7: Plastic bags can be substituted with their alternative options.

Research Methodology Target Population
Data has been collected from Islamabad (capital of Pakistan) and Rawalpindi (city of the province, Punjab). Islamabad is located adjacent to Rawalpindi on the North-Eastern side of the Potohar plateau. Connection of border of these two cities is the major reason behind naming it as twin cities. The region is at the altitude ranging from 457 to 610 meters above the sea level. It is one of the highest rainfall areas in the country with an average of 1143 millimetres because of this reason; the area humidity is 55% (Capital Development Authority, 2020). The ideal target

Plastic Bags Effects of Plastic Bags
Elements attributing in the usage

Habits of disposal and impact
Citizens' awareness about the issue

Usage trends
Available alternatives population is from Pakistan where according to the year 2017 census, 207.774 million people are living. In 2017, the total human population of the twin cities was estimated at 7.407 million in which 2.002 million lives in Islamabad and 5.406 million in Rawalpindi (Pakistan Bureau of Statistics, 2020). Most of the public living in the region can read and write. In general, public living in the constituency is students, households, government and private sector job holders and businessmen.

Sampling Techniques, Data Collection and Analysis
Information was gathered from 173 respondents comprised of 131 males and 42 females. The investigation subjects were chosen using a non-probability convenience sampling technique. The respondents were selected from universities' students, business centres, family units that were from different places of twin-city. Among the visited families, in any event, a single individual from the family was randomly selected for the examination irrespective of their age, educational status and sex as long they were willing to respond. The number of males was higher than females because males demonstrated more willingness to meet and fill the given polls. On the other side, the majority of the females were unwilling, when we asked them to fill the forms. To gather the information, survey questionnaires and google forms were distributed among the residents of the targeted region. Format and all the questions asked in the questionnaire were set in English for the convenience of citizens. The questionnaire was selected from the research article. The measurement instrument to conduct the study was extracted from the research article by Adane and Muleta (2011). Format of the research and data collection is similar to the case study mentioned earlier. Before the collection of responses, discussions were held with the chosen respondents to clarify the goal of the study. Those respondents who were willing but unable to respond to the questionnaires by themselves were assisted by the researchers of this article. It was assured that each point was explained to them clearly so that they could fill the form responsibly and with due care of the society. For segregating the gathered information, the respondents were assembled into various classes.
Most of the respondents were students (81.50%), the reason behind an excessive number of students in the collection of data was their willingness to fill the forms because they understand what we are doing and how to fill the form and they know the importance of the data. At the second numbers were private businessmen (19.07%) and the others were government servants (6.93%). The age of most of the respondents was 20-29 (57.22%) because as we already discussed in the previous paragraph that the majority of the respondents were students. At the second number were respondents of less than 20 years of age (26.58%), 30-29 years' age group was at the third position (12.13%) and in the last, minimum number of respondents were of 40 plus year (4.04%). In the last, we discuss our respondents' educational status. A large number of our respondents were highly educated and graduate or undergraduate students (61.84%), high school students were at second position among respondents (30.63%), then that of primary education (5.20%) and in the last, the number of illiterate was very low (2.31%) who never studied in their entire life (See Table-1).

Elements Behind the Increasing Trend of using Plastic Bags
Out of 173 respondents, the majority of the people use plastic bags in large quantities as compared to other plastic items. The data indicates the usage of plastic bags by males is 56.49%, plastic bottles 19.08%, plastic buckets, barrels and baskets 17.56%, plastic shoes 5.34%. On the other hand, the usage of plastic bags by females is 42.86%, plastic bottles 21.43%, plastic buckets, barrels and baskets 28.57%, plastic shoes 7.14%. This data indicates that most of the respondents in all the given categories use plastic bags in their daily life. This data indicates that plastic bags are used highly among the residents of twin cities, and the residents say that they have been observing excessive use of plastic bags concerning time. All these results indicate that plastic bags are also excessively used product in the twin cities (See Table-2). This survey result shows that irrespective of gender, education, occupation and age, 53% of the peoples of Islamabad and Rawalpindi extensively use plastic bags in their routine life activities. A portion of the primary widespread usage was the low price (16.76%), light in weight (25.43%), easy to find (33.52%) and lack of alternative materials (24.28%). These discoveries are matching with other reports portraying that light-weight, modest cost, phenomenal qualification for use and asset effectiveness are fundamental reasons for over usage of plastic bags all over the world. During our research, we observed that all the shopkeepers, stores, malls and all kinds of different stores give these plastic bags free of cost to their customers whenever they buy something from their stores. This indicates that ease of use and free dispersion of these materials by retailers or store proprietors are the main reason behind the wide usage of plastic bags. For example, our survey in Islamabad & Rawalpindi indicates that 53% of customers of markets and superstores use free plastic bags. Moreover, it has also been observed that educated people take more interest in plastic bags over other options.

Practices of Plastic Bag Wastes Removal and their Ecological Effects
After onetime use, plastic bags have to be disposed of. In this way, additional data were collected from respondents about the ways how they dispose of plastic bag wastes. The data about throwing in open areas (46.82%) and burning (30.63%) is the norm of disposal of plastic bag wastes. Open dumping to the nearby areas is done by most of the peoples. This indicates that "dumping" at open places is the common practice of peoples of the twin cities. Of the 173 respondents, just 27 (15.60%) and 12 (16.13%) of them used burying and another kind of methods to dispose of the waste, respectively. The majority of these respondents (81, 46.82%) utilized open dumping. Our survey questionnaires and google forms observations show that plastic bag wastes constituted a larger share of plastic wastes in the twin cities and its adjoining areas. As shown in our table, burning is also a commonly used method. Female respondents who throw the wastes to the environment were slightly larger in number (21, 50%) as compared to those females who burn (10, 23.81%) plastic bag wastes. It is expected that educated members of society are more concerned about the environment but the results of our survey show that these educated members of society appeared to be less worried about the environment. Therefore, all people from society need to make the effort for making the earth free of plastic bags. Because of this bag wastes, our environment is deteriorating rapidly.  In our survey, we have found that there are a few issues related to plastic bag wastes in twin cities. The information shown in table demonstrated that animal death (20, 11.56%), sewage choking frameworks (45, 26.01%), the decay of natural beauty of environment due to littering (25, 14.45%) and human health problems (29, 16.76%) were the main issues about which respondents were worried about. The outcome of the present survey demonstrates that most of the respondents, irrespective of their background, express the issues of plastic bag wastes on creatures. These realities and results of the present analysis recommend the requirement for quick action to launch an awareness campaign about the harmful effects of plastic bag wastes on the health of living organisms including human as well as animals. The spots with the high aggregation of plastic bag wastes include parks (15, 9.25%), waste dumping sites (18, 10.40%), market places (18, 10.40%) and crowded residential areas (23, 13.29%) not mentioned in the table. Other areas that were less polluted as compared to preceding areas are roadsides (2, 1.15%), open places in the city (4, 2.30%) and sewage lines (7, 4.05%). These data show that the environmental pollution brought by plastic bag wastes is a great concern in the twin cities. As it was told earlier, plastic bags are not decomposed and remain for 100 of years, if they remain in enormous amounts in soil, they forestall air and water dissemination that results into a decrease in the productivity of farmlands. During our field visits, it was seen that the district government 4

