Poul Svante Eriksen

Peter Nielsen

Order quantity distributions in make-to-order manufacturing: At what level of aggregation do they respect standard assumptions?

Keywords: Poison process, aggregate demand, order sizes, planning horizon

This paper presents both an analytical and a numerical investigation into the order quantities received by a company in the form of customer orders. A discussion of assumptions regarding the behavior of demand in the form of customer orders from various perspectives within manufacturing planning and control with a special emphasis on the make-to-order environment is presented. A methodological framework for analyzing the behavior of orders and investigate the validity of the assumptions is given. Furthermore, an analytical approach to identify the horizon needed for aggregating orders to achieve a stable demand is developed and tested on data from a real case.

Introduction

Companies are in the business of satisfying customer demands in the form of customer orders. This paper focuses on the operational characteristics of ordering behavior in the form of demand and discusses the underlying assumptions within a number of fields. These characteristics include volume per planning period (demand rate -often disaggregated to several time horizons and described as a distribution of stochastic variables), accumulation of demand over the planning period, the number of orders per product per planning period and the standard order quantities for each product. The characteristics of the make-to-order manufacturing are depicted by Hendry and Kingsman [START_REF] Hendry | Production planning systems and their applicability to make-to-order companies[END_REF] and Marucheck and McClelland [10]:

• resources are multi-task machinery and flexible workforce -a large number of possible end items within a product line, • product lead time is vital for customer satisfaction and agreed with customer before production commences, • capacity planning is based on receipt of customer orders and cannot be planned for in advance, • demand is volatile and can rarely be predicted -a small volume and high degree of demand variability both in quantity and product mix.

This paper focuses specifically on analyzing the distributions of customer orders, the transformation of these into demand rates and presents an analytical model to calculate the aggregation horizon necessary to ensure a stable planning environment.

In this context a stable planning environment is defined as having a demand pattern approximately symmetrically distributed with a given (low) Coefficient of Variance (CV) (variance of distribution divided by mean). The presented model can be used to estimate the planning horizon (i.e. length of planning periods) necessary to ensure a stable demand rate in a given situation.

The remainder of the paper is structured as follows. First, a discussion of assumptions regarding demand in the form of customer orders and their behavior is presented. Second, a methodological framework for analyzing the behavior of orders is given.

Third, an analytical approach to identify the horizon needed for aggregating orders to achieve a stable demand is developed. Fourth, a case study application of the presented framework. Finally conclusions and further research are presented.

Background, implications and approach to analysis

Manufacturing Planning & Control involves coordinating any number of decisions [START_REF] Vollmann | Manufacturing Planning and Control for Supply Chain Management[END_REF]. Several of these are directly related to the customer orders and their characteristics. The demand experienced by companies comes in the form of customer orders that may consist of multiple order lines. Each order (line) will contain the following parameters relevant in this context: desired due date, product identification and quantity. These parameters are then transformed into various forms depending on the usage. Within line balancing customer orders are likewise transformed into demand rates (also termed release or launch rates [START_REF] Becker | A survey on problems and methods in generalized assembly line balancing[END_REF]) for individual products and product mix [START_REF] Nicholas | Competitive Manufacturing Management: Continuous Improvement. Lean Production and Customer-focused Quality[END_REF] for a given line. Likewise within lot-sizing demand rates are typically considered deterministic or to stem from a stationary stochastic process [START_REF] Brander | Lot sizes in a capacity constrained facility-a simulation study of stationary stochastic demand[END_REF], despite the fact that demand rates are composed of individual (in)dependent customer orders.

Regardless of application area, the general approach is to aggregate individual customer orders into demand rates for both individual products and product families and use e.g. MRP or MRPII to generate dependent demand and resource requirements [START_REF] Silver | Inventory Management and Production Planning and Scheduling[END_REF], [START_REF] Vollmann | Manufacturing Planning and Control for Supply Chain Management[END_REF]. The aggregation can be conducted along a number of dimensions [START_REF] Zotteri | The impact of aggregation level on forecasting performance[END_REF] (typically time and products [START_REF] Wijngaard | On Aggregation in Production Planning[END_REF]) until a stabilized customer ordering behavior is identified. To facilitate the aggregation and disaggregation of plans a number of assumptions are made regarding the orders handled by the system [START_REF] Axäster | Aggregation of Product Data for Hierarchical Production Planning[END_REF]. These assumptions can be abbreviated to assuming a one-to-one relationship in aggregation and disaggregation [START_REF] Fliedner | Hierarchical forecasting: issues and use guidelines[END_REF], [START_REF] Hax | Hierarchical Integration of Production Planning and Scheduling, in Logistics[END_REF]. As a result order quantities and the number of orders per period are assumed to be constant. This facilitates calculating time needed for changeovers and the number of changeovers needed per planning period (e.g. Silver et al. [START_REF] Silver | Inventory Management and Production Planning and Scheduling[END_REF]). If this is not the case, the disaggregation of aggregate plans may result in suboptimal or even infeasible disaggregate plans. In reality this assumption can be relaxed if the order quantities come from i.i.d. symmetrical distributions (with a low CV; variance compared to the mean of the distribution). A chronological list of order lines for delivery can e.g. expect to exhibit non-stationary behavior. A typical manifestation of this will be if an order contains order lines for more than one product from the same product family. This becomes critical if the order lines are related in a manner so that their demand will be aggregated within the planning environment. On an individual product level assuming independently distributed order quantities is more reasonable, especially if many customers purchase the same products. For all areas a stabilized behavior is expected as demand is aggregated [START_REF] Chen | Performance analysis of demand planning approaches for aggregating, forecasting and disaggregating interrelated demands[END_REF], [START_REF] Fliedner | Hierarchical forecasting: issues and use guidelines[END_REF], [START_REF] Theil | Linear Aggregation of Economic Relations[END_REF]. The critical aspect is here if the customer ordering behavior allows for a simple linear aggregation along product family or time dimensions? Furthermore, if linear relationships in aggregation are an oversimplification of the issue, what should be done instead? The research presented in this paper addresses the assumptions used to aggregate demand information for various planning purposes. The aim is first to design a method for robust estimation of the behavior of order quantities, i.e. determine whether they can be assumed to be independently distributed from a symmetrical distribution. The second step is to develop a mathematical model that describes the CV for the order quantities, under the assumption that the order quantities can stem from an arbitrary distribution and are dependently distributed.

First tests of symmetrical distribution of order quantities are applied. If these are negative, they are considered to stem from a skewed distribution and are therefore also assumed to be non-constant. In order to investigate asymmetry of order quantity distributions, in this paper the following three different statistical tests will be applied:

─ The MGG-test presented in Miao et al. [START_REF] Miao | A New Test of Symmetry about an Unknown Median[END_REF] ─ The CM-test described in Cabilio and Masaro [START_REF] Cabilio | A simple test of symmetry about an unknown median[END_REF] ─ The Mira-test developed by Mira [START_REF] Mira | Distribution-free test for symmetry based on Bonferroni's measure[END_REF] These tests are implemented in the R-package lawstat [START_REF]R-project[END_REF]. From the literature review it is known that the individual orders for each product can be considered to be independently distributed, while the aggregate behavior cannot necessarily be assumed to abide by the same behavior. To test for independence the autocorrelation function is used [START_REF] Box | Time Series Analysis: Forecasting and Control[END_REF]. In the current work only one period lag is considered. Having first established whether the order quantities can be considered to stem from a symmetrical distribution, the next step is to investigate how to stabilize the demand behavior experienced in the form of customer orders. In practices this means determining the horizon needed (i.e. number of orders) to aggregate. The model should therefore be able to determine the number of consecutive orders to aggregate to achieve a distribution with a satisfactory behavior. In this case a symmetrical distribution, using the central limit theorem [START_REF] Walpole | Probability & Statistics for Engineers & Scientists[END_REF], with a low CV is considered satisfactory. The more aggregate the planning level, the lower CV is desired.

