Contingency theory, climate change, and low-carbon operations management

Purpose – Drawing on the theory of contingency, the aim of this work is to understand how supply chain-related contingencies, arising from climate change, are related to changes in the organisational structure of firms. Further, the authors explore how this relationship influences the perception of sustainability managers on the adoption of low-carbon operations management practices and their related benefits. Design/methodology/approach – To achieve this goal, this research uses NVivo software to gather evidence from interviews conducted with ten high-level managers in sustainability and related areas from seven leading companies located in Brazil. Findings – The authors present four primary results: a proposal of an original framework to understand the relationship between contingency theory, changes in organisational structure to embrace low-carbon management, adoption of low-carbon operations practices and benefits from this process; the discovery that an adequate low-carbon management structure is vital to improve the organisations’ perceptions of potential benefits from a low-carbon strategy; low-carbon management initiatives tend to emerge from an organisation’s existing environmental management systems; and controlling and monitoring climate contingencies at the supply chain level should be permanent and systematic. Originality/value – Based on the knowledge of the authors, to date, this work is the first piece of research that deals with the complexity of putting together contingency theory, climate-change contingencies at the supply chain level, organisational structure for low-carbon management and low-carbon operations management practices and benefits. This research also highlights evidence from an emerging economy and registers future research propositions.

Introduction
Few studies address the risks of climate change-related contingencies in supply chains in emerging economies and the consequent necessary responses from businesses (Gasbarro and Pinkse, 2016;Winn et al., 2011;Slawinski et al., 2015). This paper aims to understand how companies structure and maintain their low-carbon operations management and how they consider the constraints arising from climate change at the supply chain level. In addition, we also reveal the benefits that organisations could achieve by adopting operational practices of managing carbon emissions.
Climate change is a subject that generates global risks and uncertainties (Kuklicke and Demeritt, 2016;Carrao et al., 2016) due to a series of extreme weather events that have occurred in recent years (Winn et al., 2011;Slawinski et al., 2015); these events have had negative impacts, not only for companies but also for industrial operations (Gasbarro and Pinkse, 2016). Challenging weather events, such as storms, hurricanes and extreme droughts, tend to generate restrictions that can devastate supply chains.
These weather events have a strong influence on supply chain operations because they may directly impact facilities and compromise their access to natural resources and raw materials (Dasaklis and Pappis, 2013;Haverkort and Verhagen, 2008;Busch and Hoffmann, 2007), thus creating carbon-related restrictions in supply chains. However, in addition to the occurrence of extreme events, there are other supply chain-related contingencies which may affect organisations because of climate change, such as the emergence of new regulations, technologies and additional costs.
In this work, better organisational performance results from the fit between organisational structure and the external environment in which a company is inserted (Volberda et al., 2012). Organisations should consider climate change and its contingencies to optimise their overall performance. The organisational strategies related to climate change can be a source of competitive advantage and strong performance in the market (Kolk and Pinkse, 2004;Lee, 2012a). Good organisational performance, in the context of climate change, can be obtained through various benefits, as highlighted in the literature (Hoffman, 2005). However, if a company does not consider supply chain constraints resulting from climate change when managing carbon reductions, it may not be prepared to be effective in its actions to reduce emissions nor to achieve benefits from these initiatives.
Carbon management in industrial companies is presented in the literature as being a management process that requires a critical view from top managers. Effective managers must consider the following issues: managing risk (Weinhofer and Busch, 2013), an assessment of capabilities and trade-offs (Pinkse and Kolk, 2010), the establishment of policies and objectives for the reduction of CO 2 (Lee, 2012a), the definition of strategic actions (Pesonen and Horn, 2014), opting for either reduction, compensation or searching for zero emissions (Weinhofer and Hoffmann, 2010), a potential search for external partners to carry out the actions of low-carbon management (Kolk and Pinkse, 2004), a study on the benefits from projects developed by a company (Bocken et al., 2012) and, finally, the weighting of issues of climate change in organisational routines (Boiral, 2006). Therefore, a question that guides this article is: How do the perceptions of contingencies resulting from climate change at the supply chain level lead to an eventual restructuring of procedures for organisational low-carbon management? Another question that needs to be addressed is: How does the relationship between contingencies and change affect the managers' perception of benefits by adopting practices of low-carbon operations management?
Recent trends justify the relevance of this research. The recent Conference of the Parties of the United Nations (UN)  in Paris showed the intention of global leaders in setting targets to reduce CO 2 emissions to combat climate change (UNFCCC, 2015). It has the potential to influence organisational routine and strategy. Another fact is related to the extreme drought that occurred in several countries in Latin America (WWAP, 2016). Among these countries, Brazil witnessed a severe water crisis between 2014 and 2015 (The Guardian, 2015;Reuters, 2016) that affected the local economy, people's wellbeing and supply chain activities due to disruptions in the water supply.
These extreme events are not isolated; in fact, they tend to repeat themselves, so organisations can face many challenges to deal with the contingencies of climate change. In this sense, this work presents an integrated framework to help companies understand low-carbon management in terms of supply chain management contingencies. It also encourages the adoption of low-carbon operations management and helps organisations to better perceive potential benefits. To address these issues, interviews were held with managers of national and multinational companies in Brazil. Brazil was selected for the study due to its economic and geographic relevance and the severe supply chain disruptions it has experienced due to climatic events (drought resulting in water scarcity).
This article is structured as follows: Section 2 presents the concepts of managing carbon from the perspective of the theory of contingency and the potential benefits that businesses can achieve from this. In Section 3, the research method used and the instruments used for data collection and analysis are given. Section 4 presents the results, and Section 5 gathers the discussions and propositions from these results. Finally, in Section 6, the conclusions, contributions and limitations of the study are presented.

Theoretical background
Emissions of gases that cause climate change have become more intense since the beginning of the industrial revolution (IPCC, 2014). According to Slawinski et al. (2015), emission levels have reached the point where, from now, climate-related physical impacts will be observed on a large scale. Thus, climate has become a source of challenges for organisations (Winn et al., 2011) due to the disruptions it can cause in supply chain operations.
While uncertainties increase, managers will need more information on climate change to restructure their businesses (Gordon and Narayanan, 1984). In this context, the theory of contingency is relevant (Lawrence and Lorsch, 1967) because it deals with organisational management due to external events.
For Drazin and Van de Ven (1985), the proposition that the structure and processes of an organisation should be adapted to its organisational context, either to survive or to be effective, is central to the theory of contingency. However, Sousa and Voss (2008) note that studies in operations management have not fully explored the richness of the influence that contextual issues can have.
The impacts of climate change-related supply chain disruptions are difficult to predict (Winn et al., 2011) and uncertainties from the external environment influence the approach to green practices (Lo and Shiah, 2016). Because of this, the theory of contingency is paramount; managers should consider the constraints arising from climate change to develop strategies capable of conducting low-carbon operations management and, as a consequence, achieving the organisational performance desired.
As there is no unique way to apply the theory of contingency (Horisch, 2013), this work adopts the term strategy for climate change (Lee, 2012a(Lee, , 2012b, as companies deal with risk-related contingencies from climate change that affects their supply chains. Thus, this research follows the theory of contingency and suggests four main variables of study: contingency factors; internal organisation structure for low-carbon management; adoption of low-carbon operations practices; and effects on performance (Drazin and van de Ven, 1985;Gordon and Narayanan, 1984;Sousa and Voss, 2008;Volberda et al., 2012).
Contingencies are defined as outside events that affect organisations, over which organisations cannot exert direct control (Sousa and Voss, 2008). This article lists four possible contingencies resulting from climate change that can affect the management of supply chains: lack of resources and difficulty of access to raw materials; new advances in technology; regulations; and extra costs. These contingencies are derived from the fact that organisations already face, or will face, supply chain-related disruptions, such as lack of resources and limited availability of raw materials (Smith, 2013;Haverkort and Verhagen, 2008). In addition, companies may be forced to seek new technologies (Busch and Hoffmann, 2007;Plambeck, 2012;Aben et al., 2010). Organisations can also face social and governmental challenges, and new regulations may require taxes, which increase costs, changing the way the companies act globally (Jeswani et al., 2008;Choi et al., 2013;Hitchcock, 2012;Lo, 2010;Burritt et al., 2011).
The second variable, the internal organisational structure for low-carbon management, is related to the capabilities that a company has to ensure to promote actions to adapt to emergent contingencies (Gordon and Narayanan, 1984;Volberda et al., 2012). Renukappa et al. (2013) state that it is important for a company to manage internal factors, such as: • the commitment and the establishment of leadership to low-carbon management; • written policies related to climate change; • establishment of specific job positions to deal with carbon management; • systems of rewards for the initiatives of reduction of carbon; • training programmes for employees; and • creating a performance reporting procedure for emissions.
In this regard, organisations can define their internal structure through their supply chains by enacting climate change policies (Lee, 2011), aligning objectives and targets to reduce CO 2 emissions (Gopalakrishnan et al., 2012), selecting their suppliers carefully (Dou et al., 2015) and sharing their information about CO 2 emissions with suppliers (Jira and Toffel, 2013).
The third variable is the adoption of low-carbon operations practices. Per Sousa and Voss (2008), these practices can be seen as actions that organisations take in response to current or future contingencies. Thus, this work uses low-carbon operational practices called "products", "processes" and "logistics" (Bottcher and Muller, 2015).
Finally, this research aims to understand the relationship between climate-change contingencies and firms' performance. We opted for the benefits outlined by Hoffman (2005), namely: We believe that companies obtaining these low-carbon management benefits are also improving their overall performance. Figure 1 provides a summary of the theoretical background herein explored.