Role of media in highlighting the issue among citizens
Most of the respondents (53, 30.63%) valued the significant roles of TV and Radio in the sharing of data about the unfavourable effects of plastic bag wastes. A different source of data that was collected includes health experts (20, 11.56%), schools (12, 6.93%) and distributed materials (26, 15.02%). The outcome in the table recommends that it is conceivable to utilize this media to educate peoples regarding issues caused by plastic bag wastes. Although not evaluated, it has been observed that the majority of the people have access to media. In this manner, the teaching of the community through the media is easy for better comprehension of the negative impacts of plastic bags. Other things that are impacting highly in building perception and creating awareness among people is social media. In our studies, some people also said that they got awareness also from social media. In the table, it appears that just (44, 19.13%) of the respondents get data from papers and magazines. This could be ascribed to the absence of these materials having inclusion on these squanders. This reality was steady with the creators' overview of some well-known magazines and papers available in the twin-city. No data were available concerning the effects of plastic bags on nature.
Similarly, the data demonstrates that the new-born generation must be educated at primary education level regarding the protection of the environment from toxic elements. Likewise, the organizations must develop a culture for saving the green environment. The minimum use of plastic bags at schools and organizations would help reduce the pollution impact on the environment. The level of awareness must be enhanced to curtail the usage of plastic bags. The government functionaries must play their role as a model for others.
The dominant part of the respondents in each category has great knowledge about the issues related to plastic bag wastes. This recommends that it will need a little effort to prepare the twin-city residents to make a move against the disposal and usage of plastic bags. However, too much has to be done to change the habit of plastic bags usage.

Factors responsible for increasing or decreasing trend
We also gathered data from our respondents about the increasing or decreasing trend of plastic bag usage and coincidentally the result came from was 50% as half of our respondents are saying that they saw the increasing trend of utilization of plastic bags and other half were saying that they saw the decreasing trend in the utilization of plastic bags. So we are also discussing their reasons for increasing or decreasing trend in the usage of plastic bags.
In the increasing trend section our respondents said that they saw a huge increasing trend in the utilization of plastic bags and the majority of the respondents said the reason was that plastic bag was very cheap (31, 27.62%) and easy in access (23, 13.29%). Shockingly, just about 15% of the respondents referred to "lack of awareness" as an essential reason behind the increasing trend in plastic bags utilization.
It has been observed in the survey that easy availability of plastic bags on cheap rates is also causing an increase in the usage which can be curtailed by strict policing and rules on the manufacturing industry. Whereas in decreasing trend section respondents said that they had seen the decreasing trend in the utilization of plastic bags and the major factor involved in it was the awareness in the community about the harmful effects of plastic bags in the environment and how it had affected the eco-system in different ways. The respondents also said that the reason for the decreasing of plastic bag trends was that they now could easily get another kind of bags which were alternative to plastic bags. They said that the major factor was the restrictions from the government because the government took strict action against the shop keepers in the twin-city who were providing plastic bags to their customers.

Alternatives to the plastic bags
In the last, we asked questions about the solution of plastic bag alternative and (87, 50.28%) of the people responded that the best alternative for the plastic bag was cloth bags because cloth bags were reusable. In respondents' opinion, it is the responsibility of all the shops, retailers and malls that they should provide cloth bags to their customers instead of plastic bags so they will not use plastic bags in their daily life use. The respondents also say that the habit of plastic bags using came from these shops because from the beginning whenever they buy anything they get a free plastic bag with it. The second most popular answer from our respondents was about paper bags. They tell that it is also the worthy alternative to plastic bags and it is also cheap not as much like plastic bags but it is and a suitable option. They said the big problem with these paper bags was that they were of very low quality and most of the time the paper bags got cracked but still it was the opt able alternative of plastic bags. The third most popular alternative to plastic bag according to our respondents is fibre bags. Environmentfriendly fibre bags are made from a kind of paper that has cotton strands to invigorate it with added pliable to help forestall tearing or extending. These creative and stylish bags are 100% biodegradable. Some of our respondents suggest the usage of fibre bags for their daily life use. In their opinion, these are the most popular alternative and these kinds of alternatives should come to market so that we can get rid of plastic bags. From this study, we realize that some stern actions need to be taken to make our environment a plastic bag free.

Limitations to the Finding
The study was conducted in the selected region with limited population out of which majority of the correspondents was consisting of males. To collect comprehensive and precise data, it is important to gather statistics from the whole population but it was not the case with the mentioned study. Besides this, if data is collected from a limited population, the categories of correspondents whose data is collected should be based on the ratio of their presence in a certain region. Females' unwillingness for participation because of society's culture was major resistance in the collection of unbiased data.

Conclusion
Although the majority of the respondents considered plastic bags as a major problem for which they have also recommended the solutions in the form of alternative bags made up of cloth, paper and fibre. To implement the solution, the majority of the participants said that increase in awareness can help to curb the problem. On the part of the government, this can be done by empowering shopkeepers/retailers, who are the source of providing plastic bags, can be advised not to give plastic bags to their customers. Citizens can be convinced to avoid using or taking plastic bags from the shopkeepers that can stop them to purchase these bags. Manufacturers can be assisted by providing them with the alternatives at low cost and increasing the taxes on raw materials used for the production of plastic bags. The government should make new strategies to ban the usage and productions of plastic bags in the twin-city. Strangely, most of the population at Islamabad and Rawalpindi are educated but they do not bother about the harmful effects of plastic bags. It requires a massive awareness campaign for avoiding the use of plastic bags and the city administration should


Lean Six Sigma and Performance Metrics

The intensification of competitiveness and the fluctuation of industrial market were pushing the companies to ameliorate their product's quality and services in order to maintain their place in the market. They have a tendency to integrate various methods such as total quality management (TQM), Six Sigma (6-?), and Lean Six Sigma (LSS). The Lean Six Sigma method became the focus of academic researches. Hence, huge empirical studies have been raised in this field which enhances the visibility of this quality method. Some focused to identify its particular aspects, tools, and concepts. Others reveal its positive repercussions on reducing the defects, waste of time, and reworks. Others attempt to develop specific model related to Lean Six Sigma to facilitate its implementation. Regarding the literature gap reviewing and highlighting the specific features of Lean Six Sigma, the requirement of recognizing its particular aspects is needed. The focus of this chapter firstly is to identify the performance metrics then to underline the Lean Six Sigma metrics in order to seek its link with business performance. Also a guideline for the best integration of Lean Six Sigma is also offered.

Introduction
The Lean Six Sigma (LSS) quality enhancement approach has obtained recognition in the previous few years as more and more corporations affirm its effectiveness in developing their bottom lines and shareholders (i.e., [1]). Companies need to focus on creating Lean Six Sigma projects that are aligned to the business needs (i.e., process improvement, efficiency, profits, customer loyalty, and reliability). Customers increasingly require on the quality of the supplied product which leads companies to strive excellence or at least to strive for perfection in order to satisfy more customers [2].
Lean Six Sigma is recognized as a combination of Lean and Six Sigma. It is "a business strategy and methodology that increases process performance resulting in enhanced customer satisfaction and improved bottom line results" [3]. It is considered as a strategic issue of quality improvement based on the increase of process capability and the development of company performance [2].
As we have just seen, many important questions have recently been raised in the Lean Six Sigma field and performance. Thus, the purpose of this Chapter is to investigate in the second Section the multidimensional aspect of performance and measurement dimensions. The Section 3 provides more details concerning Lean Six Sigma metrics and key steps for its best implementation. Section 4 represents discussion and conclusions. Section 5 stresses the managerial implications and future direction of Lean Six Sigma.