Analytical modeling of the aggregation horizon

To formulate the models, the orders for the whole product family are assumed to come from an unbroken time series. We consider a time period of length , where the number ( ) of orders has mean and standard deviation √ . In case of a Poisson process we have = . To describe the volatility of the order quantities the coefficient of variance (CV) is used (e.g. discussed in Nielsen and Eriksen [START_REF] Nicholas | Competitive Manufacturing Management: Continuous Improvement. Lean Production and Customer-focused Quality[END_REF] and were highly significant with p-values below 10 -15 . The estimated coefficient of variation was ( ) = 1.2, likewise indicating a very skew distribution. The product specific analyses were limited to the 151 products that had more than 100 orders giving sufficient observations for applying the tests for symmetry. These products only represent 6% of the products, but cover 66% of the total quantity sold. Adopting a 5% significance level, the MGG-test showed that 77.5% of the products had a significant departure from symmetry of the Quantity distribution. The corresponding number for the CM-test was 76.9% and for the Mira-test 67.5%. The conclusion is that on an individual product level there is likewise a skewed distribution of order quantities. Another potential indicator of asymmetry is the CV. Figure 2 shows the histogram of the estimated CV's for the 151 products. Almost all the CV values are above 0.5 indicating significant skewness. For the Quantity time series for the whole product family we have an estimated mean of = 10.75 and an estimated lag one correlation = 0.1105. As we have no data on arrival times of orders, but rather delivery dates, we assume a Poisson arrival process, i.e. the aggregation level is determined by: The slightly skewed distribution, shown in figure 3, clearly indicates that if an aggregation horizon of 70 orders is used on the aggregate set, the order quantities tend to flow to a symmetrical distribution.

( ( )) = ( ) (1 + 2 ) + 1

Conclusions and further research

The analysis and subsequent application of the analytical model gives a number of significant conclusions. First, the behavior of the particular case data set is as expected rather than as assumed in literature. The individual orders are, when the whole data set is considered, neither symmetrically nor independently distributed. Second, the order quantities for the products with sufficient orders are likewise to a large extend not symmetrically distributed. Third, the analytical models allows to calculate the number of orders needed to aggregate to achieve a given CV. Aggregating 70 orders to achieve a CV of approximately 0.2 on the aggregate set gives a distribution that is almost symmetrical. The conclusion is that although the individual customer orders are not behaving as expected, it is possible to aggregate over the order time series so that demand can be considered to stem from a symmetrical distribution. However, this indicates that demand can only be considered to stem from a symmetrical distribution with a sufficiently low CV if orders are aggregated. This is especially challenging in a make-to-order environment where the ability to buffer on time will be significantly influenced by market conditions. On a product family level this may not be a problem (in this example a desired CV of 0.1 on aggregate level would require aggregating 277 orders, 0.5% of the total number of orders, c. 2 weeks of orders). However, on an individual product level with high CV's aggregating even 10 orders indicates the need to aggregate over a very large time period indeed. This supports the assumptions in e.g. Fliedner [START_REF] Fliedner | Hierarchical forecasting: issues and use guidelines[END_REF] and Silver et al. [START_REF] Silver | Inventory Management and Production Planning and Scheduling[END_REF] regarding the stability of aggregate demand. Future work will focus on simulating the impact of different order quantity distributions on simple manufacturing systems and developing methods to translate the stability of order quantities into a planning horizon for a given manufacturing system.

Fig. 1 .

 1 Fig. 1. Histogram of order quantities for the whole data set.

  ( ) Based on the data estimates, this yields the equation for determining aggregation level in If e.g. a = 0.2 is used, we obtain the integer round up ( ) = 70. Fig. 3 display the histograms of order quantities after aggregation over 70 orders. The distribution is clearly much closer to symmetry. The skewness is clearly much lower as reflected by the estimated coefficient of variation, which is 0.19.

Fig. 2 .

 2 Fig. 2. Histogram of order quantity CV's for 151 products.

Fig. 3 .

 3 Fig. 3. Histogram of order quantities, when 31 orders are consecutively aggregated.

Order quantity distributions in make-to-order manufacturing: At what level of aggregation do they respect standard assumptions?

used in Tsubone and Furuta [START_REF] Tsubone | Replanning timing in hierarchical production planning[END_REF]). The size Q of an order is assumed to have mean µ and standard deviation , i.e. Q has coefficient of variation ( ) = µ .

Furthermore, the autocorrelation function of successive order quantities is assumed to be zero except for lag one. The autocorrelation of lag one is denoted . Let , … , ( ) be the successive orders in the period. The aggregated order quantity is = ∑ ( ) , which has mean conditional on ( ) given by ( ) = µ ( ) and variance given by: ( | ( )) = ( ( ) + 2 ( ( ) -1)) ≈ (1 + 2 ) ( ) under the assumption that N(T) is sufficiently large. For manufacturing environments with a low number of orders, other methods than aggregating orders are used to estimate demand. The mean of is then given by ( ) = µ , whereas the variance is (approximated by):

µ √ Aiming at a time horizon yielding a coefficient of variation given by , this is obtained when

The conclusion is that for any given distribution of Q, for any given company and period it is (given sufficient observations) possible to estimate CV(Q) and (only included if significant autocorrelation is present). From this it is then possible to decide upon a desired stability for the system in the form of and calculate the number of order (E(N(T)) necessary to aggregate over to achieve this stability.

A case study application

To illustrate the analysis a test using a set of orders for a product family with variables ItemID, Quantity and DeliveryDate covering a 6 year period was conducted in the statistical analysis tool R [START_REF]R-project[END_REF]. The total number of orders was 54,243 and 2,160 unique products. The data was arranged based on due date, and subsequently sequenced after creation time. This way order lines from the same order would be sequenced to facilitate an investigation of independence on the aggregate set.

First, the distribution of Quantity for the whole product family regardless of ItemID is considered. 99.1% of the order quantities were below 61 and the histogram of these is shown in fig. 1. The overall picture shows an exponential decay with isolated peaks at multiples of 10 and to some extend multiples of 5 and 12. All three tests of symmetry


May Gökan
email: goekan.may@mail.polimi.it

Taisch Marco
email: marco.taisch@polimi.it

Kerga Endris
email: endris.kerga@mail.polimi.it

Assessment of Sustainable Practices in New Product Development

Keywords: Sustainability, Eco-efficiency, New Product Development (NPD), Eco-design tools

Decisions during NPD process have impact on 80-90% of a product's life cycle sustainability performance. The objective of this study is to investigate the integration of sustainability into product design, mainly focusing on the environmental aspects. The investigation has been carried out by means of a questionnaire developed based on a 3-pillar framework outlining the essential elements for successful integration of sustainability and Life Cycle thinking in NPD process. 10 manufacturing companies with high innovation cycles, operating in Italy in mechanical, electrical and automotive sectors was assessed, supporting the questionnaire with 2 complementary case studies. The results revealed that companies fail to implement sustainability in product development process and gap exists in all the enablers since companies just try to tackle the legislations, considering sustainability as a constraint rather than exploiting the opportunities for eco-innovation.

Introduction

In the last couple of decades, significant research work has been carried out in order to investigate different ways of supporting engineers in the development of more sustainable products. However, most of the efforts and studies are mainly directed towards the environmental aspect of sustainability as the industrial world has changed its approach to the environment. The importance of the environmental sustainability of industrial products and processes derives not only from the ever stricter-becoming environmental legislations issued in most of the developed countries, but also from the higher awareness of customers concerning environmental problems. In particular, the competitiveness of putting on the market more sustainable products is becoming a key factor in recent years [START_REF] Gupta | Environmental Conscious Manufacturing[END_REF]. Product development is one of the most critical aspects for companies in reaching their sustainability objectives as almost all the products are outputs of the product development process. In particular, early design decisions can have a very significant impact on sustainability. These decisions not only concern choices of material and manufacturing but also have a strong impact on the product's entire lifecycle [START_REF] Ramani | Integrated Sustainable Lifecycle Design: A Review[END_REF]. Based on the estimation from the EU report, 80-90% of all product-related environmental impacts are determined during the design phase of a product. Hence, eco-design is a way to improve products' life-cycle environmental performances by systematically integrating environmental aspects at a very early stage in product design [START_REF]Eco-design of Energy using Products[END_REF]. As a matter of fact, key challenges have to be overcome to enable ecodesign methods to be applicable in early design stages. With this study, we aim to understand the main motivations, limitations, and effectiveness of integrating sustainability in new product design and to understand how and what companies are doing currently to integrate sustainability in their products and product development processes. In doing this, the focus is mainly on company characteristics, sustainable strategies and applications of the company, ecodesign tools and relevant product development processes. In this context, we identify the main research objectives as below:

 Understand how and what companies are doing currently to integrate sustainability into their products and product design processes  Determine the priorities of companies during product design and stimuli for sustainable product design  Understand the level of consideration given to integration of sustainability into product design on the industry side  Develop insight into the use of eco-design tools in companies' product design practices  Identify the gap between the literature and the practice This paper is structured as following: State of the art for relevant concepts and the framework used for designing the survey is provided in part 2. The methodology followed is explained in detail in part 3. Next, the results of the analysis is shown and discussed in part 4. The main insights from the paper and conclusions are presented in part 5 and finally part 6 mentions the limitations of the study together with some ideas for future research.