Research method
This research adopts a qualitative approach, which has made use of in-depth interviews (Ketokivi and Choi, 2014). Interviews with experts were necessary for this research due to the fact that managers are members of organisations that decide on how to react to environmental contingencies (Horisch, 2013;Russo and Harrison, 2005;Faes and Matthyssens, 2009).
The interviews were conducted with managers of seven companies. The number of companies herein investigated is aligned with the number of companies suggested by other   (Okereke and Kung, 2013;Burritt et al., 2011;Aben et al., 2010). Brazil was chosen because more research is needed on climate change in developing countries (Lee, 2012b;Wang et al., 2013).
The choice for large companies is explained by the fact that the larger the size, the greater the exposure to regulations and pressure from stakeholders (Lee, 2012b). In addition, larger companies generally have greater financial resources to invest in low-carbon management (Boiral, 2006;Boiral et al., 2012;Wang et al., 2013). The companies belong to the sectors of energy, retail, manufacturing and agriculture.
The interview script (Appendix) allowed the collection of data during the interviews (Ketokivi and Choi, 2014;Yeung, 1995;Rowley, 2012). In total, ten managers were interviewed, including managers with expertise in sustainability, environment, supply chain, logistics and facilities management.
The interviews were conducted during 2015 and 2016. The total duration of the interviews was around 7 h, with each interview averaging 54.34 min. In this way, the number of interviewees and the duration of interviews is aligned with the literature (Galbreath, 2014;Rowley, 2012).
To start the procedure of data collection, researchers -after determining the companies that would be researched -made contact via phone and email with managers to explain the research objectives and themes (Ketokivi and Choi, 2014;Galbreath, 2014;Rowley, 2012). Once the invitation to participate and the interview schedule was accepted, the interview script was sent to respondents in advance (Yeung, 1995;Galbreath, 2014;Rowley, 2012). The interviewees were able to prepare and organise their thoughts, as well as access secondary data to respond to the issues more clearly.
The script was developed by selecting the contingency factors that impact organisations and how organisations have dealt with them. The internal organisational factors were used to formulate the questions regarding management initiatives. Finally, questions about benefits noted by managers from low-carbon operations were designed.
Secondary data, including information from sustainability reports, internal newspapers and information contained on the websites of the companies investigated, were collected and material from the database of the Carbon Disclosure Project (CDP) as suggested by others (Gasbarro and Pinkse, 2016;Jira and Toffel, 2013;Sullivan, 2009;Burritt et al., 2011;Matisoff, 2013).
All interviews were recorded, so that there would be no loss of data during the conversations. For qualitative data analysis, the interviews were transcribed. We used the NVivo software, recommended by the literature, for qualitative research (Wright, 2009;Galbreath, 2014;Gasbarro and Pinkse, 2016;Solomon et al., 2011). Finally, a tabulation of the data collected was conducted (Ketokivi and Choi, 2014;Voss et al., 2002).

Profile of the cases
The first studied company is called Alpha, a multinational company in the food manufacturing sector. It has been operating in Brazil for decades. Currently, the company participates in the CDP and GHG Protocol-Brazil programmes, in addition to receiving a low-carbon seal from the Brazilian federal government. We interviewed a manager in continuous improvement who work for the environmental department of the company.
The second company is Beta, a Brazilian company in the energy sector with operations in the country for more than 100 years. It has operations in the generation, processing and marketing of electric power, as well as service operations. The company engages in extensive participation in programmes, initiatives and indexes related to sustainability, such as the CDP, GHG Protocol-Brazil, Corporate Sustainability Index (ISE-BOVESPA), Dow Jones Sustainability Emerging Markets (DJSI Emerging Markets), and it actively participates in the conferences of the UN. We interviewed a manager of sustainability at the company headquarters in São Paulo who has worked for six years in the environmental area of the company.
The third company is Gamma, a multinational company based in São Paulo engaged in the sector of food and beverages with operations in Brazil. The company participates in the GHG Protocol and in the UN Global Compact. It fabricates such products as desserts and yoghurts. The interviewees were a manager for the supply chain and an environmental manager.
The fourth company is Delta, a multinational company in electronics manufacturing with more than 50 years of experience in the market. The company surveyed has no operational unit in Brazil but does have a headquarters and outsourcing production. The company participates in initiatives such as COP and GHG Protocol at the global level, in addition to the Dow Jones Sustainability Emerging Markets (DJSI Emerging Markets) and the UN Global Compact. We interviewed the Brazil-Argentina manager for sustainability.
Sigma, the fifth company, is a Brazilian company in the sector of agriculture in the market for over 20 years. The company has signed a public commitment with Greenpeace to fight deforestation in the Amazon. It also participates in the CDP, GHG Protocol-Brazil, the Forest Footprint Disclosure and Corporate Sustainability Index (ISE-BOVESPA). We interviewed the manager of sustainability.
The sixth company is Omega, a multinational company in the retail sector, with operations in Brazil since 1990s. The company participates in the programmes of CDP and GHG Protocol at the global level and the Climate Forum of the Ethos Institute. In addition, the company has a programme for sustainability in Brazil, wherein it works with around 30 suppliers on issues of sustainability. We interviewed three employees here: a coordinator of sustainability for Brazil, a manager of transport and logistics for Brazil and the facilities coordinator.
The seventh company is Theta, a multinational company in the sector of agriculture based in Brazil since the 1960s. The company participates in CDP and the GHG Protocol-Brazil, in addition to having signed the New York declaration on Forests and joined the Roundtable on Sustainable Palm Oil (RSPO). We interviewed the manager of sustainability.

Supply chain disruptions caused by natural events and others risks
The first variable herein analysed is the contextual factors or contingencies of climate change at the supply chain level. This work has highlighted four possible contingencies of climate changes that can affect organisations, which are resource scarcity or difficulty of access to raw materials, new regulations, technological advances, and additional operational costs.
When it comes to scarcity of resources and access to raw materials, five companies mentioned a particular episode and some have risk management practices in place for their sources of supply chain level resources. Alpha recently went through a shortage of onions, replacing the commodity with onion powder, and Sigma stated that there was a large water savings programme when Brazil experienced a long drought between the years of 2014 and 2015. In the case of Beta, the interviewee said that the shortage of water for hydroelectric generation of energy meant the use of thermoelectric power instead: So, if there is a low level of reservoir, it can be replaced by another source, for example thermoelectric plant, which was what happened last year and this year (interviewee, Beta).
With regard to regulations, six companies had some kind of regulations that affected their operations or that they had to meet to not be penalised. Omega demanded from its logistics partners the use of better fuel in their trucks to transport their goods (IBAMA, 2009), and Theta built a new sugar cane plant in accordance with the law on Brazilian biodiesel (Brazil, Law No. 11.097/2005). A Gamma interviewee pointed to the need to meet the legislation for the pollution emitted from trucks (CETESB, 2009).
Another point that we evaluate are emissions from trucks and the trucks from third parties as well. When trucks enter the factory, staff conducts environmental evaluations (interviewee, Gamma).
Necessary technological advances were also considered by studied companies as something that forced the change. Of the seven companies studied, five showed some change in technology that helped reduce CO 2 emissions. Gamma reported that the new technologies acquired by the organisation are strongly related with eco-efficiency and meet international standards for emissions because they follow guidelines from Europe. The manager of Delta said that the company produces electronic products and keeps in mind the goal of reducing emissions: I would say that the staff promotes reduction of emissions to the extent that when we develop new servers and computers that consume less energy we are collaborating to reduce emissions (interviewee, Delta).
Finally, regarding the variable additional costs arising from climate change, all seven companies reported to a greater or lesser extent that they had suffered some financial impact due extreme weather events. Beta and Omega reported that they had indicators of cost per CO 2 emissions produced for their operations. Sigma also highlighted extra cost due to scarcity of water in 2015 when it had an increase by 26 per cent. The manager of Theta said that the company monitors water shortage in its operations: So, for example, do we monitor the cost of not having water? Yes, we do. We have measures to prevent this from happening and also have measures to mitigate the event from happening. We have had events of this nature that we believe are related to climate change (interviewee, Theta).
It can be said that all companies have established a management committee to deal with issues relating to water scarcity as a consequence of the water crisis that occurred in Brazil in the years 2014-2015. It can be summarised that Beta and Theta engage in a comprehensive management of all of the factors considered (resources, regulations, technology and cost), with constant monitoring and management of risk. Gamma reports that there is a team that monitors the development of legislation to facilitate its application when enacted. Table II summarises climate change contingencies in the seven companies.