Performance concept
The performance concept has been the focus of abundant studies, investigations, and articles and is extensively renowned. Thus, various definitions and explanations have been addressed in this issue (i.e., [4]). The next subsection provides extra details concerning the multidimensional performance concept.

The multidimensional performance concept
Much confusion exists on the performance concept as [4] attempt to explain. The first explanation would be is that the performance is a construct, not a concept. The identification of all the variables related to the performance field allows the first clarification of construct (i.e., [5]). Performance is defined as "the art of doing the right things right" [6]. Briefly, it means the act of drawing the best of the available resources of the company to achieve its goal.
The performance concept is distinctly assimilated to efficacy, competitive capacity, efficiency, performance, and productivity. Venkatraman and Ramanujam [7] propose to represent the performance in three levels (financial, operational, and organizational performance). In this proposal they stress the idea of intermediate measurement of performance and distinct measures used according to the objectives pursued (see [7]).

Performance definition
An important number of researches converge in the notion that the performance has a global sense and implies efficiency and effectiveness (i.e., [8]). An organization is successful if it accomplishes its goals (effectiveness) using a minimum of resources (efficiency). Seashore and Yutchman entirely define organizational effectiveness from this perspective as "the ability to exploit its environment in the acquisition of scarce and valued resources to sustain its functioning" (see [9]).
From a strategic point of view, performance can be defined as the ability of an organization to implement its strategy. The purpose of the performance is to improve the torque value-cost [10].

Performance measurement dimensions and indicators
Given the rising interest accorded to study the performance measurement systems as tools for successful strategy integration, this part offers definitions of performance measurements, dimensions, and indicators. The performance measurement is defined as "the process of quantifying the efficiency and effectiveness of past actions" [11]. However, Moullin considers it as "the process of evaluating how well organizations are managed and the value they deliver for customers and other stakeholders" [12].
Neely et al. provided an important distinction between these three terms: a performance measurement, a performance measure, and a performance measurement system (see [11]). More clarifications are offered in Table 1.
Grafton et al. provide a constructive work assessing the role of performance measurement and evaluation in building organizational capabilities and performance. The results suggest to encourage managers to employ both the multiple financial and nonfinancial performance indicators increasingly included in current performance measurement systems (in [13]). Therefore, the performance measurement refers to the use of a multidimensional set of performance measures which include financial measures and nonfinancial measures. Financial performance is generally defined as the use of outcome-based financial indicators that are assumed to reflect the fulfillment of the economic goals of the firm, and nonfinancial performance measures are often used for performance evaluation.

Organizational performance dimensions
The manner on which the authors perceived and measured the organizational performance is different. Arumugam et al. measured organizational performance based on quality performance specifically the quality of product and service, customer relations, customer satisfaction with product quality, and level of quality performance relative to industry norms (see [14]).
Deshpande focused on supply chain performance and organizational performance, outlining the financial and market components and customer satisfaction dimensions. The financial and market performance is determined by reference to market share, return of total assets, and annuals sales growth (see [15]).
Several works have treated the organizational performance dimensions; for example, Venkatraman and Ramanujam [7] identify three dimensions of firm performance: • The financial performance: it contains criteria such as sales, turnover growth, profitability (return on investment, return on sales, and return on equity capital), profit by shares, the market value of the company, or the cost of asset replacement.
• The economic performance: it incorporates chiefly marketing measurements such as market shares, new products introduction, products quality, or marketing effectiveness.
• The organizational effectiveness: it consists of internal criteria having an overall image of organizational performance (see [7]).
The link between quality management practices and organizational performance is the focus of various studies (i.e., [16]). The results of these studies

Performance measurement
Defined as the process of quantifying the efficiency and effectiveness of action. It refers to the use of a multidimensional set of performance measures. It includes both financial and nonfinancial measures [1] Performance measure "Defined as a metric used to quantify the efficiency and/or effectiveness of action" Performance measurement system "Defined as the set of metrics used to quantify both the efficiency and effectiveness of actions" designated that there are a variety of measures (i.e., organizational performance, corporate performance, business performance, operational performance, financial and nonfinancial performance, innovation performance, and quality performance). Based on the work of Scodanibbio, the key components of company's performance are highlighted in six elements which are commercial performance, operational performance, innovation performance, financial performance, economical performance, and cultural performance (see [17]). More explanations are provided in Table 2.

Performance indicators
The performance indicator has been the subject of numerous researches. Based on this literature review, the performance indicators acquired various definitions.

Commercial performance
Market penetration-market share/expansion  Berrah et al. offered a performance indicator a quantitative aspect. It is considered as a quantitative data expressing the effectiveness and/or efficiency of all or part of a system (in [18]). Performance indicators synthesize in qualitative or quantitative terms, some information to sit judgment on the performance evaluation: • Indicator of objectives (or lagging [19]) that control the best achievement of strategic objectives • Indicators on the stock variables and action plans (or leading [19]), which provide information on the means used to achieve these strategic objectives Through there is an extensive literature review of performance measures, different indicators used for measuring organizational performance some of these are identified in Table 3.

Performance metrics
Performance metrics has been the focus of diverse studies in different fields. The present section highlighted the key Lean Six Sigma metrics presented in the literature.

Lean Six Sigma focus on metrics
Lean Six Sigma focuses on metrics; it is a combination of set of statistical tools as DMAIC of Six Sigma employed in order to define, analyze, measure, improve, and control process variability as presented in Table 4 and critical-to-quality (CTQ ) (Lean) for customer requirement [23].
The basic objective of Lean Six Sigma method is the implementation of measurement strategy focused on reducing the process variability and improving the projects to meet the customer requirement. This is realized through the combining of Lean and Six Sigma.

Author(s)
Measure Indicators [20] Organizational efficiency Organizational effectiveness Return on assets Share of deposits [21] Organization performance Financial performance Operational performance Product quality [22] Operational performance Organizational performance Internal operation performance Productivity improvement Financial and nonfinancial measures Table 3.
The main components of company's performance.
The DMAIC structure with five modalities for intervention (define, measure, analyze, improve, control) is used to specify the problem of process variability to put the suitable solution in order to achieve a company performance.
We can give the example of some techniques related to Lean Six Sigma tools: "CTQ" companies focus on what the customer want by reducing wastes and nonvalue added activities in production process. Failure mode and effect analysis (FMEA) necessitates a step-by-step approach to identify all the possible failures in the design, manufacturing, product, or services. The aim of the FMEA is to adopt actions of removing or diminishing failures, beginning with the highest-priority ones, the suppliers, inputs, process, outputs, and customers (SIPOC), which is normally used throughout the defined stages of a process improvement project, as it helps to obviously understand the purpose and the scope of a process; a Pareto chart is defined as a series of bars whose heights reflect the frequency or impact of problems which are classified in descending order.
Based on diverse researches studies as [25], we have selected these principal tools of Lean Six Sigma illustrated in Table 5.