2

State of the art

Framework of Enablers for Integrating Sustainability in NPD

The study and the survey are constructed based on a framework from a previous study of the authors. The framework has 3 main components: Drivers/barriers, the enablers which foster efficient and effective integration of sustainability in NPD (i.e. strategic paradigms, supporting tools and manufacturing process paradigms) and impact of integrating sustainability in NPD on NPD performance measures, as shown in Figure 1 below [START_REF] Kerga | Integration of Sustainability in NPD Process: Italian Experiences[END_REF]:

NPD Process Paradigms

Analyzing NPD process paradigms concerns assessing how companies organize their NPD processes in such a way that sustainability is effectively integrated into product design. To design any product, some set of processes should be followed and types of processes depend on the type of products as well as companies' considerations of different aspects and related decisions in product development. Hence, the structure of a design and development process affects the sustainability performance of a product to be designed [START_REF] Hallstedt | A Foundation for Sustainable Product Development[END_REF][START_REF] Cooper | New Product Processes at Leading Industrial Firms[END_REF]. Conventional NPD process is generally structured in a sequential manner called serial engineering [START_REF] Cooper | Benchmarking the Firm's Critical Success Factors in New Product Development[END_REF]. Sequential design process models are characterized by freezing design specifications early in a design process so that designers have a single design option to discern till it reaches a control gate. At design gates, the design concept will be tested if it meets design requirements, and at that point if the design doesn't meet the requirements either design iterations or sub-optimal product will be the result [START_REF] Cooper | New Product Processes at Leading Industrial Firms[END_REF][START_REF] Cooper | Benchmarking the Firm's Critical Success Factors in New Product Development[END_REF][START_REF] Cooper | Maximizing Productivity in Product Innovation[END_REF]. Thus, companies first decide the fate of the product early in the process and problem will be revealed later at the design gates in such process models. If sustainable products need to be designed following such process paradigm, two problems will happen [START_REF] Melnyk | Integrating Environmental Concerns into the Design Process: The Gap between Theory and Practice[END_REF]; the first one is that, if the designers found that the product does not meet some environmental requirements at latter design gates they need to redesign again, which in turn affect time to market and incur additional cost for the company. Second, since environmental considerations are taken secondary in industries, once environmental problems have been found at the gates, designers overlook the problem and prefer to launch sub-optimal products from sustainability perspectives. Concurrent engineering (CE) was born to improve the problem of serial engineering approach of NPD process [START_REF] Winner | The role of Concurrent Engineering in Weapons System Acquisition[END_REF]. In CE, manufacturing engineers intervene in a design process to consider and improve the manufacturability of the design. Such NPD paradigm is more effective in addressing sustainability issue than sequential paradigm [START_REF] Hallstedt | A Foundation for Sustainable Product Development[END_REF]. Therefore, successful integration of sustainability in NPD depends on how NPD process is structured in a company. This phenomenon has been a focus of investigation for the companies surveyed in this paper.

Ecodesign Concept and Tools

Ecodesign is a practice by which environmental considerations are integrated into product and process engineering design procedures. Ecodesign practices are meant to develop environmentally compatible products and processes while maintaining product, price, performance and quality standards [START_REF] Graedel | Industrial Ecology[END_REF].

Many efforts have been made to develop tools that support integration of sustainability in NPD. The most powerful and prevalent tools used in sustainable product design are those which consider environmental aspect of sustainability, so called "eco-design tools". Many the so called eco-design tools and methods exist [START_REF] Devanathan | Integration of Sustainability into Early Design through the Function Impact Matrix[END_REF]: some are extremely simple and qualitative (such as checklists), while some are complex and quantitative (Such as LCA), and others based on QFD (such as Green QFD). The selection of the best tool for a given application depends on the individual situation of the context of the design and development process [START_REF] Taisch | Integration of Sustainability in Product Development Process: Supporting Tools[END_REF].

The simplest classification of tools is into those which perform data analysis, and those, which are aimed at improvement. Analysis tools provide a measurement of the potential environmental impact of a product. They are mostly used before design starts, by analyzing a previous product or that of a competitor. Alternatively, they may be used at the end of a design project to verify the result. Improvement tools, on the other hand, are used during the design process to direct activity and provide information on the process. Mistakes in selecting the most suitable tool depending on the specific situation may limit the effectiveness, usability and applicability of the tools. Criteria that should be taken into account during the selection of the adequate tools could be: the aim of conducting the study, the type of business or product considered, level of information available, the time available, the nature of data input, the quality of the expected results, the intended user and the design stage a tool is intended to be used (i.e. concept stages, system design level, embodiment design, and detail design) [START_REF] Sakao | Coordinating Ecodesign Methods in Early Stages of Industrial Product Design[END_REF].

In this study we have considered around 30 eco-design tools that have been found in the literature. In the survey, we investigated companies if they adopt these kind of tools in their practices and how efficient and effective they are in applying such tools.

Research Methodology

In this study, literature published in the last 15 years (1995-2010) have been studied, including academic journals, books and conference proceedings, to understand what have been written and practices in literature and industries till now to integrate sustainability in new product design. This literature review formed the basis to identify the research objectives and the structure of the survey questions. The investigation has been carried out by means of a questionnaire developed in alignment with the research objectives based on a framework to assess manufacturing companies operating in Italy in mechanical, electrical and automotive sectors. The analysis was carried out on 10 companies with high innovation cycles, which are subject to many product based EU legislations (i.e. WEEE, ELV, EuP, REACH, RoHS, and others).

The questionnaire was supported by 2 complementary case studies including face to face interviews and analyzing the internal documents, to increase the relevance of the work.

Survey Design and Procedures

Based on the research objectives and framework described in section 2.1 that identifies essential elements to successfully integrate sustainability and life-cycle thinking in NPD process, a questionnaire of 25 questions has been developed to assess the companies. This survey was composed of questions about company characteristics, sustainable strategies and applications of the company, ecodesign tools and relevant product development processes. The questionnaire has been approved after some revision phases in which some of the questions have been modified in order to simplify their understanding, and other questions have been added, in order to gain all the possible information aligned with our objectives. The expected recipients of the questionnaire were product development department responsible.

On-line version of the questionnaire has been created using Survey Monkey and was sent to companies via the following link: http://www.surveymonkey.com/s/ZD5ZLPR The on-line questionnaire has been proposed to over 200 contacts, of which 10 companies replied directly via the link provided by e-mail.

Survey Questions

Questionnaire was based on the framework to implement sustainability in new product development (NPD): So, questions have been identified considering the main components of the framework as listed below:

1. Drivers/Barriers:



B. Supporting tools

 Types of sustainability design tools used  Criteria to choose specific tools  The impact of using sustainability design tools on the NPD performances, etc.

C. NPD Process Paradigms

 Systematic integration of sustainability issues throughout a design process  Coordination between product's lifecycle partners  Product's lifecycle consideration  Exploration and utilization of past project's knowledge  Level of innovation adopted (e.g. product improvement, product redesign, new product concept, new product system, etc.)