Enabling an organisational structure for carbon management
Inner organisational structure for carbon management is subdivided into factors of structuring of companies that help answer climate change and the factors that relate to monitoring and controlling emissions. Of the seven companies, Beta, Delta, and Theta have policies on climate change. However, climate change is considered as an item included into a broader sustainability policy. Beta highlights a policy for climate change, a fact that is also found in the company's annual report: The items number eight and nine of our policy are specific to climate change and in parallel, to strengthen them, we have a proper declaration for climate change (interviewee, Beta).
In relation to targets and goals, six of the seven companies have that items in their management policy. Alpha and Omega highlight goals and objectives relating to energy efficiency, whereas the other companies have targets on reducing emissions. The exception is the lack of emissions reduction targets in Sigma.
Regarding the hierarchy of job positions relating to climate change, only Beta and Theta have a committee responsible for the theme but neither of them specifies an exclusive position for activities relating to carbon management.
[. . .] among other responsibilities, we manage carbon governance, which includes internal planning and institutional relationships (interviewee, Beta).
The item "reporting of emissions" was found in all companies. Companies in the CDP disseminate data on CO 2 emissions in Three companies (Beta, Gamma and Theta) report having some type of training on the reduction of carbon in place. Theta reports the existence of workshops and training relating to the change of land use. Beta highlights the role of the behaviour of employees towards emission reductions: [. . .] employees need to know their role day-to-day, and that the role will contribute to the reduction of emissions (interviewee, Beta).
Respondents were asked whether the company's employees received some reward for their results pertaining to emissions reductions achieved. Managers do not gain remuneration for instituting climate change, except the senior managers of Beta are rewarded for achieving reduction targets.
Finally, the internal management of information relating to climate change was found in four (Alpha, Beta, Gamma and Theta) of the seven companies surveyed. The data shows that the management of information flows throughout data panels, in which systematisation of data is routinely performed. Table III summarises internal organisational structure of carbon management policies in the seven companies studied.
The monitoring of emissions was highlighted in all annual reports of the companies and also reported by the respondents in all seven companies. Companies seek to monitor their carbon emissions on a daily basis by means of indicators and consolidate them annually. Omega reports the calculation made for the monitoring of emissions in its fleet of trucks: So how do I calculate the amount of carbon dioxide avoided? We use a measure per litre of fuel (interviewee, Omega).
Regarding the possible managerial approaches (reducing, compensating or zero-emission), five of the seven companies seek to reduce their emissions. The manager of the company Beta declares the adoption compensation and zero emissions: One example is that we've bought credit to compensate for the issue of a plant out here within the group (interviewee, Beta).
Finally, the respondents were asked about the extent of managing different types of emissions. The surveyed companies, Beta, Delta and Sigma are working on Types 1, 2 and 3 of emissions, whereas Alpha, Gamma and Theta, only Types 1 and 2. Omega only reported emissions for the GHG Protocol in 2008, which included Types 1 and 2, referring to the consumption of electric power and transport. Table IV summarises the organisational structure of the monitoring and control of emissions.

Low-carbon operations practices
Alpha has actions for adequate land use in place, and it has begun the exchange of fuel for power generation and standardising the size of trucks with logistics partners.
Beta is engaged in three types of operational practices. The company offers products and services with eco-efficiency to public buildings, low-income communities and for businesses with intensive use of electrical energy. In relation to its process, the company uses biomass for production of electrical energy, replacement of mineral oil for vegetable oil in electrical transformers and investing in wind farms and photovoltaic panels for the production of energy. The company has an initiative in low-carbon logistics and uses electric cars in their operations.
Gamma features actions related to low-carbon processes and logistics. Processes that are highlighted include the exchange of diesel oil for steam generation, reduction in the consumption of electric energy when cooling milk and the exchange of gas-based forklifts with electric ones. As for the practices of logistics it declares, the use of trackers to determine the best routes, to facilitate vehicle exchange and to efficiently maintain its fleet for fuel consumption.
Delta declares the adoption of low-carbon products and logistics. The interviewee said that products consume less energy during their use. It seeks to reduce the number of trips using transport logistics with suppliers of raw material through a better scheduling plan.
Sigma is engaged in the control of deforestation when managing cattle in the Amazon, and uses renewable fuels for energy production.
Omega reports improvements in its thermodynamic refrigeration units and the switch of fluorescent lights for

Scarcity of resources/Raw materials
LEDs. Logistics has improved considerably because it has used software to optimise routes. Finally, Theta engages in three types of low-carbon operations management operational practices. "Product" is related to the production and certification of biodiesel on a commercial scale. "Process" is the use of biomass for energy production and proper use of soil, avoiding deforestation in different regions of the country, including the Amazon region. The practices of "logistics" are exchanges of transport modals and intensified exchange of road with rail. Table V summarises the operational practices adopted by the seven companies surveyed.

Benefits from adopting low-carbon operations practices
The first type of benefit was access to new sources of capital. Companies may receive investments and financial contributions when they act proactively in the context of climate change. Only companies Beta and Theta get this benefit. Theta exemplifies the government's incentive to produce biodiesel, whereas Beta ensures that disclosures of rates of emission/sustainability on the stock market attract the attention of investors for the company: For people looking to buy shares or for a bank that will finance us, they will look at carbon management aspects (interviewee, Beta).
Thereafter, an improvement in the company's reputation is beneficial because it lowers criticism from stakeholders and improves the company's standing in the marketplace. Four companies perceive this benefit: Beta, Theta, Delta and Sigma. Beta associates the benefit with new sources of capital. Theta reports that customers of large multinationals sought to understand how it engages in soil management. Delta and Sigma say their attitude directly influences the consumer's behaviour: [. . .]  The third benefit, identification of new markets, concerns the provision of new technologies or services related to climate change. In this case, Beta reports that it identified the opportunity to acquire a company to generate energy from renewable non-polluting forms: wind and solar power. Theta reports that it realised this benefit after the promulgation of the law on biodiesel; in fact, the company built a new plant for the production of fuel: [. . .] we built a plant for the production of biodiesel here in Brazil. This is a regulation that has had an impact that I consider positive and inclusive and that generates other related impacts that are, in my view, quite useful (interviewee, Theta).
The fourth benefit refers to the improvement of human resource management. It is considered as a way to improve morale within the company, reducing costs of hiring and training new employees and increasing productivity in the workplace through actions to combat climate change. Of particular note is Gamma, in which the interviewed recounts the feeling of employees: [. . .] they feel motivated, yes. They think "I have identified something related to environment" (interviewee, Gamma).
The fifth type of benefit is anticipation and influence on the climate. This consideration addresses the possible benefits of new regulations in the market of carbon credits and the creation of new taxes; it also considers the possible influence that the industry can exert so regulations may be softened. Beta reports that it needs to draw up an inventory of emissions and send it to the governmental authority, and this will help the government to create taxation or penalties in the future. Finally, Theta recounts its participation in the regulation of deforestation: For example, the forest code, we participated in the processes [. . .] we were able to anticipate, to help, and even to promote this new legislation that we believe is very important and relevant (interviewee, Theta).
An inventory of emissions is a way in which the Government verifies companies in a specific sector which are carbon intensive and creates a tax or penalty (interviewee, Beta).
The sixth type of benefit is improvement in risk management. This deals with the expected loss and extra costs caused by physical damage to structures and facilities and government regulations in certain economic sectors. Gamma reports that it is able to anticipate any kind of regulation because there is a team dedicated to managing risk-related issues within the company. Theta reports they constantly manage their energy usage and resources, and those actions make it more resilient to possible interruption of operations. Beta reports that its risk management provides distribution of power without interruptions by electrical discharges.
This operating model makes us a little more resilient, let's say that those impacts are very relevant and that they occur with some frequency: energy shortage, and the shortage of water, in particular (interviewee, Theta).
[. . .] today has a lot of incidence of lightning, bigger than before; and this year will hit a record electrical discharge in São Paulo State and also experience concentrated rain with much wind that also ends up affecting the distribution of power. So we also have to conduct some risk analysis [. . .] (interviewee, Beta).
The final benefit is operational improvement. This benefit relates to improvement in efficiency, reduction of waste in the production process and optimisation of fleets used in transport, among others. Five of companies realise this benefit: Alpha, Beta, Gamma, Omega and Theta. In general, they recognise that there are operational improvements as a result of dealing with the issue of climate change.
Table VI summarises the perception of respondents regarding the benefits of adopting low-carbon operations practices. Reduce Extension of the management of emissions (scope) 1 and 2 1, 2 and 3 1 and 2 1, 2 and 3 1, 2 and 3 1 and 2 1 and 2 Table V Examples of low carbon operations practices adopted by the studied companies