Guideline for the best implementation of Lean Six Sigma project
Before starting the Six Sigma implementation, it will be important to know these precious aspects mentioned as the antecedents of its implementation. It is necessary to create an encouraging environment and platform to succeed in its implementation.  The visions and point of view of authors concerning the success in implementing Lean Six Sigma are varied and valuable [28]. Jones et al. stressed the importance of strategy adopted, and the success of any organization is directly related to the effectiveness in implementation of Lean Six Sigma (in [29]).
The implementation of project should meet the objectives of firms and their ability to execute it. The project succeeds when it is able to achieve its goals. The objective of the Lean Six Sigma programs in any organization is the "project." The importance of roadmap of project, process mapping, and team responsibilities explains the success of integrating such method. Indeed, the project charter identification, planning, and integrating steps, tasks, and recurrent milestones help to maintain track of progress and adjustment as required. Also, it creates a sort of dynamism for the project team.
Regarding the specificity of the project and its requirement, the focus is to answer these questions: "what," "who," "how," "when," and "how much." "What" refers to the customer needs. The higher the requirements are identified, the higher the probability of success will be. "Who" designs the allocation of the resources to achieve the project. "How" is the technological need that will convene to the "what" of the customer. "How" is very decisive to the project because if a connection between the project and the customer's expectations does not exist, there will be a gap in anticipations. "When" identifies "the schedule" and the tools of project management. Taguchi methods [27] Measure capability [26] Regression analysis [27] Correlation Cause and effect matrix [26,27] Descriptive statistics [27] Project selection and assessment matrix [27] Source: [25][26][27]. Table 5.
Lean six sigma focus on metrics.
Montgomery and Woodall affirm that in "Aligning projects with both businessunit goals and corporate-level metrics helps ensure that the best projects are considered for selection strategic business objectives" (see [30]).
Tenera and Pinto's work provides a project management improvement of Lean Six Sigma in order to facilitate its development by reducing the potential problems (see [31]). One of the chief challenges of Lean Six Sigma implementation program is to succeed in the selection of the organization project, insuring the suitable identification of the critical-to-quality characteristics.

Discussion
It is important to know that Lean Six Sigma is not only a quality method for improving process and reducing costs. It is also an approach for engaging and implicating all the employees to achieve business goals, as well as to learn how to improve the effectiveness and efficiency of the company. Thus, this quality method develops the empowerment of employees and the share of responsibilities.
The Lean Six Sigma has positive repercussions in different levels, as social (company social responsibilities) and financial (boost of returns and profits) impact, employee empowerment (continuous training and culture), process improvement (reduce of process variability, wastes, defects), amelioration of product quality and efficiency, enhancement of customer satisfaction, and amelioration of competitiveness and brand image.
Furthermore, the assessment of Lean and Six Sigma link is important and has been the focus of diverse studies. Indeed, Lean Six Sigma or just-in-time goal aims to reduce as maximum as possible the stocks and outstandings. However, the Six Sigma objective is to eliminate variations and have as output coherent finished products without defects. It seeks to identify the defects, determine the causes, and eliminate them. Thus, we can state that both methods are complementary and independent. Undeniably, a process can be Lean, but it has a rate of change at the output, or it can have a rate of change at the output under control and is not Lean. Consequently, the Lean Six Sigma crosses simultaneously the Lean and Six Sigma advantages which give it a major substance.

Conclusion
This chapter is a prerequisite to understand the Lean Six Sigma specificities. It started by a brief explanation of performance concept, dimensions, and indicators in order to facilitate the second section, the assessment of the link between performance and Lean Six Sigma metrics. Section 3 outlines the main Lean Six Sigma tools, objectives, and impact. It allows the improvement of the process capability by reducing defects and wastes which consequently impact positively on the company performance, outcomes, customer satisfaction, and loyalty. Also, it offers a highlight of the success steps for Lean Six Sigma project integration.
Studying the link between Lean Six Sigma and performance is precious. In terms of assessing the impact of Lean Six Sigma on organizational performance or in order to assess the factors that affect the company business performance, it is not advised to presume these factors on the financial evidence but to focus in the other factors that can have a relevant impact on Lean Six Sigma outcomes.

Research implications and future direction
The originality of this chapter resides on its focus on the surroundings of Lean Six Sigma. Hence, regarding the lack of academics and empirical studies investigating in depth the real features of Lean Six Sigma, this chapter offers the chance of stressing the advantages and illuminating the Lean Six Sigma-specific concepts and tools.
From a managerial point of view, revealing a brief distinction between Six Sigma, Lean, and Lean Six Sigma can facilitate the decision for professionals hesitating to implement such methods within their quality management system. Also, the LSS is an available quality method in both manufacturing and service companies (as healthcare, financial, engineering) which attract the interest of the executives in the effectiveness way of Lean Six Sigma project integration in diverse sectors.
The implications of Lean Six Sigma are varied and touch diverse stages and area as well as the internal and external environment. Generally, it has positive repercussions on the product quality, enhancing customer satisfaction, faithfulness, and consistency, improving the business incomes, competitiveness, ameliorating its image, and bringing new stakeholders and investment.
This chapter can be a useful support for future researches interested in this filed. Therefore, future studies can focus in the assessment of LSS challenges and weakness in diverse sectors or develop comparative studies between LSS and other quality methods as Six Sigma, in order to seek out their similarities, dissimilarities, or complementarity.


A Long-Term Evaluation on Transmission Line Expansion Planning with Multistage Stochastic Programming

The purpose of this paper is to apply multistage stochastic programming to the transmission line expansion planning problem, especially when uncertain demand scenarios exist. Since the problem of transmission line expansion planning requires an intensive computational load, dual decomposition is used to decompose the problem into smaller problems. Following this, progressive hedging and proximal bundle methods are used to restore the decomposed solutions to the original problems. Mixed-integer linear programming is involved in the problem to decide where new transmission lines should be constructed or reinforced. However, integer variables in multistage stochastic programming (MSSP) are intractable since integer variables are not restored. Therefore, the branch-and-bound algorithm is applied to multistage stochastic programming methods to force convergence of integer variables.In addition, this paper suggests combining progressive hedging and dual decomposition in stochastic integer programming by sharing penalty parameters. The simulation results tested on the IEEE 30-bus system verify that our combined model sped up the computation and achieved higher accuracy by achieving the minimised cost.