NPD Performances

 Financial and non-financial benefits gained  Impact of integrating sustainability on the traditional NPD performances such as time to market and project costs  Internal changes due to sustainability consideration in NPD

Sample Firms and Response Collection

Questionnaire was sent to a combination of large companies and SMEs that might have already been integrating sustainability into their product design processes for several years. Sample firms were selected from manufacturing companies operating in Italy in mechanical, electric and automotive sectors. Although the questionnaire was proposed to over 200 companies, we got the responds from and analyzed 10 companies with high innovation cycles, which are subject to many product based EU legislations (i.e. REACH, RoHS, WEEE, EuP, ELV and others). The respondents were all relatively large companies. Some of the SMEs responded to mails to inform whether they don't consider this kind of approaches during product design or they are not interested in such activities. Thus, this information might be considered as a clue for a low-level adoption of sustainable practices and especially ecodesign tools among SMEs.

Complementary Case Studies

We carried out two complementary case studies to support the results achieved by the survey analysis. The aim was to collect relevant information about sustainability practices and sustainable product design processes of the companies via face to face interviews, analysis of their internal documents and going deeper in their responds to survey, as complementary to survey analysis. The two companies selected for case studies were globally known large enterprises; one automotive manufacturer and one tire manufacturer. Face to face interviews have been made with technical responsible in both cases. The other dimension of the analysis was to analyze the documents such as annual sustainability reports, sustainable strategy reports, etc. for supporting the results gained by the prior survey study.

Research Results and Discussion

First of all, almost 90% of the companies responded that they consider sustainability in NPD. However, the definitions of sustainability differ from company to company and most of them take sustainability and environmental consciousness as same without a comprehensive approach of sustainability as the balance between Economic-Environment-Social dimensions. However, the results demonstrate that companies still consider sustainability as a constraint rather than opportunity for eco-innovation. Furthermore, companies are trying to meet only the minimum requirements asked by legislations despite the efforts from academia side to drive strategic push, effective tools, and suitable NPD process paradigms to foster sustainable product innovations. In fact, companies won't be spending time and money in implementing sustainability unless government legislations forced them. Indeed, quality and cost seem to be the most important factors considered during product design. Environmental aspects and legal requirements are not the priority ones for the companies. Indeed, companies showed mostly used environmental parameters in product design as raw material consumption, energy consumption and energy efficiency, all of which can be directly related to costs. Companies implementing sustainability in NPD could have many reasons or drivers to do so. Among them; long-term benefits (i.e. image improvement, new market opportunities) and innovation potential, genuine environmental impact reduction, improved resource and process efficiency, customer demand due to increasing environmental consciousness, reduction of costs and risk are the reasons given by companies interviewed. In reality, most of the decisions and interest depend on either costs or long term plans as image improvement and entering to new markets. On the other hand, there are many barriers on the way of companies for implementing sustainability. Companies mentioned that the lack of time and budget to discern sustainability (in terms of investment in new or modified technologies, materials, etc.) in NPD are the most important barriers. Most of the companies interviewed have high level sustainability initiatives such as CSR (corporate social responsibility) strategic scheme, ISO14001 EMS (Environmental management system), and EH & S (Environment, health and safety) polices. This shows that top managements are also committed for overall sustainability of the industries. However, when it comes to the ground level, as of NPD, there is no evidence that sustainability is properly integrated in top-down approach. Almost all interviewed companies adopt only mandatory EPR (extended product responsibility) EU policies (i.e. REACH, RoHS, ELV, WEEE and EuP, etc.) which ask only minimum requirements to be fulfilled. Hence, the main focus is on the current legislation with little effort to impact future EU policies that might give further competitive advantage.

Investigating how tradeoffs are handled between Economic considerations (cost, performance, and functionality), environmental and social considerations gave us the possibility to check strategic alliances of sustainability in NPD. Therefore, companies seem to consider sustainability in a balanced way although high priority is given for economic considerations (about 50-60% importance comparing to environmental (30%) and social ones (20%)).

The level of investment for sustainable innovations shows that only 5-10% of total R&D budget is invested in average. This figure cannot be taken as absolute measure since 5-10 % might be huge for one industry and small for another. However, sustainable innovation level is limited to product upgrading or modification instead of investing in new and more sustainable materials and technologies. The reason why companies mostly talk about or direct to environmental commitment appears to be mostly a matter of marketing and advertisement. Even though top managements seem to focus on green marketing on strategic level, there is no evidence that sustainability is properly integrated in top-down approach when it comes to ground level, as of NPD.

Companies interviewed emphasized the fact that fully integrating sustainability in NPD projects cost them more than the gain they could have achieved. Moreover, time to market could be extended if sustainability issues are addressed effectively. As mentioned above, the reasons are mainly internal problems (lack of designers' knowledge, eco-design tools are time consuming, new innovations in terms of material and technology take time and huge investments). On the other hand, they also stress that non-financial gains have been achieved such as; new skill and competencies, company image, customer acceptances, and overall sensitivity towards environmental impacts have been raised inside the company. However, the performance benefits come with penalty in development cost and time to market. Therefore, the main issue here is how to structure NPD strategy, tools, and process in such a way those traditional NPD performances are either unaffected or even improved.

Although the selected companies have claimed that they adopted sustainability for so long (5-10 years), only six out of the ten companies adopted 'proper' eco design tools ranging from simple checklists (e.g. Banned material and chemical lists, disassembly lists and so on) to full or simplified LCA tools. LCA based, QFD based and checklist based tools are the most prevalent tools used in companies' practices. Most of the other tools present in the literature are not used and even sometimes not recognized by companies. This is probably due to the fact that current ecodesign tools are too much expert tools that are little adapted to designers' current needs, tools and practices. Indeed, the methods available in the literature are not good enough to support designers and there are few to help designers find solutions in Design for Environment (DFE) for variety of processes. That is to say, most of the current methodologies and tools serve in a fragmented way which limits designers in finding effective solutions to sustainability problems in product design. There is a huge gap here between literature and the applications of companies. In all likelihood, ecodesign has not been routinely practiced in design teams.

In real, companies have multiple criteria to choose among tools, and the important ones are: easy to implement and easy to learn, delivering accurate results, less amount of required information and less resources for the assessment. This shows that sophisticated ecodesign tools have little importance to bring sustainability to the mainstream NPD practices. Hence, there is a need to modify effective but sophisticated tools such as LCA (Life Cycle Assessment) so that they could be adopted more in new product design. Disseminating and introducing such tools to industry is a viable way to foster sustainability in product design.

Certainly, most eco-design projects fail for two main reasons according to the industries interviewed. The first one is due to insufficient information available and knowledge about the impact of complex product systems on the environment and society. The other one is the existence of many uncertainties in developing sustainable products such as: Suppliers' compliance issues, integrating manufacturing capabilities, and uncertainty about the market acceptance of the product by the customer. Although these reasons are obvious, proper attention should be given to deal with supply chain and lifecycle uncertainties for the success of ecodesign projects.

Many companies reported that they have life cycle view of the product they are designing and they consider all except logistic phase of a product life cycle (material extraction, manufacturing, use, and end of life phases). In particular, manufacturing is given high priority to be considered in design. This could be from the fact that CE is almost applied in all companies nowadays, and it is easy to coordinate and evaluate the manufacturing phase compared to other parts of the life cycle phase. Crucially, companies responded that they consider sustainability issues mostly at embodiment design phase (60% of the time) and detail or prototyping phase (30% of the time) and never at concept development stage. This gives an intriguing insight as designers have a lot of potential for sustainable innovation at concept design but they don't consider it at this phase. Moreover, design arrives at embodiment stage or prototyping stages after committing a lot of resources (time, cost). If sustainability targets are not met at these phases, designers tend to ignore them and prefer to launch inferior products, since sustainability requirements are considered as something additional comparing to time to market or cost. Even if designers want to improve the sustainability performance of the design, they need to re-iterate the process, which in fact is additional waste of time and cost. Last, in general companies have no means of using past product's knowledge to be used for future product development. This might hinder the continuous knowledge development inside the company about products' sustainability performances.

Conclusion

In this study, we assessed the companies in terms of their level of sustainability practices and found out that companies fail to implement sustainability in product design due to below reasons:

 Decisions depend mostly on cost factors.  Existent tools are not adapted to designers' needs (especially relevant tools not available for product design phase). Most of the tools present in the literature are not used and even sometimes not recognized by companies.  Companies especially SMEs consider it as a time consuming and costly activity.  Companies are mostly focused on improving processes instead of improving products by means of implementation in product design.  Companies are just trying to meet the minimum requirements asked by legislations despite the efforts from academia side to foster sustainable product innovation  Sustainability is not integrated during early design in most of the cases but in the later phases.  There is not enough coordination and cooperation between academia and industry, which might foster the use of applicable theoretical solutions in practice.