Discussion
Using the theoretical perspective of contingency, this work has sought to identify first if the studied companies have already witnessed some contingencies relating to climate change that have created difficulties at the supply chain level and then to determine how they manage these contingencies in their operations.
Each organisation was questioned about the existence of possible risk management. Beta and Theta stand out by having risk management in place for contingencies (Weinhofer and Busch, 2013;Pinkse and Kolk, 2010). The other organisations present a less comprehensive risk management. In this way, it appears that companies react to the context of climate change when they witness risks to their operations. With regard to the regulations related to climate change, the studied companies also witnessed such contingencies. Some reported the need to issue a report at the end of each year for regulatory agencies of the government, and others reported the need to monitor the emissions level of trucks and the addition of chemical additives as per the law for the reduction of emissions of CO 2 or equivalent.
Finally, all companies have reported, in some way, that climate change affected their business in financial terms. The 2015 CDP questionnaires confirm that extreme weather events affected their facilities, supply of raw materials and the sale and distribution of their products. Hence, each company reported climate-change related disruptions at the supply chain level.
Therefore, companies do face contingencies arising from climate change, and they try to monitor them as much as possible. However, some of the companies have a more structured and better way of managing risk (Beta and Theta).
In general, the companies studied have been monitoring at least one contingency (scarce resources, new regulations, technological advances or extra costs). As a way to synthesise the results, it seems that there is a relationship between contingencies arising from climate change and corporate attention paid to risk management. Thus, it is possible to put forward the following proposition for future studies:

P1
Organisations that face risks from climate change trigger a more structured approach to management of climate risks.
According to the theory of contingency, when faced with external contingencies, organisations change internally in terms of organisational structure (Sousa and Voss, 2008;Schneider et al., 2014;Horisch, 2013;Gordon and Narayann, 1984). Overall, the studied companies do not have a managerial structure with all the characteristics suggested by the literature (Lee, 2012a). The climate policies found in three of the seven companies show that the issue of climate change tends to be part of the environmental policy previously established.
In relation to targets and objectives, most of the companies seek to establish goals for the reduction of impacts and better efficiency. To this fact, it is observed that all employees have a certain way of managing their responsibilities towards achieving these goals and objectives. On the other hand, except in the cases of Beta and Theta, businesses do not have high hierarchical job positions to perform activities closely linked to climate change.
In general, Beta, Gamma and Theta train their employees by embedding the climate change in their training sessions on environmental issues. However, the companies do not establish training unique to the topic in their daily routines of training.
Rewards for achieving such goals and objectives still remain an exception. Only Beta reports that its managers receive some kind of reward for achieving the reduction targets proposed by the organisation.
The reporting of emissions occurs in all the companies interviewed. They are looking for ways to share their efforts to combat carbon emissions and participate in the CDP. This objective is accompanied, in many cases, by managing emissions information that passes through all the hierarchical levels of the company.
In this way, neither complete adherence was found in the managerial structure for low-carbon management when compared with what is proposed in the literature in terms of defining policies, roles, goals and objectives and training (Lee, 2012a;Renukappa et al., 2013) nor there was a systematisation of data for communication and definition of proper climate change strategies and action plans (Pesonen and Horn, 2014). The only companies that are approaching this kind of structure are Beta and Theta, in which there is a definition of climatic aspects in the environmental policy of the companies, existence of goals and objectives, communication of results and indicators, systematisation of information management by a committee that is responsible

Anticipation of regulations
for carbon emissions, as well as training and rewards for managers. Hence, one can check for an integration of factors related to climate change and environmental management in organisations, because there is no exclusive and totally different approach for low-carbon management currently in existence (Renukappa et al., 2013;Lee, 2012a;Pesonen and Horn, 2014). Thus:

P2
Organisations integrate low-carbon management initiatives into the previously existing environmental management structure.
Some companies that have little internal structure to deal with climate change seek a way to compensate for that lack by adopting control and monitoring of emissions (Alpha, Delta and Sigma). It seems that these cases focused on monitoring and controlling emissions as a way of compensating for the lack of managerial structure. However, to adopt practices of low-carbon operations (products, processes and logistics), organisations should seek to align the managerial levels, strengthen the need for managerial support for monitoring practices of low-carbon and then ensure the most appropriate response to the contingencies faced are enacted (Correia et al., 2013;Schneider et al., 2014;Horisch, 2013). It was noted that the adoption of practices of low-carbon operations management of three companies (Alpha, Delta and Sigma) do not present a wide and innovative variety of activities related to reducing CO 2 emissions. These practices of low-carbon operations management run by these companies are similar to the practices studied in the literature (Okereke and Küng, 2013;Sharma and Henriques, 2005;Pourbafrani et al., 2014;Daneshi et al., 2014;Islam and Olsen, 2014) and seems to confirm a statement made by Renukappa et al. (2013) that the practices related to logistics prevail initially in organisations.
In relation to the monitoring and control of emissions, three companies (Alpha, Delta, and Sigma) have an appropriate management in place. All three have an inventory of emissions and two of them (Alpha and Delta) state that their actions are designed to reduce CO 2 emissions.
The benefits perceived by the respondents from all three companies (Alpha, Delta and Sigma) are also reduced. The interviewee from Alpha says it realises the operational improvements, whereas the interviewees from Delta and Sigma declare the importance of these practices are to improve the reputation of the company.

P3a
There is emphasis on managerial monitoring and control of emissions, with little explanation on the adoption of low-carbon practices and the perception of their benefits. The adoption of low-carbon practices and the perception of benefits tend to be related more to the organisation structure in charge of climate change issues.
Thus far, the discussion has analysed the results aligned with the theory of contingency. In other words, if there is no internal suitable organisational structure, there will be few practices and few perceived benefits. However, this article also found two other cases, Gamma and Omega, in which the companies diversify their practices of low-carbon management, adopting a wide range of practices in terms of products, processes and logistics. According to the theory of contingency, if a company diversifies its operations, it does not guarantee greater effectiveness in its performance (Sousa and Voss, 2008;Drazin and van de Ven, 1985;Volberda et al., 2012;Horisch, 2013). Beta, Theta and Gamma, showed greater contingency management of climate risks, but only Beta and Theta may be considered internally well-structured according to the literature (Renukappa et al., 2013;Lee, 2012a;Pesonen and Horn, 2014).
In terms of benefits, both Beta and Theta illustrate almost all the types of benefits listed by Hoffman (2005). Gamma was more restricted and declared the improvement of human resource management, anticipation of regulations and operational improvement. Omega mentions only operational improvement.
Thus, by drawing on the concepts of contingency management, companies may diversify their actions to reduce CO 2 emissions but do not guarantee the effectiveness of these practices (Sousa and Voss, 2008;Drazin and van de Ven, 1985;Volberda et al., 2012;Horisch, 2013). Therefore, it is the structure for managing low-carbon that matters and leads the company to realise more benefits. Consequently: P3b According to the perspective of the theory of contingency, even if an organisation diversifies its practices towards low-carbon operations management, these practices themselves do not guarantee benefits. What matters is the organisational structure which supports carbon management.
Alpha, Gamma, Sigma, Omega and Theta state that they have made changes in their logistical activities to reduce their emissions. These companies utilize software and dedicated teams for the monitoring of logistics with objective of optimising routes and exchanging vehicles to reduce fuel consumption and emissions. The focus on low-carbon logistics, therefore, is aligned to the literature (Handler et al., 2014;Islam and Olsen, 2014;Norlund and Gribkovskaia, 2013). If we examine the companies Beta, Theta, Gamma and Omega together, the practices of low-carbon operations are more prominent than low-carbon logistics. Thus, this finding suggests alignment with an affirmation by Böttcher and Müller (2015) which states that companies give more importance to the practices of processes than to the logistics. However, both Beta and Theta have diversified their actions by adopting three possible practices.
Therefore, taking into account the cases studied and the use of the theory of contingency, the better the structure for low-carbon management, the greater the variety of low-carbon operations management practices adopted. Thus: P3c From the perspective of the theory of contingency, the better the organisational structure for managing climate change, the greater the adoption of the three types of practices of low-carbon operations management.