Introduction
Development of renewable energy has been expedited by the global effort to reduce greenhouse gas emissions. These include emissions from fossil fuels used in transportation, which are declining as electric vehicle use increases [1][2][3]. The global move to electric vehicles and new facilities to support renewable resources now requires much higher electricity consumption and generation capability. If transmission line capacity fails to catch up to the growth of them, the failure will cascade and cause shortages in the grid requiring expensive repairs for the power system network [4].
Transmission line expansion planning (TLEP) has been suggested to avoid future shortages. Economic effects of probable transmission line failures are compared against the investment budget spent on new transmission lines [5]. The TLEP is usually implemented by system planners to analyse old transmission lines that would be uneconomical in a long-term evaluation of the growth of electricity demand [6]. In the evaluation process, the planner decides locations for a new construction from the present point of view to optimise the future cost. Thus, optimal decisions for the planner are conveyed by considering probable uncertain scenarios of the growth of demand and representing the most suitable candidate among all possible realisations. To find optimal expansions in the TLEP process, the planner reconciles system reliability and energy economy over a long-term time horizon. The typical optimisation formulation of TLEP determines a minimised cost for organising transmission lines and operating generators. In this regard, the investment budget for expansions can be found by optimising the use of resources. Considering more detailed scenarios of future demand usually helps planners to mitigate this uncertainty and yields lower costs than only considering the worst-case [7].
Many stochastic optimisation processes such as the robust method, the chance constraint method and multistage stochastic programming (MSSP) have been developed to account for uncertainty in the power system [8][9][10]. Typically, they predict the impact of future events by calculating the value of their possibility as costs of the objective function and compare them to the current decisions. MSSP shows an outstanding performance among the three methods but usually requires many scenarios and variables depending on time horizons [11]. Considering many scenarios and variables helps to verify results, but the size of the computational load becomes intractable. Therefore, decomposition methods are used to break the original problem into several smaller problems, called subproblems. However, the decomposition is followed by the coupling constraint added between separated subproblems. The constraints are treated as a price for solving them independently so that one subproblem can consider the others' decisions as they should pay for not having a unified value [12].
Meanwhile, there are two types of decomposition methods to consider for uncertain electricity demands in MSSP. One is the primal decomposition, represented by Bender's method and the L-shape method [13], which divides the problem into two parts: the master and the slave problem. Yet, it is hard to calculate more than three stages, since too many master and slave pairs are generated as the time span is extended, so it is not appropriate for a long-term evaluation process. The second, dual decomposition (DD), horizontally separates the scenario tree by its time horizon, so that it is inherently possible to consider a long-term horizon since subproblems are sufficiently smaller than the original. Instead, subproblems for the DD method could generate inconsistent results of subproblems since they also separate decision variables, thus the coupling constraint is added to obtain the unified solution. The coupling constraint is defined as a nonanticipativity constraint (NC) in DD methods, which explains the indistinguishable state of variables in which all separations should be converged to the one nodal solution. However, optimality of expansions is not achieved due to the independence of subproblems when integer variables are decomposed. Indeed, some decision variables used to construct a new line in the TLEP problem are comprised by integers to define a disjunctive decision; therefore, the system planner cannot decide on the construction when results diverge.
To solve the variable convergence issue, various DD methods have been developed and a few of them are adopted in this paper. Progressive hedging (PH) can transform the NC into a Lagrangian function then heuristically approach the optimal based on the proximal operator and augmented Lagrangian [14,15]. PH can quickly obtain a reliable solution, but its convergence is not guaranteed when integer variables are involved, and the integrated solution could be infeasible if the convergence rate is not sufficient. A generalised process for the dual decomposition for stochastic integer programming (DDSIP) in [16] was developed to consider integer variables, and it solves the Lagrangian dual problem of the NC [16]. Dual variables for the NC are obtained by the proximal bundle (PB) method [17], which determines a delegate among candidates from subproblems only if it is plausible. However, it is slow because of the branch-and-bound (BB) process, which bounds constraints for integer variables and usually takes a long time to calculate branched cases.
Recent studies have consistently reported improved DD methods, and numerical results have proved reliable. Studies in [12,18] mitigated the penalty of the NC by formulating it in various ways, which verified that a better matrix formulation of the NC can improve the result. Studies in [19,20] suggested methods to transform dual functions. Since the NC can be relaxed as a dual function, better objective bounds could be obtained in those studies by reversing the approach to the formulation to solve dual variables. Studies in [21][22][23] developed methods to support the heuristic approach inherent in DD methods to achieve high convergence speed and accuracy. However, those improvements were not properly implemented in practical studies of power system. The TLEP in [24], where a long-term scenario for transmission lines was decomposed and bundled according to its similarity, also in [8,25], where the DD was introduced to make generation resource schedules with many integer variables, could have been assessed better if they adjusted their DD methods according to upper and lower bounds of results and the consistency of the results was verified over a long-term time span if methods were generalised regardless of the program size. Numerical results reported in [26,27] achieved the cost-effectiveness of plans through the methodological improvement, enhancing the convergence of stochastic variables.
In this paper, a long-term evaluation problem by MSSP is proposed for the TLEP. Typical TLEP formulations are used, where decisions on new construction and reinforcement of existing transmission lines can be made by considering DC optimal power flow (OPF). However, we extend the problem in a form of MSSP to involve 30 years (with six stages) in the plan. As the time stage increases, binary variables devastate the solving process to obtain unified results and slow down the process. By adjusting DD methods in various cases studies with different sizes, we verify that stochastic variables can deliver varying convergence and expansion results with respect to algorithm. With the analysis on those spectral outputs, general forms of stochastic optimisation of DD methods are examined, and the solving process is unfolded to construct a generalised optimisation environment on varying sizes. We combine the PH and PB methods where the penalty value in PH is concatenated as a warm-start value of the PB method since they have an equal target value. Exchanging the penalty value could speed up the medium-iteration convergence and improve the quality of the solution. This contribution can make a combined method less affected by the program size. The expansion results are compared in three aspects: simulation time, nonanticipativity and objective cost. The nonanticipativity results are delivered to rectify and classify the failed results. Thus, the method termination and the feasibility are separately considered in a scope on the results. Moreover, with modified IEEE 30-bus system, the overall optimisation formulation and expansion results are given over a 30-year time span. We observed that a methodological improvement enables cost-effective evaluation, finding the best with the coherency among the feasible candidates obtained by improved boundaries of objective functions for the NC.
The organisation of this paper is summarised as follows. In Section 3, the overall process for solving MSSP with mixed-integer variables is introduced. In Section 2, TLEP problems are modelled and are assessed from the viewpoints of economy and reliability. In Section 4, the numerical results of the TLEP are presented and analysed. In Section 5, conclusions are drawn.

Transmission Line Expansion Planning Modelling
In this subsection, we introduce our multistaged transmission line expansion planning formulation.

Objective Function of TLEP
The formulation represents one subproblem, where stage is allocated to a five-year investment period. Symbols used to formulate the TLEP problem and their descriptions are presented in Table 1. The objective function of TLEP is structured as follows: In (1), we take into account the following terms in our objective functions as a view of power system planner: transmission line expansion cost (investment cost), power generation cost (operation cost) and the cost of probable load curtailments due to single line outage (load shedding cost). The investment cost is further divided into new construction cost and reinforcement cost of existing transmission lines. We only consider peak load scenarios. K c/r is a unit costs' vector of line investments, which is the hourly long-run marginal cost (LRMC) of transmission line capacity. Its dimension is $/MWh, which balances the finance scale with operation and investment cost. The investment cost is calculated by dividing annuitized LRMC by the number of hours in a year. For this parameter, discount rates can be utilised [28], but in this paper we do not consider the present value of annual cost. K g/s is the unit cost of generation and outage, respectively, whose dimension is also $/MWh.

Constraints of TLEP
For the constraints of TLEP problems, first, a balance between power supply and demand should be obtained. This constraint can be represented as follows: In (2), the sum generator outputs PG and load shedding amount PS should be equal to the sum of power flow f whose direction is out of each bus, and power load PD. Second, constraints on expansion decision u are enumerated as follows: In (3)-(5), the DC-OPF constraints are considered. Power flows f are defined by the phase angles of the buses θ and the reactance of the transmission lines X. In (4) and (5), the power flow of newly constructed lines is constrained by a disjunctive decision u with a large number Q. In this constraint, power flow of newly constructed lines and expansion decisions are linked.
In (6) and (7), power flows in all existing lines and expansion candidates abide by the maximum capacity of line loading. This capacity can be increased depending on expansion decisions.
In (8) and (9), construction decisions are expressed as binary variables and reinforcement decisions are expressed as integer variables. Finally, in (10) and (11), the sum of expansion is constrained by one, meaning transmission lines can only undergo one construction event. Constraints on the generator output PG and load shedding amount PS are enumerated as: In (12), the maximum capacity and minimum generation output is considered to decide generation output. In (13), the load shedding amount of each bus should be within the load of each bus. Finally, in (14), the generator's cost function is simplified into piece-wise linear functions for constant a and b with H pieces. Replaced transmission lines include old lines whose regular lifetimes or life expectancies are less than their initial operation periods plus the panning time horizon.