To sum up, cases in this study revealed that the consideration of sustainability is not matured enough to attain the general sustainability goal expected by multiple stakeholders. Thus, academia should not only focus on developing sophisticated tools but also on the need to investigate new way of NPD process structures and to better align strategy objectives with sustainability goals.

Limitations and Further Research

First of all, as most of the companies are not interested in such activities or do not apply such practices effectively, it is hard to make a detailed analysis on companies, especially on SMEs. So, it is hard to get respond to requests from the industry side. It is not so hard to see that there is a huge difference between what is in the literature and what is applied in companies' current practices. Another limitation lies in the companies' responds to the questionnaire. For many of the questions, intentional or unintentional bias would occur in the answers as some companies would be willing to see/show themselves more sustainable than what they really are. A potential weakness of the study is the impossibility to use a number of tools and techniques to compare the data obtained by our on-line survey. For example, because of the nature of the data (mostly qualitative) it is difficult to use a correlation analysis or other BI analysis techniques.

From this research, we realize that this topic is still at its earliest stage and the extensions of this research filed are unlimited. Here we recommend the following topics by worthy of further study:

 Further researches should be done taking more cases and samples to better understand the maturity level of integrating sustainability in new product design and development.  A modified or new method of integrating sustainability criterions into the product development processes that fill the existing gap would be developed for a better application in the industry.  Sustainable product design in a SBCE (Set Based Concurrent Engineering) environment would be studied.

Fig. 1 .

 1 Fig.1. Framework of enablers for successful integration of sustainability in NPD[START_REF] Kerga | Integration of Sustainability in NPD Process: Italian Experiences[END_REF]

Acknowledgement

This work was partly funded by the European Commission through the LeanPPD Project (NMP-2007-214090, www.leanppd.eu). The authors wish to acknowledge their gratitude and appreciation to the rest of the project partners for their contributions during the development of various ideas and concepts presented in this paper.


Julien Maheut

Jose P Garcia-Sabater

Josefa Mula
email: fmula@upv.es

The Generic Materials and Operations Planning (GMOP) problem solved iteratively: a case study in multi-site context

This paper addresses the Generic Materials and Operations Planning (GMOP) problem, a multi-site operations planning problem based on the "stroke" concept. The problem considers a multinational company subject to positive and negative backlogs imposed by using returnable racks that have to be filled by end products and transported to customers, alternative operations (purchase, transformation and transport), different BOM structures given the different operation types (injection operations, assembly operations) performed in the various factories of the supply chain, and capacitated production resources. This paper describes and defines the "stroke" construct that mathematically models the relationships between operations and materials. The mathematical modelling approach is provided, as is a brief description of an operations planning tool that has been implemented. Furthermore, some results obtained in a first-tier level supplier of the automotive industry have been introduced.

Introduction

One of the most well-accepted definitions in the literature of supply chain management (SCM) is that SCM is a task that involves integrating organisational units through the supply chain (SC) and coordinates the flow of material, information and financing for the purpose of fulfilling customer demands [START_REF] Stadtler | Supply Chain Management and Advanced Planning: Concepts, Models, Software and Case Studies[END_REF]. [START_REF] Dudek | Collaborative planning in supply chains. A negotiation-based approach[END_REF] states three SCM objectives: improve customer service; lower the amount of resources to serve customers; improve the SC's competitiveness. Improving competitiveness lies on two main pillars: integrating the SC and coordinating it [START_REF] Stadtler | Supply chain management and advanced planning--basics, overview and challenges[END_REF]. Many managers tend to think that Enterprise Requirement Planning (ERP) systems will solve their planning issues, but despite their name, ERP systems are usually transaction-based systems rather than planning systems. Traditional production planning methods, such as Material Requirements Planning (MRP), consider only availa-bility of materials, and completely ignore factors such as capacity limits and SC configurations [START_REF] Caridi | Trends in planning and control systems: APS -ERP Integration[END_REF]. In most software, alternative operations can be introduced as data, but the optimisation methods available do not consider them simultaneously. Moreover, packaging and its planning is a special concern in some industries and, to the best of our knowledge, ERP cannot plan them in any detail. Furthermore, operations planning functions in large companies are usually executed by different organisational units at distinct locations. Generally, excess inventories, poor customer service and insufficient capacity utilisation are due to the lack of coordination between these operations planning functions. Broadly extended ERP systems have led to the emergence of the so-called Advanced Planning and Scheduling Systems (APS), which may be viewed as "add-ons" of the ERP system to plan and optimise the SC. For this support, APS uses optimisation techniques to model and determine the quantities to be produced, stored, transported, and procured by respecting the SC's real constraints [START_REF] Garcia-Sabater | A two-stage sequential planning scheme for integrated operations planning and scheduling system using MILP: the case of an engine assembler[END_REF][START_REF] Günther | Supply chain planning and Advanced Planning Systems[END_REF].

The commonest name with which to consider the mathematical model that simultaneously solves the materials and operations planning problem is the Multi-level Capacitated Lot-Sizing Problem (MLCLSP). All in all, most works on the MLCLSP still assume that BOM is made up of assembly products. A series of problem variants based on amending the structure of BOMs may also be found in practice and in the literature. In [START_REF] Garcia-Sabater | A new formulation technique to model Materials and Operations Planning: the Generic Materials and Operations Planning (GMOP) Problem[END_REF], an extensive literature review about the MLCLSP and the need to use the stroke concept in the GMOP problem is introduced. In (Maheut and Garcia-Sabater 2011), a variant of the GMOP problem is introduced, which considers scheduled receptions and the initial stock level. Nevertheless, to the best of our knowledge, a case study about the multi-site, multi-level, capacitated operations planning problem with lead times that simultaneously considers alternative operations (purchasing, transport -replenishment, transshipments and distributionand production) and returnable packaging has not yet been studied.

This paper proposes an alternative modelling technique that stresses what is known to be done rather than the result of the action (the product). The proposed modelling method is useful given its simplicity and generality. Furthermore, its proposal is feasible since the mathematical programming solving technology has considerably improved in the last 10 years. The model's objective is to minimise total costs by fulfilling lead times and by considering alternative operations and returnable racks. The model has been designed for a first-tier level company of the automotive sector and operations plans are performed daily.

2

The "stroke" concept

To consider this proposal, it is necessary to specify some concepts. Products must consider the site where they are stored at and also their packaging. This implies loss of generality, which is compensated by simplified data loading. For example:

-Part item "01" stored in factory A will be called P01@A, -Rack "01" filled with 12 "02" part items stored in factory B will be called R01#12P02@A, -Empty rack "01" in factory C will be considered R01#00@C.

Each stroke corresponds to a specific located operation [START_REF] Maheut | A supply Chain Operations Lot-Sizing and Scheduling Model with Alternative Operations[END_REF]. It is characterised by the use of located resources. A set of products is assigned to each stroke, which is consumed when a stroke unit is executed. This set (known as "stroke input") can be null, unitary or multiple, while its coefficients (the Gozinto factor) can be above one unit. A set of SKUs is assigned to each stroke, which is produced when a stroke unit is carried out. This set (called "stroke output") can consist in several different items, a single item or none, and its coefficients (amount of each item produced) can be above one unit [START_REF] Garcia-Sabater | A new formulation technique to model Materials and Operations Planning: the Generic Materials and Operations Planning (GMOP) Problem[END_REF]. Moreover, lead times, setup times and costs, time consummation and the costs of performing one stroke unit are assigned to the stroke and not to the result of the operation. Resources are associated with each stroke, but not with the product (or the series of products) obtained.