Conclusion
This article has explored how organisations deal with the contingencies arising from climate change at the supply chain level. We adopted the perspective of the theory of contingency to discuss how companies understand climate change-related issues, how climate change is translated into creating a structure for managing issues of low-carbon within the companies and how the companies adopt low-carbon operations management and realize its related benefits. The theoretical background was analysed considering the Brazilian context. Through interviews with managers of seven large companies from different sectors in Brazil, a country that has recently witnessed climatic adversity (drought), it was possible to obtain the following major evidence: • A suitable structure for managing carbon emissions (definition of management of climate risks, policies and targets to reduce CO 2 emissions, training the staff and communication of results) is essential to improve the perception of the benefits derived from the adoption of low-carbon operations management practices (products, processes and logistics).
• Initiatives for controlling and monitoring of carbon emissions seem to be insufficient to allow managers to recognise the benefits of embracing climate change strategies.
• Controlling and monitoring of climate contingencies should be something permanent and systematic (risk management) to enable a suitable organisational structure for managing carbon emissions and, consequently, for improving the perception of benefits.
• Low-carbon management initiatives are started from environmental management systems that already exist. Therefore, organisations interested in starting a strategy for managing emissions may have already commenced working on environmental systems and practices to start embracing low-carbon management practices.

•
The findings of this research can potentially contribute to teaching case studies for discussing the implications of climate change in business strategy and the impacts of contingency theory for planning inner organisational structure in response to climate change risks.
Future research could explore the research propositions highlighted in Section 6 and pursue further discussions to promote additional evidence on the complex issues of climate change contingencies, supply chain, low-carbon operations management and the benefits of low-carbon management in emerging economies. Finally, it should be emphasised that the exploratory nature of the study has its limitations. Therefore, it is suggested that the propositions made are still subject to confirmation and any tentative generalisations can be seen as fragile.


Optimization of Multi-Period Bilevel Supply Chain Planning for Single Supplier and Single Retailer under Demand Uncertainty *

This paper presents the optimization of multi-period bilevel supply chain planning for single supplier and single retailer with leader-follower relationship under demand uncertainty. The multiperiod production planning problem for the supplier and the retailer is formulated as the mixed integer nonlinear bilevel programming problem. In order to improve the total proﬁt, the eﬀects of the replacement of leader-follower relationship are investigated. The eﬀectiveness of the replacement of leader-follower relationship is examined by some numerical experiments. A quantity discount contract with quadratic function is also proposed to maximize the total proﬁt under demand uncertainty.

Introduction
Global supply chains are receiving much attention due to globalization of market places. In such situation, it is required to optimize total supply chain with cooperative or non-cooperative relationship among supply chain companies in order to maximize the total profit. However, it is difficult to coordinate the production planning between these companies because companies sometimes individually make decisions in order to maximize their own profit. The total profit in decentralized situation is inferior to the profit in centralized situation. It is important to consider the leader-follower relationship in the production planning because the organizations in global supply chain make their decisions under the leader-follower relationship in realistic situations. The game theoretical approach can be applied to find the equilibrium. The game which is conducted by a leader and a follower is called a Stackelberg game. In the Stackelberg game, the leader can predict the follower's optimal response when the leader determines its production planning. On the other hand, the follower can optimize its own sales planning under the leader's decisions. In [10], the multi-period production planning problem has been formulated as a nonlinear bilevel programming problem under uncertain demand. Sev-eral solution algorithms to find the equilibrium have been compared and the effectiveness of utilizing the Karush-Kuhn-Tucker (KKT) condition for reformulation of the bilevel programming problem into the single-level problem has been confirmed. Then, the replacement of leader-follower relationship in a multiperiod supply chain planning has been proposed. However, the effectiveness of the replacement of leader and follower has not been examined in several cases and the introduction of optimal quantity discount policy has not been considered. In this paper, we investigate the effects of the replacement of leader-follower relationship in the bilevel supply chain planning under demand uncertainty. The purpose of the study is to propose the optimal policies in the bilevel production planning for single supplier and single retailer. The supplier is the leader at the beginning of the period, and then the leader is changed from the supplier to the retailer in the middle of periods in the multi-period bilevel production planning. This study examines the effectiveness of the replacement of the leader-follower relationship to the total profit in the decentralized problem and the effects of quantity discounts to improve the total profit from numerical experiments.
The paper is organized as follows. Section 2 introduces literature review. Section 3 states the problem description and the formulation of the replacement model of leader-follower relationship. Section 4 presents the optimization method of multi-period bilevel production planning under demand uncertainty. Section 5 describes the optimal quantity discount contract to improve the total profit of the bilevel production planning for single supplier and single retailer. In section 6, the effects of the replacement of leaderfollower relationship in the middle of periods are stud--1 -

Special Issue on Flexible Automation
Transactions of the Institute of Systems, Control and Information Engineers, Vol. 30, No. 3, pp. 73-80, 2017 ied. Then, the effectiveness of the quantity discount contract is examined to improve the total profit. The conclusion and future works are stated in Section 7.

Literature Review
The general optimization algorithms for bilevel programming problems have been introduced [2]. Yue and You proposed an optimization approach for a multi-echelon supply chain in a Stackelberg game by using a piecewise linear approximation of nonconvex functions [11]. Qu et al. studied the optimal configuration of cluster supply chains [6]. They proposed the policies to convert the cluster supply chains into a reconfigurable model. Almehdawe studied the leaderfollower relationship in a supply chain in which a manufacturer and multiple retailers make decisions [1]. They compared the total profit in the leader-manufacturer problem with the total profit in the leader-retailer problem. However, the replacement of the leaderfollower relationship has not been studied so far.
The multi-period bilevel production planning is analyzed in order to respond to some changes such as demand uncertainty or inventory quantity through multi-period models. In some cases, it is considered that the leader-follower relation should be exchanged in the middle of periods [4]. There are some studies on nonlinear bilevel programming models for multiperiod production planning under demand uncertainty. Zhang and Shi analyzed the retailer's multi-period production planning with a quantity discount contract under demand uncertainty [12]. Yoshida and Nishi addressed an analytical approach to the multiperiod production planning for single supplier and single retailer under demand uncertainty [9]. The production planning problems were formulated in order to be analyzed theoretically. However, these models are not detailed for the realistic models where the optimal solution cannot be derived analytically, e.g. the setup costs cannot be considered. We extend the model into the mixed integer nonlinear bilevel programming model that can represent more realistic situations in this paper. Supply chain contracts are introduced into the bilevel production planning in order to improve the total profit. Tsai introduced an optimization approach to supply chain with quantity discount policy [7]. Yin et al. studied the bilevel production planning [8]. They also studied the optimal quantity discount contract in order to maximize the total profit in the Stackelberg game.

Problem Definition
We consider the multi-period production planning for single supplier and single retailer. In the model, the supplier and the retailer make their decisions according to the Stackelberg game. We assume twoechelon supply chain where there are a single supplier and a single retailer. The supplier produces the product items and the retailer deliveries the product items to customers. The supplier and the retailer make their decisions individually. The customer's demand is assumed to be uncertain, and the demand is given by a probability distribution. The supplier has enough raw materials and storage space to produce product items in order to satisfy the retailer's order quantity. The setup cost is incurred when the supplier produces different product item from that of a previous time period. The inventory holding cost is required when the supplier holds inventories due to over production. The supplier deliveries the product item to the retailer and the retailer deliveries the product item to the customer. The product items of the retailer is delivered to the customer at the end of a period. If the quantity of the product item delivered by the retailer is less than the realized demand, the retailer pays the penalty cost for inventory shortage. The quantity of shortage in a certain period is not the demand in the next period. The supplier and the retailer make their decisions under a price contract in which the supplier decides the wholesale price and the retailer decides the order quantity for the supplier's wholesale price. In the multi-period bilevel production planning, the single supplier and the single retailer maximize their own profit under the Stackelberg game where the supplier is the leader and the retailer is the follower. The supplier decides the wholesale price in order to maximize its profit. The retailer decides the order quantity with the supplier's wholesale price in order to maximize the profit under demand uncertainty. Customer's demand is represented by a normal distribution. The supplier's objective function is the wholesale revenue minus production cost minus inventory holding cost minus setup cost. The retailer's objective function is the sales revenue minus inventory holding cost minus the penalty cost of the inventory shortage minus wholesale cost.
The multi-period bilevel production planning problem where the supplier is a leader and the retailer is a follower is formulated as follows. Parameters c tj : supplier's production cost of one unit of product item j in period t D tj : random variable of demand of product item j in period t f (D tj ) : probability density function followed by demand of product item j in period t Φ(D tj ) : cumulative distribution followed by demand of product item j in period t g tj : retailer's penalty cost for inventory shortage of one unit of product item j in period t h r tj : retailer's inventory holding cost of one unit of product item j in period t h s tj : supplier's inventory holding cost of one unit of product item j in period t J : number of product items K tj : ratio of the average demand of product item j to retailer's sales revenue in period t M : positive large number p tj : retailer's unit sales revenue of one unit product item j in period t s tj : setup cost of product item j in period t T : total time horizon U t : number of product items which can be produced by the supplier in period t w min , w max : minimum and maximum values of the supplier's wholesale price of one unit of product item j per period Decision variables H tj : retailer's inventory shortage quantity of product item j in period t I r tj : retailer's inventory quantity of product item j in period t I s tj : supplier's inventory quantity of product item j in period t O s tj : supplier's production quantity of product item j in period t Q tj : retailer's order quantity of product item j to the supplier in period t R tj : retailers sales revenue of product item j in period t S tj : retailer's delivery quantity of product item j to customer in period t V tj : retailer's inventory quantity of product item j in period t w tj : supplier's wholesale price per unit product item j in period t x tj : 0-1 variable which equals 1 if supplier does not produce product item j in period t − 1 and produces product item j in period t, otherwise equals 0 y tj : 0-1 variable which equals 1 if supplier produces product item j in period t, otherwise 0.