Decomposition Method Formulations
In this section, we introduce two dual decomposition (DD) methods, PH and DDSIP, and their theoretical backgrounds. PH and PB methods propose a pathway to the optimal solution, recursively updating the decisions. The BB process enforces the convergence of integer variables.

Basic Form of MSSP and Nonanticipativity Constraint
The most intuitive and intrinsic approach to represent uncertainty in possible realisations is to formulate a finite number of scenarios with relative probabilities. This is the basic form of the MSSP called the extensive-form (EF) problem and requires the scenario tree which is a set for bundles of scenarios. A scenario tree is structured by branching to possible realisations from a precedent scenario, which gives conditional probability for its succeeding scenario, as depicted in Figure 1 (left). The basic form of the MSSP problem for the scenario tree that structured over the time horizon T stages with decision variables x = [x 1 , x 2 , ..., x T ] T can be defined as follows: In (15), a simplified form of MSSP problem for TLEP is given, where f (x) is the objective function, and G is a simple expression of a set of all constraints involved in the problem for x t . The operator E[·] represents expectation of costs over related scenarios, and the scenario tree Ξ consists of all nodes of scenarios ξ t , such that ξ t ∈ Ξ. The objective function and constraints in MSSP can be decomposed into subproblems. Therefore, f (x s ) and G s represent the objective function in (1) and constraints (2)- (14), which can be extended to the multistage problem by the time span T.
In (16), the representative formulation of DD is presented, where x s is set of variables for each scenario subproblem, and ξ s is the corresponding scenario, and separated variables x s is equal to the node solutionx, which is the NC. The structure of scenario tree and subproblems are presented in Figure 1, where DD can divide the scenario tree horizontally so the number of subproblems is determined by the number of branches. In the same figure, if the NC forx b , which is the solution of node b is satisfied in the corresponding subproblems, then it is also satisfied for the second stage variable in subproblems s 1 and s 2 , such that x s 1 ,2nd = x s 2 ,2nd =x b . However, NC cannot be presupposed since x s is the optimal solution of MSSP. DD methods add a relaxed form of NC in the objective function in (16) to mitigate the constraint.
The Lagrangian function in (17) can be solved for PH and PB methods by using heuristic approaches as follows: 1.
The PH designates implementablex by the projection but derives λ S proximally. 2.
The PB solves the dual problem of (17) to get a representative for λ s and verify its degree of improvement.

Progressive Hedging Method
We provide formulations of the PH from the Lagrangian function. Independent scenario projection to the nonanticipativity solution space is assumed in the PH. The projection operator averages the subproblem solutions by considering probabilities of scenarios. The projected solution can be regarded as optimal when the NC is satisfied for all nodes in the scenario tree. An implementable solutionx can be generated by the projection.
The assumption in (18) that the optimal is the average of subproblem solutions inherently makes the NC solution space N . The solutionx ∈ N deduces the direction toward the optimal solution, and it is aligned by the probabilities ρ s . Hence, the alignment to N is possible just once so that Proj 2 = Proj and then Equation (19) is satisfied.
Decision variables in PH are updated as follows. First, in the middle of iterative process of the PH, subproblems untied from the scenario tree are solved and saved in the subproblem space S. Second, node solutions are updated by the quadratic formulation of the augmented Lagrangian. Each subproblem in (17) is transformed to be quadratic since a penalty constant ω of the NC is updated by the proximal operator for subdifferential of the dual function, ∂ λ D(λ) = (x s −x), with step size γ [15].
To update the dual variable λ s , the PH uses constant penalties for the NC in (20), which represents the distance between S and N such that ω s = x s −x. The dual variables satisfy the NC in (21) because of (19), only if the initial value for penalties is zero, and make an even boundary for the dual variables as shown in Figure 2. In short, ω represents the NC penalties according to the projected solutions, and it is orthogonal to the Proj as in (21) such that S ⊥ N .
Finally, the augmented Lagrangian is derived from iterative updates of penalties in (20) and the Lagrangian function in (17).
The first order necessity condition to find the optimal solution for (22) yields the augmented Lagrangian as follows: The overall process is summarised in Algorithm 1.

Algorithm 1 Progressive Hedging Algorithm
Convergence strategy comparison between progressive hedging (left) and proximal bundle (right).

Proximal Bundle Method
DDSIP uses PB method to solve subproblems and bounds integer variables after PB method is terminated. The PB method solves the dual problem of (17) by sharing the dual variable λ with corresponding subproblems. The lower boundary (LB) of (17), which is z, can be updated by finding the better upper bounds of the D(λ).
The NC in (24) is relaxed and added to the objective in (25), where H s is structured artificially for each scenario as studied in [16,29]. Therefore, dual variable λ is shared with corresponding scenarios in same nodes, assuming that the difference is indicated by H s respective to the same radius λ as depicted in Figure 2. The underlying problem becomes maximising objectives concerned with λ, andx is ignored as derived in the second line of (25). It should be noted that subproblems are still minimising objectives regarding x s as denoted in the third line of (25).
The differential of D(λ) and its expected bounds z are used to update λ. We can derive (26) by differentiating (25) with λ. The z in (27) is decision variables for the LBs for the dual function, and its differential is decided by step size p. PB uses the stability centre pointλ to represent the implementable value of λ and it decides the better LB of (17), giving higher value of bounds with the smallest possible radius from the optimal point as depicted in Figure 2. Therefore, a new λ is obtained by maximising the following optimisation problem as follows: In (28), z s is maximised to satisfy its optimal condition ∂z − p k (λ −λ) ∈ 0, which is the maximisation of the objective with constraints for its cutting planes that are indicating the possible movement for z s with the differential of subproblems (26). During iterations, k ∈ [1, ..., k max ] , PB updatesλ only if the improvement is higher than the plausible minimum value.
The differential of subproblems given in (29) represents the actual improvement of solutions with a new λ k . The difference between the feasible boundary z s and current boundary D(λ k−1 ) given in (30) represents the expected improvement of subproblem solutions with λ k . PB accepts new λ asλ when the improvement of the solution which can be confirmed by comparing subproblem solutions, ∂D(λ) to ∂z. If the improvement is higher than mL it will updateλ, or else it will go through the null step [29].
Thus, the stability centreλ can be updated if the actual improvement is larger than mL ∈ (0, 0.5] of the estimated improvement as given in (31). The convergence of variables is thus indicated when there is no expected improvement of the bounds of (27) such that ∂z ∈ 0. In each iteration, the step size p k is calculated according to results of (31) and (32) to smooth the heuristic searching process. When the actual improvement is too small, the step size decreases; on the other hand, when the actual improvement is sufficiently high with mR ∈ [0.5, 1) as given in (32), the step size increases. The step size is determined as follows: In (33), new step size for the next iteration h k is yielded by assuming that the actual improvement is the same as the expected improvement as follows: Therefore, p k+1 is adjusted by h k and initial configurations.
In (35), the step size is decreased when (31) is satisfied, and in (36), the step size is decreased when (32) is satisfied. Note that h k ≤ u k when the factor mR ∈ [0.5, 1) as follows: The detailed process to update the step size is featured in [17], and the detailed process of the PB method is summarised in Algorithm 2.