Mathematical formulation of the GMOP problem

Due to software limitations, the problem is solved on an iterative basis. Therefore, the GMOP problem was modelled by considering that each stroke level, or each stroke, was independent of the rest. The GMOP model presented herein has been, therefore, slightly modified to represent this new approach. To mathematically formulate the problem, it is necessary to define the nomenclature presented in Table 1. Quantity of i that it is to be delivered at the end of period t q it, Quantity of demand of product i at the end of period t that it is not to be delivered w it, Requirements of product i at the end of period t Binary variable which indicates if stroke k is set up in period t

Positive/negative backlog of product i in period t

The GMOP problem adapted for an iterative resolution can be formulated as shown below:

        , , , , 1 1 1
, , ,

T T T F C it it it it i t i t i t i t it it k kt k kt i P t i P t k Z t Maximize F o z y P o P w C C H y CO z CS                                  (1) Subject to ,, , , 1,..., it i t i t o q D i P i FP t T      (2)   , 1 , ( ) , ,
, , 2,...,

rec it i t it ik k t LT k ik kt i t i t kZ y y X SO z SI z CA o i P i FP t T               (3)   , 1 , 1 , ( ) , , 2,..., rec it it i t i t it ik k t LT k i t kZ X SO z q i FP t T                       (4) kr TO kr TS rt K M k CO k CS ik SO ik SI () LT k i B , , i t i t C C     kt  , , i t i t       0 0 ,1 ,1 ,1 ,3 ,1 ,1
,

rec i i i ik k ik k i i kL y Y X SO z SI z CA o i P i FP             (5)   0 0 ,1 ,1 ,1 ,1 1 rec i i i i ik k i kL B X SO z q i FP            (6)   , ,1 , , i t ik k i t k w SI z X i FP t      (7) 0 , 1,..., kt kt z M k Z t T       (8)   , 1,..., r k kt k kt rt kZ TO z TS K r R t T          (9) 0 , 1,..., kt z k Z t T     (10) , , , ,
, , , , 0 , 1,...,

i t i t i t it it it o q w y i P t T      (11)   0,1 , 1,..., kt k Z t T     (12)
Objective ( 1) is to maximise the profit of delivering products minus the sum of the storage costs, the stroke execution costs, the stroke setup costs, and the positive (classical) and negative (serving in advance) backlogging costs. Equation ( 2) splits external demand into real sales and the demand that is to be delayed. Equations ( 3) and ( 5) provide the continuity equation of the inventory levels. The inventory level at the end of a period considers the inventory level at the end of the previous period, planned receptions, product demand, and the products generated and consumed after executing those strokes with their associated lead times. Equations ( 4) and ( 6) provide the continuity equation of the backlogging levels. Two types of backlogs exist: the traditional positive backlog (also called Delay at the shipment level or the underdelivery level) and the negative backlog (also called Serve in Advance or the overdelivery level). Given the difference with inventory levels, Backlogging levels are generally applied to the product in the inventory at customers' locations. Backlog levels are the determined inventory levels of products based on demand plans, but they do not have to be physical inventory levels in plans. This concept is regularly used in the automotive industry because products are sent in packaging (pallets or racks). In this case, if demand is regular and not proportional to the packaging capacity because of the cost of negative backlogging and the policy of optimising resources, packaging is fulfilled and a negative backlog level is generated. Constraint (9) evaluates the quantity of products i that should be acquired in order to fulfill requirements. Constraint ( 8) is introduced to know if stroke k is produced in t by, therefore, employing the capacity associated with the setup (setup forcing). Constraint ( 9) is a capacity constraint that limits the use of resource r in period t by considering both the setup and operations times. Constraints (10), ( 11) and ( 12) define the range of variables.

The model is solved iteratively for each product with internal or external demand. The value of o will be converted for the following iterations into a constant CA since it has been accepted. The value of w will be converted into new demand that will be fulfilled in subsequent iterations.

4

Case study

This model is implemented if it is particularly motivated by the problem faced by a company manufacturing plastic products from two factories located in Spain and which sells the product in this country. Production management develops a 3-month operations plan by considering the inventory level, resources capacity, routes and packaging availability to fulfill demand.

A specific operations planning tool has been deployed by the ROGLE research Group. The development process of the information system has been carried out completely. The system not only includes the model presented herein, but also other features related with SC activities, like Demand Planning or Scheduling tasks. The software runs beyond the official ERP system. To obtain data from it and to generate a parallel database that stores official company data and the rest of parameters that need to be used, specific connections were created using XML files. Users interact with the software by using standard browsers (to activate and input data) and spreadsheets (to analyse and use the results). The operations plan consists in listing those operations with quantities to be performed with the different resources in the various factories for each time period of the horizon in order to serve customers in terms of time and quantity. Basically, operations are:

-Purchase operations, which determine the amount of raw material (plastic powder) to be purchased in each period by considering different lot sizes. -The raw material is injected into a press injection machine and different products are obtained depending on the mould used.

-After injecting the obtained products, they are assembled on an assembly line to obtain the end products. -End products must be stored in filled returnable racks and are transported to the customer's site. Figure 1 displays a sharp drop in backlog levels. Throughout the horizon, a negative backlog is maintained because customers force the company to maintain a safety backlog level. Thanks to the operations planning tools, the company has been able to cut its overdelivery costs, while demand levels remain constant. In fact, this reduction might be considered the effect of simply applying the MRP concept.

With the software, we solved the GMOP problem by employing LP Solve IDE. We tested performance in a full-sized case study problem with seven different factories with approximately 500 end products, 30 resources and more than 700 different operations for distinct instances. The results show an average running time of 6 hours, for instance using a Pentium IV 1.22 GHz processor, 2 GB RAM and Windows XP as the OS.

Fig. 1 .

 1 Fig. 1. Demand and Backlog levels

Table 1 .

 1 Table 2 contains the notations per parameter and Table 3 presents the notations per variable. Sets and indices

	Symbol	Definition
	iP 		Index set of products (includes product, packaging and site)
	r R 		Index set of resources (includes product and site)
	k Z 		Index set of strokes (includes stroke and site)
	j J 		Index set of sites
	t		1,...,	T	Index set of planning periods
	Z	r			Set of strokes that are performed in resource r 	Z	r		Z	
	FP			Set of end-products 	FP P 	

Table 2 .

 2 Parameter notation Capacity required of resource r required for the setup of stroke k (in time units) Capacity available of resource r in period t (in space units) A sufficiently large number Cost of performing one stroke k unit Cost of the setup of stroke k Number of product i units produced by performing one stroke k unit (stroke output) Number of product h units required for performing one stroke k unit (stroke input) Lead time of stroke k Initial backlog of product i Cost of positive/negative backlogging for one unit of i in period t

	Symbol	Definition
	D	Demand of product i in period t (due date)
			it
	, it CA	Acquired compromised in product i in period t (due date)
	X	rec it	Planned reception for products i in period t
	H	Non-negative holding cost per period for storing one unit of prod-
			i
				uct i
	i Y	0	Initial inventory of product i
	P	F	Benefit of delivering product i
		i
	P	P	Cost of purchasing product i
		i

Table 3 .

 3 Variable notation

	Symbol Definition
	z

kt Quantity of strokes k to be performed in period t y it, Inventory of product i at the end of period t o it,

Acknowlegments

The work described in this paper has been supported by the "CORSARI MAGIC DPI2010-18243" project from the Spanish Ministry of Science and Innovation within the Programme entitled "Proyectos de Investigación Fundamental No Orientada". Julien Maheut holds a VALi+d grant funded by the Generalitad Valenciana (Regional Valencian Government), Spain (Ref. ACIF/2010/222).


Jafar Rezaei
email: j.rezaei@tudelft.nl

J Roland Ortt
email: j.r.ortt@tudelft.nl

Two Multi-criteria Approaches to Supplier Segmentation

Keywords: supplier segmentation, supplier relationship management, buyersupplier relationship, fuzzy rule-based system, linear programming, DEA

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction and review of literature

Supplier relationship management (SRM) provides a structure for firms to develop and maintain relationships with their suppliers [START_REF]Supply chain management: Process, partnership, performance, 3th edition[END_REF]. SRM does not refer to managing individual relationships with suppliers, but means that different groups of suppliers, each of which with different characteristics, can be handled in different ways [START_REF] Wagner | Configuring and managing strategic supplier portfolios[END_REF]. A close relationship should be developed and maintained with key suppliers, whereas the traditional procurement strategies may be adopted for other suppliers. Supplier segmentation is a prerequisite for SRM, it provides a framework to identify different groups of suppliers.