Supplier's decision problem
The supplier's profit maximization problem is formulated as follows.
The supplier's decision variables are the quantity of inventories, production quantity, wholesale price, and 0-1 variable x tj which represents the setup of product item j in period t. The supplier's objective function is the wholesale revenue to the retailer minus production cost minus inventory holding cost minus setup cost. The supplier's constraints include the inventory balancing constraints (2), the constraints on the lower value of the production quantity (3), the constraints on the number of product items to be produced (4), the setup constraints (5), the constraints on the production capacity of production quantity (6), and the lower and upper value of the wholesale price (7). The retailer's profit maximization problem is formulated as (10)-(16) where E(X) is the expected value of the term X in the objective function due to demand uncertainty. The retailer's decision variables are the inventory quantity, the order quantity and the delivery quantity. The retailer's objective function is the sales revenue to the customer R tj minus the inventory holding cost V tj minus the penalty cost of the inventory shortage H tj minus the wholesale cost w tj Q tj . The retailer's constraints include the inventory balancing constraint and the constraint on the upper value of the delivery quantity. In the retailer's profit maximization problem, the sales profit, the inventory holding cost and the penalty cost for the inventory shortage are expressed as the expected values due to demand uncertainty.

Replacement of Leader-follower Relationship
Most conventional study on the bilevel production planning assume that the configuration of the leader-follower relationship is fixed. In order to respond to demand uncertainty and cost changes caused by uncertain factors, we propose a model that can change the leader-follower relationship in which the supplier is the leader at the beginning of period and the leader is changed from the supplier to the retailer in the middle of periods. The multi-period bilevel production planning problem with (1)-(16) is the leadersupplier problem. In order to formulate the leaderfollower replacement model, it is required to formulate the leader-retailer production planning problem. The leader-retailer problem is formulated by using the supplier's optimal response function to the retailer's decision making. However, the supplier's optimal response function of the problem with (1)-(16) is assumed to be constant because the supplier's objective function (1) is the monotone increasing function with the supplier's wholesale price regardless of the retailer's order quantity. In this section, the multiperiod bilevel production planning is reformulated in order to obtain the supplier's optimal response function. In the revised multi-period bilevel production planning model, customer's demand is assumed to depend on the retailer's sales revenue p tj of product item j in period t. The average of customer's demand µ tj is reformulated as (17) with the retailer's sales revenue p tj .
Both e tj and K tj are positive constants. In the leaderfollower replacement model, the retailer's sales revenue p tj of product item j in period t is the retailer's decision variable. In a realistic situation, the retailer's sales revenue p tj is larger than the supplier's wholesale revenue w tj . In order to realize p tj > w tj , the following equation (18) is introduced in the model.
a tj is positive number which is larger than 1 (a tj > 1). The lower and upper bounds of the supplier's wholesale revenue (7) are reformulated as (19) because the upper bound of the supplier's wholesale revenue is restricted by (17) and (18).
By introducing (17), (18) and (19) into the bilevel production planning problem in the previous section, the leader-supplier bilevel production planning problem (LSP) is formulated as follows.

Solution Approach
The multi-period bilevel production planning is formulated as a mixed integer nonlinear bilevel programming problem. However, it is difficult to solve the problem by commercial solvers. Therefore, an effective solution approach to derive a Stackelberg equilibrium is required.

Normalization of the Retailer's Decision Problem
The retailer's objective function is represented as the expected value due to demand uncertainty. However, it is difficult to solve the retailer's profit maximization problem by numerical computations. Petkov and Maranas addressed the normalization technique of the expectation of the costs under demand uncertainty [5]. The retailer's objective function is reformulated by the normalization of the probability distribution. The expected values are reformulated as follows.
f (D tj ) and Φ(D tj ) are the probability density function and the cumulative distribution function of the product item j in period t, respectively.D tj is the average and σ tj is the standard deviation of the customer's demand. The customer's demand is assumed to follow the normal distribution. Φ(D tj ) and f (D tj ) are formulated by (21)-(23).

Reformulation of Bilevel Model into Single-level Model using the KKT Condition
The bilevel programming model is reformulated as a single-level programming model by the KKT condition of the lower-level problem. The KKT condition is the necessary condition which guarantees that the solution x is the local optimal solution. The Lagrangian function L is formulated as (24). J r is the retailer's objective function. U and V are the number of equality constraints, inequality constraints in the retailer's profit maximization problem. g 1 u (x) = 0 (1 ≤ u ≤ U ) are the equality constraints, and g 2 v (x) ≤ 0 and (1 ≤ v ≤ V ) are the inequality constraints. α u and β v are the dual variables related to these constraints.
The KKT condition of the retailer's profit maximization problem is obtained. The mixed-integer bilevel programming problem is reformulated as the mixedinteger single level programming problem.
By applying the KKT condition to the leader-supplier problem, the bilevel programming problem is reformulated as the single level programming problem as follows.
( These problems are reformulated into single-level mixed integer nonlinear programming problems where bilinear terms such as w tj Q tj are included. A generalpurpose solver for solving mixed integer nonlinear programming problems is used to solve these problems.

Quantity Discount Contract to Improve the Total Profit of the Bilevel Production Planning
In the bilevel production planning, the total profit of the Stackelberg equilibrium is inferior to the optimal profit of the centralized problem because the supplier and the retailer make decisions according to their own preference. In this section, the quantity discount contract model in the bilevel production planning is proposed to improve the total profit.

Quantity Discount Contract with a Linear Function
If the quantity discount contract is considered in the bilevel planning problem, the supplier's wholesale revenue w tj Q tj is formulated as the function of the retailer's order quantity Q tj . A linear quantity discount model was introduced in [3]. The supplier's wholesale revenue is formulated as the linear function of the retailer's order quantity. Then, the customer's demand is assumed to follow the normal distribution. In this case, the supplier's wholesale price is formulated as (32).
where W tj and a tj are positive constants. The multi-period production planning is formulated only as the LSP. In this case, the multi-period bilevel production planning with quantity discount is formulated as follows.

Quantity Discount Contract with a Quadratic Function
A quantity discount contract with a quadratic function is proposed in order to maximize the total profit. Q c tj is defined as the optimal solution of the retailer's order quantity of product item j in period t in the centralized problem. The supplier's wholesale revenue of product item j in period t, w(Q tj ) is minimized if Q tj = Q c tj . We propose a quadratic function of the retailer's order quantity with respect to the wholesale revenue function. In this case, the supplier's wholesale revenue is formulated as (35). b tj and c tj are positive constants.
Equation (26) in the KKT condition is reformulated as (36) by introducing the quadratic quantity discount function of (35). This is included in the optimization model in the quantity discount bilevel planning model.

Computational Experiments
Computational experiments are conducted to show the validity of the proposed models. The effects of the replacement of the leader-follower relationship in the multi-period bilevel production planning are studied in Section 6.1. Then, the effects of the optimal quantity discounts are examined in Section 6.2.