Branch and Bound in MSSP
Solutions of MSSP given in Section 3.1 can be obtained by using the methods suggested in former subsections. However, the solution is infeasible if the integrality and the NC are not satisfied. The BB algorithm bounds unconverged variables with all corresponding subproblems. A search tree is generated to observe varying results of the bounding process for the NC and manages multiple scenario trees in it; the bounding process is not limited to the single MILP problem. Moreover, the gap between the true solution of (17) and the boundary of (25) is resolved by controlling the additional cost from BB constraints. Thus, the gap between the true solution of (17) and the boundary of (25) is resolved during the process of BB.
First, after the process of Algorithm 2 is done, it generates a search tree where branches B are structured to find solutions with different conditions. Constraints added by the branching are applied to all corresponding subproblems. These constraints are added in addition to the original constraints G, so that G B includes G for all branches in the B. Second, to branch variables which violate integrality, it splits B into B and B by adding two disjunctive constraints.
In (38) and (39), x t is a node variable for time stages t = [1, ..., T], and the projection in (18) is used to generate the integrated solutionx t . We can choose a node variable having the most fractional value. On the other hand, it is possible to branch over continuous variables where the NC is not satisfied.
In (40) and (41), NC is a tolerance of the NC to make a disjunction. The measurement of violation can be used to choose the variable, e.g., the highest distance between subproblems.
Termination of BB is determined when there is no need to branch further or no feasible solution. We can define a node as fathomed when the branching on this node is clearly meaningless. This node becomes a permanent leaf. The process will be terminated when all branches are fathomed. If all variables satisfy NC and the objective value is lower than the current best upper boundary (UB) and also feasible, the node is fathomed as the best UB. On the contrary, a node can be also fathomed if the solution is infeasible or is higher than the best UB. The best LB is designated by the lowest boundary among leaf nodes that is not fathomed, which makes it possible to have better results than the current best UB. Therefore, the BB algorithm can also be terminated when LBs closely approach the best UB.
Since BB yields the higher boundary of (25), so that Z LB ends up with the same value of the UB or higher, it is obviously not required to branch on nodes that satisfy the inequality in (42). Finally, Z UB is accepted as the final solution of MSSP that obtains the condition of global optimality. The termination process can be summarised as follows:

1.
The node would be "fathomed" if new bound D(λ) is higher than the current optimal or is infeasible.

2.
The node would be updated as the Best UB if new bound D(λ) is lower than the current Best UB, and the NC is satisfied.

3.
The node would be updated as a candidate for the Best LB if new bound D(λ) is lower than the current Best UB, but the NC is still not satisfied.
The overall process of BB methods is detailed in Algorithm 3.

Simulation Results
Our simulation conditions are described, and the results are discussed in this section. The time horizon is considered up to 30 years with five years per stage; therefore, six stages are considered at maximum horizon. We use predicted data of economic growth and electrification rates to forecast the demand scenario tree, where both components are considering the electrical demand growth [30,31].

Test System Configuration
Our test bed system contains 22 load buses with 41 existing lines and 6 generators, modified from the IEEE 30-bus network. In the scenario tree, we consider 2, 4, 6 stages with 10 way, 7 way, 5 way splits for demand scenarios, respectively. The split for the scenario tree is the number of branchings from a node in the tree to the succeeding nodes.
Candidate lines for construction are marked with dotted lines in Figure 3 and featured in Table 2, so that the planner can construct lines, or else augment the capacity of existing lines. In Table 2, there are 12 candidate lines for the system network. Among candidates, there are 8 lines A-H (red) selected from the IEEE 30-bus network, and 4 lines I − L (blue) nearby bus 11, where additional load of 17 MW will be added. We assume that no more generation resources will be added, and the demand will increase every five years. That is, the number of generators is enough to cover expected demand loads, but power flows will not be delivered without expansions.

Stopping Criteria Testing
In this paper, estimations required to obtain valid results from the DD methods are reported through empirical results concerning the initial parameters of each method. Those parameters are associated with the intensity of the NC as the methods to deduce the optimal decision. We measure the method performance on the PH's step size γ, PB's NC matrix H and its step size p to verify the impact on the termination condition. Moreover, branching results from BB are reported.

Progressive Hedging
The step size γ represents the slope of the NC to update the penalty ω. A steep slope for the NC with a small γ takes less progressive steps for the gaps enclosing the optimal decisions. On the other hand, a gentle slope with a large γ more rigorously forces convergence. However, the simulation time does not directly follow the step size; in fact, subproblem solutions are more likely to cycle around the optimal solution when the step size increases. The cycling effect of decisions can cause a weak convergence rate that disturbs the integrated solution to satisfy the original constraints of the TLEP. As shown in Table 3, very small or large step sizes lead to expensive termination in our cases, requiring a lot of time to solve. Figure 4 depicts 4 cases with different γ values tested on the 4 stage 7 split TLEP problem. Cases with step size 1 and 5 successfully terminated, yet cases with 0.1 and 10 failed to reach the stopping criteria 0.0001 under the given 100 iteration limit. We observed that the simulation time to solve subproblems was longest using the largest step size and the objective function was not properly minimised. This case shows poor convergence rate with no further updates of the penalty for NC ( Table 3). The objective obtained by the smallest step size was better than others but failed to terminate. The convergence rate is not sufficient when the step size is too small or too large. Valid solutions were obtained with step size 1 and 5, however, the objective was not minimised compared to the value for step size 0.1. Hence, there was a weak convergence rate in later iterations, which is entailed by using a fixed step size and inevitable when the problem size increases. This clearly shows the requirement of parameter tunings to accelerate the process and obtain high-quality solutions, by continuously modifying the step size accordingly. However, it is difficult to designate the appropriate NC penalty for every decision variable.

Proximal Bundle
The measurements for the PB method are compared in Figure 5. Initial parameters described in Section 3.3 represent the step size p, which is proportional to the improvement of the dual function, and NC coefficient H s , which finds the gradient for cutting planes. We measured the variable convergence (nonanticipativity), simulation time, and the objective cost of the TLEP problem. Given parameters are described by per-unit values based on the objective cost and the stopping criteria was 0.0001. Given NC coefficient H s in Figure 5, different simulation results were observed according to the initial step size. When the initial step size is very low or H s is very large (grey), simulations take more steps with little improvements to the solution. Iterations wasted to draw redundant cutting planes take a long time to deduce the dual function. On the contrary, immediate terminations were observed for the highest p of 100 respective to 0.5 and 1 H s . However, they did not perform the best on the NC results since expected new boundary of the dual function was not able to be improved without changes of dual variable λ. Among results with the same H s (green, magenta), the step size 0.1 performs the best for the NC and objective. As a result, we verified that the wrong choice for parameters can bring premature termination or expensive termination. It is difficult to distinguish which cost performs the best as the process is premised to incline from the minimum to the maximum, yet the original problem involves minimisation. Thus, we excluded the high costs that violated the NC from acceptable solutions.

Branch and Bound
The BB algorithm was applied to the results from the previous subsection, and the associated results are analysed by comparing the best performance and the worst performance in the same search tree.
Intermediate n-th branching results until they are fathomed are marked in Figure 6, where the best and the worst are distinguished. The best case can quickly converge integer variables with low additional cost for the NC, which support the objective function closely approaching to the optimal value. However, the result highlights the importance of first branching nodes, and objectives increased by the NC do not always guarantee the optimal solution. In Figure 7, results for every node in the branching tree are marked, in which nodes are distinguished, following the best case or the worst case. There were significant differences between the two groups. First, the best-case nodes converge close to the optimal cost, however, the worst-case nodes dramatically increase for the first few branchings and produce an overestimated cost. Second, the worst-case nodes spend more time solving additional PB processes to converge the integer variables. Therefore, the quality of the objective function is not guaranteed if we follow the worst branching results and this is determined from almost the first branching.