Compared to customer segmentation [START_REF] Smith | Product differentiation and market segmentation as alternative marketing strategies[END_REF], supplier segmentation has received relatively little attention. Customer segmentation is aimed at dealing with heterogeneity on the demand side of the market, while supplier segmentation focuses on the supply side of the market [START_REF] Erevelles | Enhancing the business-to-business supply chain: Insights from partitioning the supply-side[END_REF].

The term supplier segmentation originated in early 1980s, when Parasuraman [START_REF] Parasuraman | Vendor segmentation: An additional level of market segmentation[END_REF] and Kraljic [START_REF] Kraljic | Purchasing must become supply management[END_REF] proposed two different approaches to supplier segmentation. Parasuraman [START_REF] Parasuraman | Vendor segmentation: An additional level of market segmentation[END_REF] proposed a four-step process for supplier segmentation: (1) Key features of customer segments are identified; (2) Key characteristics of suppliers are identified; (3) Relevant variables for supplier segmentation are selected; and (4) Suppliers are segmented based on these variables. Parasuraman [START_REF] Parasuraman | Vendor segmentation: An additional level of market segmentation[END_REF] did not specify the variables to segment the suppliers. By contrast, Kraljic [START_REF] Kraljic | Purchasing must become supply management[END_REF] pre-specified the segmentation variables when he proposed two dimensions, profit impact and supply risk, for segmenting suppliers, which are measured for different products supplied to a firm. Considering two levels (low and high) for each dimension a 2×2 matrix distinguishes four segments: (1) Non-critical items (supply risk: low; profit impact: low); (2) Leverage items (supply risk: low; profit impact: high); (3) Bottleneck items (supply risk: high; profit impact: low); and (4) Strategic items (supply risk: high; profit impact: high). Kraljic [START_REF] Kraljic | Purchasing must become supply management[END_REF] then suggested different strategies for handling these supplier segments. Kraljic's approach [START_REF] Kraljic | Purchasing must become supply management[END_REF] is extended by several researchers. For example, Olsen and Ellram [START_REF] Olsen | A portfolio approach to supplier relationships[END_REF] proposed a supplier segmentation based on two dimensions: difficulty of managing the purchase situation, and strategic importance of the purchase. Bensaou [START_REF] Bensaou | Portfolios of buyer-supplier relationships[END_REF] considered two other dimensions: the supplier's specific investments and the buyer's specific investments. Kaufman et al.' segmentation [START_REF] Kaufman | Collaboration and technology linkages: a strategic supplier typology[END_REF] was based on two dimensions: technology, and collaboration. Supplier commitment and commodity importance are the two dimensions of Svensson' approach [START_REF] Svensson | Supplier segmentation in the automotive industry: A dyadic approach of a managerial model[END_REF]. Hallikas et al. [START_REF] Hallikas | Risk-based classification of supplier relationships[END_REF] used supplier dependency risk and buyer dependency risk as the two dimensions of their proposed approach. For a discussion of supplier segmentation approaches, see Rezaei and Ortt [START_REF] Rezaei | A multi-variable approach to supplier segmentation[END_REF].

Several two-dimensional approaches have been proposed for supplier segmentation, each of which includes some important segmentation variables, while neglecting some other important ones. The shortcoming of the approaches can lead to a lack of homogeneity within segments and a lack of heterogeneity between supplier segments. Recently, Rezaei and Ortt [START_REF] Rezaei | A multi-variable approach to supplier segmentation[END_REF] have proposed a supplier segmentation framework that consists of two overarching dimensions: supplier capabilities and supplier willingness. They define supplier capabilities and supplier willingness as follows: "Supplier's capabilities are complex bundles of skills and accumulated knowledge, exercised through organisational processes that enable firms to co-ordinate activities and make use of their assets in different business functions that are important for a buyer." "Supplier's willingness is confidence, commitment and motivation to engage in a (long-term) relationship with a buyer".

These two dimensions encompass almost all of the variables previously proposed for supplier segmentation. Methods to measure and combine the variables in each of the dimensions are proposed to satisfy another general requirement of a segmentation approach: measurability. This approach also creates a connection between different supplier-related activities such as supplier relationship management and supplier development, in the supply chain management framework. Finally, this approach enables a buying firm to explicitly assess the combination of segmentation variables that best fit its specific company, supplier and market conditions.

In this paper, we adopt the supplier segmentation framework proposed by Rezaei and Ortt [START_REF] Rezaei | A multi-variable approach to supplier segmentation[END_REF]. To measure and integrate the variables of the different dimensions, we apply a fuzzy rule-based system and a DEA-like linear programming model, which are briefly discussed in section 2 and 3 respectively. In section 4, the two approaches are illustrated for the suppliers of a broiler company. The managerial implications of the outcomes are discussed and future work is described in section 5.

Fuzzy rule-based system

A fuzzy rule-based system [START_REF] Jang | ANFIS: Adaptive-Network-Based Fuzzy Inference System[END_REF] is a system that is used to govern the relationship between input and output variables. Here, supplier capabilities and willingness are considered as the output of two fuzzy rule-based systems, while the criteria used to evaluate the different dimensions serve as input. First of all, based on expert knowledge, these variables are fuzzified, which means that linguistic values (fuzzy subsets) are used (like low, medium and high) and fuzzy numbers are formed for each linguistic value. Secondly, a fuzzy rule base is provided based on the expert knowledge. These rules make a logic connection between different linguistic values that have been defined for input and output variables. A typical fuzzy rule has the form: IF antecedent THEN consequent. The number of rules is a function of the number of input variables and the number of linguistic values defined for inputs. If we have n inputs and k linguistic values for each input, then the total number of rules is . Next, a fuzzy inference engine should be designed. The evaluation of a rule is based on computing the truth value of its premise part and applying it to its conclusion part. This results in assigning one fuzzy subset to each output variable of the rule. This inference engine performs mathematical computations based on the fuzzy numbers. As the final operation of a fuzzy inference system, the fuzzy output produced by the system is converted to a crisp number. More information about fuzzy rule-based systems can be found in [START_REF] Jang | ANFIS: Adaptive-Network-Based Fuzzy Inference System[END_REF][START_REF] Ross | Fuzzy logic with engineering applications[END_REF].

Data Envelopment Analysis (DEA)-like

Here, we describe a simple DEA-like linear programming model introduced by Rezaei et al. [START_REF] Rezaei | Measuring entrepreneurship: Expert-based vs. data-based methodologies[END_REF]. Suppose we have N suppliers. The level of willingness of supplier i (Ei) is seen as the sum product of its item measures by their weights (∑

). We can measure the level of capabilities of the supplier in the same formulation. Now, if supplier i is allowed to maximize its level of willingness/capabilities, providing the level of willingness/capabilities of other suppliers do not exceed 1, then the calculated maximum level of willingness/capabilities of this supplier denotes its relative willingness/capabilities. The mathematical programming model for supplier i is as follows.

( ) ∑ (1) s.t. ∑ (N is the number of suppliers) (J is the number of items) Solving N models for supplier willingness, and N models for supplier capabilities, the relative level of willingness and capabilities for each supplier are determined in the range of [0,1]. The results can then be used as a base to segment suppliers. For example if we consider the middle of the range of supplier willingness and supplier capabilities scores as two cut-off points, then we can form two levels for willingness and capability scores and combine them to segment the suppliers into four segments.

Implementation of the approaches, and discussion

In this section, we describe the implementation of the supplier segmentation using the two approaches discussed above: (1) A fuzzy rule-based system, and (2) a DEA-like linear programming model for a broiler company.

The broiler company receives newly hatched chicks, feed, medications and other equipment and materials from 43 suppliers. The company raises the chicks to market weight in about six weeks and the chickens are then delivered to a processing plant to be stunned and undergo further processing. To manage the relationship with a large number of suppliers, the broiler company needs to segment them. Interviewing the managers of the company yielded six criteria (price, delivery, quality, reserve capacity, geographical location and financial position) for measuring the supplier's capabilities, and another six criteria (commitment to quality, communication openness, reciprocal arrangement, willingness to share information, supplier's effort in promoting JIT principles, and long term relationship) for measuring the supplier's willingness (to see a comprehensive list of the relevant criteria and their selection procedure, see [START_REF] Rezaei | A multi-variable approach to supplier segmentation[END_REF]). We then asked the manager to evaluate all the suppliers using scores between 1 (very low) to 5 (very high) for all criteria.