Effects of the Leader-follower Relationship
end of periods is T = 2 and the number of product items is J = 1. Three cases of computational experiments are conducted.
Case 1: The supplier is the leader in all periods. Case 2: The retailer is the leader in all periods. Case 3: The leader is started from the supplier and the leader is changed from the supplier to the retailer at the start of period t = 2.
In the Stackelberg game where the leader is changed in period t = 2, the supplier is the leader in period t = 1. The supplier makes a decision in order to maximize its own profit for whole periods. Then, the leader is changed from the supplier to the retailer, and the retailer makes decision as the leader in periods t = 2. In this case, the decision variables of the supplier and the retailer in period t = 1 are obtained and used in order to solve the Stackelberg game where the leader is the retailer in period t = 2. The problems in Case 1, Case 2, and Case 3 were coded by mixed integer nonlinear programming problems. The experiment was performed by Intel (R) Core (TM) i7-2700 CPU 3.50GHz with General Algebraic Modeling System (GAMS). LINDOGLOBAL was used to solve the mixed integer nonlinear programming. The parameters were set as a tj = 1.5, c s t1 = 100, g r t1 = 120, h r t1 = 20, h s t1 = 20, I s 0,1 = 30, K t1 = 8.5×10 4 , s t1 = 1500 and σ t1 = 20. I s 0,1 is the supplier's initial inventory quantity which are obtained by the optimization in the bilevel programming problem.
We investigated the effects of parameter e tj on the replacement of leader-follower relationship because the parameter e tj may influence on the selection of the optimal wholesale price and we have identified that other cost parameters do not have an impact on the replacement of leader-follower relationship in the problem. Table 1 shows the comparison of the total profit among three cases when e tj = 1.30. The total profit in Case 2 is the largest in all cases. In the LRP, the wholesale revenue w tj is the smallest in t = 1 and t = 2. Therefore, the sales revenue and the average of the customer's demand are the smallest in all cases because of (17) and (18). In Case 2, the average of the customer's demand becomes larger with the small wholesale price, and the total profit is maximized compared with Case 1 and Case 3. Table 2 shows the comparison of the total profit among three cases when e tj = 1.40 (1.31 ≤ e tj ≤ 1.48). The total profit in Case 3 is the largest in all cases. The wholesale revenue in period t = 1 is equal to the wholesale revenue in period t = 1 in the LSP and the wholesale revenue in period t = 2 is larger than the wholesale price in period t = 2 in Case 3. The retailer's wholesale cost is the same with the wholesale revenue multiplied by the order quantity. In the LRP of Case 2, the retailer who is the leader in period t = 1 decides larger order quantity than that in Case 1 in   order to enlarge the retailer's wholesale revenue. In Case 3, if the retailer decides the order quantity with larger wholesale revenue compared with that in LSP in Case 1, the average of the customer's demand is decreased compared with that in Case 1. Therefore, the retailer's profit is increased because the retailer can reduce the penalty for the inventory shortage. Table 3 shows the result of the comparison of the total profit among three cases in case e tj = 1.50 (1.49 ≤ e tj ≤ 1.50).
The total profit in Case 1 is slightly larger than the total profit in Case 3. The increase of the wholesale revenue in period t = 2 in the replacement of leaderfollower relationship hardly improves the total profit and the total profit in the LSP is the largest. From our computational results, the total profit in the LRP (Case 2) is the largest if e tj = 1.30, the total profit in Case 3 is the largest if 1.31 ≤ e tj ≤ 1.48 and the total profit in the LSP is the largest if 1.49 ≤ e tj ≤ 1.50. If e tj is large, the impact of the mean of the customer's demand to the retailer's profit is small. In this case, the total profit depends on the costs such as the inventory holding cost or the penalty for inventory shortage. In case, 1.31 ≤ e tj ≤ 1.48, though the sales revenue is not so large, the penalty for inventory shortage is small in Case 3 compared with Case 1. Therefore, the total profit in the leader-follower replacement model is larger than the total profit in the LSP. On the other hand, in case 1.49 ≤ e tj ≤ 1.50, the retailer's total cost in the LSP is smaller than the retailer's total cost in the leader-follower replacement model because the supplier makes decision in each period. Therefore, the total profit in the LSP is larger than the total profit in the leader-follower replacement model.

Effects of the Quantity Discount Contract
The effects of introducing the quantity discount contract to the total profit in the decentralized model are examined from computational experiments. The experiments are conducted in four cases. In Case 1, the centralized problem is solved. In Case 2, the decentralized problem is solved without a quantity discount contract. In Case 3, the decentralized problem is solved with the wholesale price of the linear quantity discount. In Case 4, the decentralized problem is solved with the wholesale revenue with the quadratic quantity discount. The parameters of three instances are shown in Table 4. a tj = 0.1, b tj = 10, c tj = 15000, U tj = 500 and W tj = 15000. The number of product items is J = 3. Table 5 shows the comparison of the total profit among four cases. Time is the computation time with the maximum 3600 seconds. (3600) indicates the tentative results within 3600 seconds. From the results in Table 5, the total profit in the decentralized problem is improved by introducing the wholesale revenue of the linear function of the order quantity compared with that in the decentralized problem without contracts (Case 2). By introducing the wholesale revenue of the quadratic function of the order quantity, the total profit in the decentralized problem becomes much closer to the optimal profit in the centralized problem compared with the optimal profit introducing the wholesale revenue of the linear function. The results show that the total profit in the decentralized problem is improved by introducing the quantity discount contract. That is because both the production quantity  and the delivery quantity increase in the decentralized problem by introducing the quantity discount contract compared with the production quantity and the delivery quantity in the decentralized problem without contracts. The wholesale revenue of the quadratic function is more effective to improve the total profit in the decentralized problem than the wholesale revenue of the linear function. That is because the wholesale revenue of the quadratic function is constructed with the optimal order quantity in the centralized problem. Therefore, the production quantity and the delivery quantity with the wholesale revenue of the quadratic function are much closer to those in the centralized problem.

Conclusion and Future Works
In this paper, we have proposed an optimization method for multi-period bilevel production planning for single supplier and single retailer under demand uncertainty. In order to improve the total profit, the replacement of the leader-follower relationship is proposed. The effects of the replacement of the leaderfollower relationship have been investigated. In this paper, we have shown that there is a case when the replacement of leader-follower relationship makes the profit better for the problem instance of T = 2 only for the cases even when all the cost parameters are constant. There will be some cases where the replacement of leader-follower relationship makes the total profit better when the cost parameters are dynamically changed. The selection of the proper timing of replacement and the effects on the total planning horizon under dynamic change of cost parameters will be studied in future works. A quantity discount contract with quadratic function is also proposed in order to improve the total profit in the decentralized problem. By introducing the optimal quantity dis-count contract into the decentralized problem, the equilibrium solution in the decentralized problem is very close to the optimal solution in the centralized problem. Therefore, the total profit in the decentralized problem is much improved by introducing the optimal quantity discount contract.


extfieldsofstudy:
Physics
Computer Science

text:
Computer aided fixture design - A case based approach

Automated fixture design plays important role in process planning and integration of CAD and CAM. An automated fixture setup design system is developed where when fixturing surfaces and points are described allowing modular fixture components to get automatically select for generating fixture units and placed into position with satisfying assembled conditions. In past, various knowledge based system have been developed to implement CAFD in practice. In this paper, to obtain an acceptable automated machining fixture design, a case-based reasoning method with developed retrieval system is proposed. Visual Basic (VB) programming language is used in integrating with SolidWorks API (Application programming interface) module for better retrieval procedure reducing computational time. These properties are incorporated in numerical simulation to determine the best fit for practical use.

Introduction
The function of fixtures is to locate and constrain a workpiece during a machining operation. A machining fixture can be classified to have two basic functions: (a) To locate the component at correct position in relation to cutting tools; (b) To hold the component firmly in order to prevent motion during the machining. Fixtures find application in machining, welding, assembly, inspection, and other operations. Machining fixtures directly influence the productivity, machining quality, and the cost of machined parts. So two samples of different densities are taken into consideration and tests are performed to obtain their exact material properties and numerical simulation is done.
The procedure of fixture design is complex and experienced based, so deign of modular fixtures requires over 10 years of practical experience, and furthermore, there is no intensive solid theory to bolster it. In a large portion of the cases, machining installations are planned and produced by experimentation approach. Consequently, Computer Aided-Fixtures Design (CAFD) is answer for the complex fixture design types. Further automated CAFD frameworks have turned out to be more useful since the CAM activities for assembling have enhanced quickly in late decades. Fully automated CAFD framework enables the user-end to characterize the attainable apparatus design together with, finding techniques and clipping instruments and format for a given component. Various methodologies have been utilized for this reason by application of CAD programming. This paper proposes another installation plan technique in light of a case-based reasoning (CBR) approach incorporated with SolidWorks API. At first, different CAFD methodologies are studied to clear up the requirement for the advancement of the CAFD approach. Case-based thinking has so far observed effective application in the period of apparatus format arranging, i.e. characterizing of the finding and clipping surfaces for a predefined design conspire. It relies on upon surveying the closeness between the cases. CBR includes recovering, and systemizing the past cases of fixture design on a component in library as database all together that they can be reviewed, promptly reused or possibly adjusted when user need few alterations. Essentially to take care of a plan issue, a CBR approach must have the capacity to perceive the best coordinated case among the current cases in information base to the present outline prerequisite by a proper case recovery framework. At that point, the user can select the recovered case to meet the plan prerequisites in the new outline issue if necessary. The primary objective of CBR process is to locate the most comparative workpiece with the number of workpieces existing in the database. This similitude estimation framework is called CBR method.
However, the current CBR based fixture design approach faces a great difficulty in converging to single ideal solution for a given problem because of clichés in case-retrieval strategy. Majority of the systems end up giving more than one part for fixture design solution. It is then up to the designer to select the optimum one. Further improving the accuracy of case retrieval will reduce the number of selected fixture designs that will be suggested. Hence, there is an opportunity to improve the case retrieval of CBR-based CAFDs if we can study and have a better similarity function in order to determine similar fixture design among many fixtures stored in the database.