Numerical Results Analysis
Based on the empirical test for the initial parameters, we report the TLEP results based on MSSP with different program sizes in Table 4. Line construction and generation cost amounts are displayed to show which line has been augmented or constructed according to DD methods. The termination conditions considered two points: method termination and feasibility. Method termination indicates whether the stopping criteria was reached within a time limit of 48 hours. Node feasibility indicates that the integrated node solutions from the projection satisfy constraints involved in the TLEP. In general cases, if obtained solutions satisfy the NC, the node feasibility also is satisfied.
The PH method contains quadratic terms in the objective function in subproblems and updates penalty parameters andx by projection. The quadratic terms in the subproblems usually take more time to solve single subproblems than that of PB. However, the PB method has the main optimisation problem of updating the dual variable λ, which takes more time than calculating the projection. According to the numerical results, solutions from the PH method satisfy the NC because its termination condition pertains to the NC. However, the PB method can violate the NC since the termination is based on boundary improvement not on variables. The DDSIP which implements the BB algorithm after the PB termination finds integer variables implementable across corresponding subproblems. Therefore, we used medium-iteration penalties and concatenated them for the warm-start of the PB method to speed up the process. We convert the penalty parameters for the PH method as follows: The parameter exchange enables the penalty matrix from the PH method to support the PB method to find the initial point. Among the cases featured in Table 4, constructions for new lines occur in Case 2 and 3, whereas Case 1 decides to upgrade existing lines. In general, construction for a new line is more expensive than upgrades so the results reveal the cost savings that construction can provide over 30 years. The selected candidate lines are J and L, which would lower the cost for generating power flow by linking end bus 11 to the central area off the network. Line 8-28 was the most frequent upgrade choice, which is the connection for end bus 8. On inspection, there is a candidate line E for bus 8 that obviously links the network to bus 8 but this is not as beneficial as linking the bus 11. As shown in Case 1, PH and PB determine an upgrade for 16-17 whereas others determine an upgrade for 21-22; the cost effectiveness can be verified by the value of objectives and proximity to the EF results. Growing the system demand, it becomes obvious that the TLEP problem in Case 2 requires new lines as the PH method gave the worst objective in spite of using the best plan from Case 1 (note that there were no more expansions after the first stage in Case 2). The expansion for J is displaced by L in Case 3, observing that most of the generators were fully contributed in a 30-year time span and subproblems determined expansion L and upgraded 21-22 to work better with other plans. This change accounts for the more severe demand conditions of the few scenarios where further upgrades to 23-24 after the first stage are decided.
Specific optimisation results are shown in columns 7-10, Table 4. The objective comprises the cost for generation, line expansions, and supply deficits. This paper depicts the sum of costs for individual results to illustrate all obtained objectives for comparison (even though the solution is infeasible). Generation cost rises as expensive fuel generators are committed, which can be seen when phase angles are not physically modifiable or line capacity is limited. Therefore, line expansions to provide energy from cheap generators can minimise the generation cost, yet the mitigated cost should be balanced against the cost of deficits.
Despite the decrease in speed as problem size is enlarged and the slight overestimation of the objective entailed by projection, PH in [14] sufficiently satisfies the NC if it can terminate and it obtains the solutions in a reasonable time. Whereas PB in [17] rarely succeeds at the same feasibility test; actually, the results of PB rank lowest but are not implementable (the expansion result in Case 1 merely fulfils the integrality). Feasibility can be satisfied by the BB algorithm with an adequately reduced objective as verified in DDSIP [16] and PH + DDSIP (proposed) results. Moreover, simulation time for the DDSIP process is lowered by the penalty matrix of the PH. The reconciliation of two different DD methods is observed from this result that mitigates both problems for finding the parameter organisation in the PB and the cycling effect that the PH undergoes.
The EF results formulated as (15) can represent a reference result for the optimality in Case 1 and 2, but it requires myriad time and a larger MIP gap. Considering the test bed is based on a simplified 30-bus network with some electrical equipment omitted, it is not suitable to use EF in a practical evaluation process. In Case 3, the EF failed to solve the problem within the given time. Instead, the objective 6256.58 was obtained through a 3-split problem, which was slightly overestimated. Considering more detailed scenario trees usually lower the cost, the expected cost for extreme scenarios is discouraged in DDSIP and PH + DDSIP for Case 3 as the gap between scenarios is smaller compared to the 3-split case. As a matter of fact, the objective does not necessarily need to be the same to obtain the unified results as shown in Case 3. DDSIP has a higher objective as many scenarios chose expansions to avoid supply deficits. On the other hand, PH + DDSIP chose expansions in only a few extreme scenarios, and the additional cost for the deficit was not that significant. Regardless of the extremes, expansions for L and upgrades for 8-28, 21-22 are necessary to provide energy throughout the 30 year time span. Particularly, as the number of scenarios increases as the scenario tree branches, so probabilities for single scenarios decrease and an influence to first stage decision is shrunk. Finally, required transmission lines for the network and times needed for completion can be estimated in chronological order.
The purpose of our simulation was not to find the one true solution for the test system. Yet, we focused on verifying variable convergence of MSSP problem, composed of typical TLEP problem, and we extended up to six stages. In this long-term evaluation process, we accomplished the feasibility of the results making the integrated variables from DD methods implementable. Various test cases revealed that the expansion plan can be relative according to method type regardless of the feasibility condition. Not only considering the accuracy, our test revealed the problem of time. The PH method shows contradictory results depending on the problem size where decision variables do not converge despite many iterations of the long-term problem. Whereas the proposed method that combines PH and DDSIP shows coherency over various sizes. Moreover, expansion results over different time spans sufficiently explain the consistency in response to the electricity demand. Many studies have focused on the financial benefit of resources in the objective function. It represents the expense, which apparently appears during the production or is induced subsequently [7,28,32]. Instead of that, we provide a framework for DD methods to handle integer variables in MSSP. Through the experiments, algorithms are tuned to cover multistaged problems and they give variety to the assessment results when there is uncertainty in the network organisation.

Conclusions
In this paper, we introduce the methodological basis of dual decomposition methods for multistage stochastic programming, tailored toward the transmission line expansion problem. Since the role of transmission lines is as substantial as generation resources are, careful planning is required as expansions are not retractable. We evaluate this investment decision on the 30-bus test network by considering three costs-reliability, operation and investment-based on future demand uncertainties. Despite the shortcoming in integer variable convergence in conventional dual decomposition algorithms, the proposed method enables the utilisation of several scenarios over a long-term horizon by finding correlation between scenario subproblems represented by the nonanticipativity constraint. Furthermore, we bring three dual decomposition methods-progressive, proximal bundle, dual decomposition in stochastic integer programming-and combined them to account for the convergence issue by adjusting warm-start values for internal parameter settings. The results not only convey optimal decisions among furcated future realisations but also achieve the economical use of time. We illustrate the significance of a long-term evaluation by showing that empirical tests over different time spans can yield various combinations of expansions, enabling planners to confirm them according to potential benefits under uncertainty. However, further studies for realising adequate reliability cost and evaluating power system flexibility with newly constructed lines should be considered in the future studies.