The rule-based systems

To measure the aggregated degree of supplier's capabilities and supplier's willingness, we designed two fuzzy rule-based systems each of which consists of six input variables and a single output. To fuzzify the variables we considered two fuzzy subsets (e.g., Low and High, or Bad and Good) and their equivalent triangular membership function based on the knowledge of the company manager and two experts. The intended fuzzy rule-based systems are shown in Fig. 1.

Considering the number of criteria and the number of fuzzy subsets, we had to make rules for each system. Below, an example rule of the second system is presented that is designed to measure a supplier's willingness.

"IF 'supplier's commitment to quality' is Low AND 'communication openness' is Low AND 'reciprocal arrangement' is Low AND 'willingness to share information' is Low AND 'supplier's effort in promoting JIT principles' is High AND 'length of relationship is Short, THEN supplier's willingness is Low"

This rule shows how particular values (i.e., high or low) of the criteria are combined into an overall value for supplier willingness. We then use the inference engine developed by Mamdani and Assilian [START_REF] Mamdani | An experiment in linguistic synthesis with a fuzzy logic controller[END_REF] by applying a compositional minimum operator, which represents a conservative attitude towards measuring the supplier's capabilities and willingness. At a minimum inferencing, the entire strength of the rule is considered as the minimum membership value of the input variables' membership values.

{ } The output of the fuzzy inference engine is a fuzzy number that needs to be defuzzified. We applied the Center of Gravity (COG) defuzzification method, one of the most commonly used defuzzification methods, as follows:

∫ ( ) ∫ ( ) (2)
where is the representative value of the fuzzy subset member i of the output, and ( ) is the confidence in that member (membership value) and is the crisp value of the output.

To calculate the final aggregated scores, we used MATLAB's Fuzzy Logic Toolbox. Based on the two final scores for each supplier, the suppliers are assigned to four segments (see the left side of Fig. 2) (it is, however, clear that more segments can be formed). Of the 43 suppliers, three are segmented as Type 1 (low capabilities and low willingness), nine as Type 2 (low capabilities and high willingness), three as Type 3 (high capabilities, and low willingness) and, finally, 28 as Type 4 (high capabilities, and high willingness).

DEA-like linear programming model

To measure the aggregated degree of a supplier's willingness and capabilities, we formulate 86 linear programming problems of type [START_REF]Supply chain management: Process, partnership, performance, 3th edition[END_REF]. That is to say, two linear programming problems for each supplier are formulated and solved: one to determine the relative willingness and one to determine the relative capabilities of the supplier. As such, two aggregated scores are obtained for each supplier in the range of [0, 1]. Considering the actual minimum and maximum aggregated scores for supplier willingness and capabilities, two cut-off points are determined to divide the suppliers into four segments. In our case, the minimum and maximum aggregated scores for supplier willingness are 0.6 and 1.0 respectively. The minimum and maximum aggregated scores for supplier capabilities are 0.8 and 1.0 respectively. Therefore, we determined 0.8 and 0.9 as the cut-off points for supplier willingness and supplier capabilities, respectively, as a base to segment the suppliers to four segments (see Fig. 2). Of the 43 suppliers, four are identified as being Type 1 (low capabilities and low willingness), nine as Type 2 (low capabilities and high willingness), two as Type 3 (high capabilities and low willingness) and, finally, 28 as Type 4 (high capabilities and high willingness).

As can be seen from the right side of Fig. 2, the number of suppliers assigned to each segment is almost the same in the two approaches, but there are some differences. For example, both approaches assign 28 suppliers to segment Type 4. However, only 22 of these 28 suppliers are assigned to this segment in both cases, which has to with weight of the various criteria.

Managerial implications

Generally speaking, firms can use our approach to formulate different strategies for handling different segments. Our approach condenses a comprehensive set of segmentation criteria into two overarching dimensions: supplier willingness and supplier capabilities. The values that specific suppliers assign to on these dimensions are subsequently used to segment the suppliers. In this article, we created 2×2 = 4 segments. Each of these segments requires a different strategy from the buying company. Type 4 suppliers, for example, are the most capable suppliers who are also highly willing to cooperate with the buying firm. However, because of their capabilities, they are likely to be attractive to other firms as well. Therefore, the firm in question should try to maintain strong relationships with those suppliers. Type 3 suppliers are also highly capable, but they are less willing to cooperate with the firm. The firm should try and become more attractive to these suppliers and show greater loyalty, for example by increasing communication and purchase volume. Type 2 suppliers are very willing to cooperate, but less able to meet the buyer's requirements. A general suggestion is to help these suppliers improve their capabilities and performance. Finally, Type 1 suppliers are less capable and less willing to cooperate with the firm. In all likelihood, it is best to maintain an arm's length relationship to manage the relationship with these suppliers.

Type 2 In addition, strategies can be formulated to improve the (capabilities or willingness of) suppliers and thereby upgrade them to other segments. The main supplier development strategies mentioned by Krause et al. [START_REF] Krause | A Structural Analysis of the Effectiveness of Buying Firms' Strategies to Improve Supplier Performance[END_REF] are: supplier assessment, providing suppliers with incentives for improved performance, instigating competition among suppliers, and direct involvement of the buying firm's personnel with suppliers. These strategies to a large extent focus on improving capabilities. Although, as a result of these strategies, supplier willingness may also increase; specific strategies can be used that focus specifically on this aspect. We believe that the key concept here is trust. Trust is a crucial component in the dimension of supplier willingness. As has been argued in various studies (e.g. [START_REF] Doney | An Examination of the Nature of Trust in Buyer-Seller Relationships[END_REF]), a buyer's trust in a supplier can enhance that supplier's willingness to share information, make investments specifically with regard to the buying firm and maintain a long-term relationship.

These strategies can be implemented to promote suppliers in segment Type 1 to segment Type 3, for example. Type 4 suppliers are key suppliers with whom a firm should try to maintain a close long-term relationship.

Specifically, the analysis yielded interesting insights into some of the broiler company's suppliers. Some suppliers with low scores on both dimensions were nevertheless allowed to continue as suppliers to meet seasonal peaks in demand. The company has already started implementing strategies to manage the relationship with its suppliers, and to develop those who are segmented as Type 1 to 3, especially Type 2 and 3.

Conclusion

In this paper, we proposed two multi-criteria methodologies to measure supplier capabilities and willingness: A fuzzy rule-based system and a DEA-like linear programming model. The final scores of these two dimensions are used to divide suppliers into four segments. Supplier segmentation allows firms to maximize its efforts to formulate suitable strategies for handling different suppliers. The approaches to assess the suppliers' positions on the dimensions of capability and willingness help connect the related activities of supplier selection, supplier relationship management and supplier development. The rule-based approach proved a very flexible approach that can be designed by interviewing a limited number of knowledgeable managers or experts within the company. It has some advantages over other methods, such as the ability to handle the inherent interdependencies, vagueness and contingencies of segmentation variables. The DEA-like methodology, on the other hand, is a data-based methodology that requires a minimum number of data [START_REF] Rezaei | Measuring entrepreneurship: Expert-based vs. data-based methodologies[END_REF]. However, it is more flexible in terms of weighting the criteria. Both approaches are suitable when a high data volume is not available and advanced statistical methodologies are not possible.

As pointed out by several researchers (e.g. [START_REF] Wilkinson | Business mating: Who chooses and who gets chosen?[END_REF]), matching certain characteristics between buyers and suppliers is an important factor in the success of their partnerships. Therefore, as a future research direction, we suggest studying the relationship between symmetry in capabilities and willingness between various buyer and supplier segments and partnership success. It is interesting to compare the proportion of different segments for different industries and situations. We also suggest integrating supplier segmentation into other supplier-related activities, such as 'lot-sizing with sup-plier selection' [START_REF] Rezaei | Multi-objective models for lot-sizing with supplier selection[END_REF]. Finally, we suggest studying the relationship between partnership with suppliers from different segments and firm performance.

Fig. 1 .

 1 Fig. 1. Fuzzy rule-based systems (FS). Left: FS1 (capabilities); Right: FS2 (willingness).

Fig. 2 .

 2 Fig. 2. The final supplier segmentation results; Left: fuzzy rule-based, Right: DEA-like.