Literature Survey
Various studies and research have been done in field of automated modular fixture for past few years. Many authors have experimented with various numerical models to design a successful retrieval system. Number of new theories and concepts has been put forward to address obstacles in systems architecture design.
A new method for computer aided fixture design is CBR approach [1,3]. Based on developed model, it was implemented using software on standalone system. Similarity assessment and retrieval of solid models play a crucial role in reusing number of solid models [2]. He used multi-resolution skeleton model to achieve similarity using database management system (DBMS) and successfully implemented. Scale-space technique can obtain features that are invariant compared to global structure of model [11]. On integrating CAD package it was found that solution obtained was very crucial in feature identification. Algorithms to determine existing parts in a database that are similar to query part provided by user [4]. Reduced feature vectors on each feature was applied, analysed and compared with the same of query part to obtain acceptable results in form of similar parts. CBR and RBR approach for automating modular fixture by combing these two methods [2]. With help of software 3D user interface was provided incorporating the above mentioned methods. A new fixture layout using CBR approach. The method was impended on large database having different attribute [9]. The result was found satisfactory as it provided in majority of the cases. Automated method for assembling modular fixtures using SolidWorks API. A plug-in code was generated to create entire new module of fixture design within SolidWorks GUI. An attempt to improve the effectiveness of case based reasoning system by finding similarity between symbolic features has been made [5,6]. Similarities between parts are derived based on machining features and size using numerical model. The results obtained are found to be astonishingly accurate. A method for improving the search method in database for fixture design using similarity method to compare the similarity between the parts [6]. Focus was on fixture design, working principles, and pertinent proposed approach [6]. Several AI models techniques have been studied to use optimum method for evaluating all stages of CBR system with high accuracy. An Internet-enabled fixture design system was also implemented that utilizes Case-Based Reasoning paradigm derived from instances based on previous solutions of similar problems [7,8]. CBR is type of comparison based method on similarity. It is created in the artificial intelligence field environment. It is able to process the new problems using past experiences encountered by the system on which this method is employed. Hence, it requires a database to be constructed where past problems encountered are stored with their relevant solutions, and then, the new cases as confronted issues can be classified by deciding the best-coordinated case from the database. So, CBR method works by giving solution as solution of similar stored cases. To design a CBR-based system, the crucial areas which affect the performance of the whole process, are the right case characterisation (i.e. indexing method), similarity function (retrieval strategy) and arrangement of the number of cases in database. In case of fixture design, a CBR technique ought to be capable of distinguishing the best coordinating case among the current cases in database to the target design requirement by utilizing a legitimate ordering and recovery methodology. Then, the system allows the designer to modify the retrieved workpiece and the related fixture to meet the design necessities in the new design problem. The general steps of a typical CBR fixture design system are expressed in Figure 1.

Indexing
The purpose of indexing is to determine the relation of feature of previous cases in database with the existing case. Case indexing is an important part of CBR method as insufficient indexing may lead to case inseparability. Case retrieval is concerned with finding a related case in the database that is exceptionally impacted by indexing approach.
The proposed methodology can be broken down into two sub steps, first is the main searching process in the database and second to find the solution for the query part based on the result obtained in the first step. Based on this, the method demand to have database inform of two subcategories, that is workpiece information, machining information in one group while solution of workpiece (fixturig solution) in the second.
Therefore the key processes in indexing can be said as going through the database in first steps to obtain optimal results and based on the result obtained, second step to provide ideal fixture solution. Based on this we can define various feature parameters required to differentiate and provide similarity ranking.

Template Search
In this research, template search as the initial step of this CBR retrieval stage is to maintain a strategic distance from repetitive similarity calculations between superfluous in the database. The objective of template search is to verify and to reduce computational search time removing unwanted, irrelevant cases for next step [10]. For example if the query part is prismatic, then it will remove all cylindrical and semi cylindrical part from of consideration. Hence only filtered cases containing required specific attributes will proceed for further evaluating methods.
In our approach the key parameters of workpiece attributes are Workpiece Type, Workpiece Size, Machine Type, Axis of Machining, and Machining Operation. These are the most basic attributes of component to be machined defining its basic characteristics. Hence the above listed five parameters have crucial impact on template search method. In this we have not considered more number of attributes to filter the cases as it may lead to conflicts in filtering process thus giving insufficient or no filtered cases.

Similarity assessment
The filtered cases from template search will be further evaluated in this method. Since the total numbers of selected cases are much less as compared to that of present in the database, Computational time for similarity assessment reduces drastically. The main goal of this method is to locate the most comparative case in database which is the fundamental target of all CBR-based fixture design applications.
In our approach, similarity assessment has been simplified in two main steps. The first step is dimension similarity of the two components (i.e. between query component and case component from database) using the Eq.1 while the second step is to evaluate these cases for machining similarity. This is basically achieved by using Distance function equation as mentioned in Eq.2. This study has been restricted to only prismatic parts.
The first step of dimension similarity uses dimensions of component to find the similarity between two parts. Here outermost dimension of two parts to be compared are used for evaluation. Hence as the difference of two increases, similarity index decreases. In the second part machining similarity is defined by considering the number of drilling and milling features. It also takes into account the normalised volume of feature along cardinality. Finally Eq. 4 gives the overall similarity by adding all the similarities obtained. The result obtained is used to rank the components in database for finding the most similar one.

Reuse and Adaptation
The most similar parts obtained from case retrieval are then displayed to user to select the most appropriate cases of all. The selected case gives its corresponding fixture solution stored in database. Based on this user can perform further case adaptation such as adjusting the clamp and locator as required. If the new fixture arrangement is found valid then the system retain this new case in database. This is done so as to provide solution if similar problem is encountered in future.

Case study
CBR method via a case study is illustrated stepwise as follows.
Step 1. Input the test workpiece Input the test workpiece for which the fixture is to be designed. A prismatic part named test workpiece is utilized as a case study and shown in Figure. 7. Run the feature extraction command where it automatically recognizes the features of workpiece. A pop up window appears which asks for the workpiece and machining information and this information is used for the template retrieval.  Step 2: Indexing and retrieving similar workpieces First retrieval stage: A few key attributes for template retrieval step are used to distinguish workpieces with the same attributes. The attributes are used for this step are (i) workpiece type, (ii) size of workpiece, (iii) machine type, (iv) axis of machining, and (v) machining operation. First pop up userform allows user to select these attributes for query part. In our case study, the query part is prismatic, Size of workpiece is Medium, Machining type as milling machine, Machining operation is milling, Axis of machining as vertical. After this stage, five parts from the database are filtered out and displayed to user in second user-form. It also allows user to open CAD file of selected parts by using view command option in user form. Parts in database which do not have attributes in mutual with the test workpiece are omitted. Then, the selected five parts are sent to the next stage as the key step to determine the solution among them concerning fixture design criteria.
Step 3: Similarity assessment The similar workpiece found in the template retrieval stage are used in this stage. This stage is the important part of the process, which gives the most similar workpiece as the solution by similarity assessment method. After template retrieval a pop window appears which ask for the dimensions such as length, width, breadth, slot and hole dimensions of the test workpiece and these are used to find out the individual similarity between the test workpiece and workpiece from the database which are found similar in the first stage.

Figure 5. Second Retrieval Stage-Similarity assessment
Step 4: Fixture design reuse Based on the proposed method, the workpiece rank ordering is done within database and their fixture designs, which are also stored in the database. So, the most similar part is one in the ranking list having larger value of similarity equation. Similar to previous case it also allows user to view the part. Further on clicking next, it gives fixture solution of corresponding part with its image at right.

Conclusion
A CBR method is developed and implemented successfully for machining parts. Implementation is done with the help of SolidWorks API using macros. In this research attempt is made to increase efficiency of CBR system by improving the accuracy of fixture indexing, Template Search, Case Retrieval process. Indexing proposed in this paper is such that the effect of part inseparability is made negligible in database. As a result of which the implemented method works successfully for prismatic parts. The dimension similarity and feature similarity equations instigated in retrieval stage of CBR method provide optimal solutions over its predecessor methods. However this method provides solution based on the data available in its database. In case of query part not having similarity with none of the parts stored in database, this method does not provide valid solutions. In such circumstances, various other methods such as Rule based reasoning can be used.