Kwabena Agyapong-Kodua

Bilal M Wahid
email: b.m.wahid@lboro.ac.uk

R H Weston
email: r.h.weston@lboro.ac.uk

integrated process cost modelling technique for complex manufacturing systems

Keywords: Cost modelling, Manufacturing Enterprises (MEs), Enterprise Modelling (EM), Simulation Modelling (SM), complexities

Towards the derivation of an integrated process cost modelling technique for complex manufacturing systems

Introduction

Cost Engineering and its associated modelling techniques have been used dominantly in research and academia to support cost estimation of projects, lifecycle analysis, technology down selection and assessment of economic viability of engineering projects [START_REF] Humphreys | Basic Cost Engineering[END_REF]. Because of inherent complexities and dynamics associated with current design and production systems, it is fairly difficult to estimate, control and monitor cost consumption appropriately and instantaneousness without incurring errors [START_REF] Son | A cost estimation model for advanced manufacturing systems[END_REF][START_REF] Wiendahl | Simulation based analysis of complex production systems with methods of nonlinear dynamics[END_REF]. A study reported by Maskell [START_REF] Maskell | Performance Measurement for World Class Manufacturing -A model for American Companies[END_REF] shows that cost estimations in MEs have become very complex since the adoption of IT systems. In essence, manufacturing practices have advanced tremendously, making traditional cost accounting practices unsuitable for dynamic manufacturing environments [START_REF] Agyapong-Kodua | Process cost modelling in Manufacturing Enterprises[END_REF]).

This paper is centred on: 1) reviewing current cost modelling methods; 2) observing advancement in manufacturing practices and 3) based on understandings gained from 1) and 2), specifying requirements for a next generation cost modelling methodology. A State of the Art (SOA) survey on current methods and processes for cost modelling in academia and industry is reported. Based on the observed limitations of existing cost modelling techniques in the literature, and with an understanding of the needs of MEs, a new cost modelling method capable of meeting the requirements for effective cost modelling in MEs is proposed. The authors are of the view that the proposed cost modelling method is capable of managing aspects of risk, uncertainty, change and complexities associated with dynamic MEs.

Development of cost modelling practices in Manufacturing Industries

In general terms, manufacturing industries have moved from highly data-driven environments to more cooperative information-driven environments, taking into account more of enterprise knowhow, commonsense and application semantics [START_REF] Vernadat | Enterprise modelling and integration; Principles and Applications[END_REF]Agyapong-Kodua 2009). In recent times, cost engineering principles and modelling methods have been applied by some researchers to support cost estimation, business analysis and planning, project management, profitability analysis and scheduling of major engineering projects (Curran, Raghunathan et al. 2004).

However in most environments today, Business Administrators and Economists take hold of the overall business planning and management, pushing the cost engineer into his core elements of cost estimation, scheduling and cost control [START_REF] Samid | Computer-organized Cost Engineering[END_REF]).

To effectively estimate and control cost in manufacturing environments, three sub layers have been recommended [START_REF] Liebers | An architecture for cost control, the use of cost information in order-related decisions[END_REF]). These are: 1) production monitoring; 2) cost calculation and evaluation; and 3) cost modelling. Many researchers [START_REF] Roy | Cost estimating and risk analysis in manufacturing processes[END_REF]Rush and Roy 2000;[START_REF] Curran | Development of an aircraft cost estimating model for program cost rationalisation[END_REF]Agyapong-Kodua 2009) in the domain of cost engineering have reported that many cost estimating projects broadly consist of: 1) first sight estimate, usually at the early stage of the design process and 2) detailed estimate for precision costing. They explained that first sight estimates are suitable for 'Rough Order Magnitude' (ROM) estimates [START_REF] Curran | Development of an aircraft cost estimating model for program cost rationalisation[END_REF] and provide good background for initial product definition but are not very useful for detail product specifications and manufacturing process designs and optimization (Curran, Raghunathan et al. 2004;[START_REF] Agyapong-Kodua | Process cost modelling in Manufacturing Enterprises[END_REF]). The next section is dedicated to reviewing State of the Art (SOA) cost modelling systems as expressed in academia and industries.

SOA survey of cost modelling methods

The Association of Cost Engineers (ACE) has indicated that because of the increased changes in manufacturing industries and the need to adjust product designs and manufacturing systems to meet market needs, Cost Engineers are required to play key roles in cost estimation and control. To achieve this, scientific methods and frameworks are required to capture existing data and using the existing data to generate estimates that are timely, relevant and meaningful [START_REF] Rush | Expert judgement in cost estimating: modelling the reasoning process[END_REF].

Cost modelling provides the platform on which cost estimation and project planning Derivation of process cost modelling technique may be built [START_REF] Roy | Development of airframe engineering CER's for aerostructures[END_REF]. Also researchers in the domain of enterprise and systems engineering [START_REF] Bernus | Enterprise integration-engineering tools for designing enterprises[END_REF][START_REF] Kosanke | Process oriented presentation of modelling methodologies[END_REF][START_REF] Baines | A consideration of modelling techniques that can be used to evaluate manufacturing strategies[END_REF][START_REF] Weston | A model-driven, component-based approach to reconfiguring manufacturing software systems[END_REF][START_REF] Agyapong-Kodua | Modelling dynamic value streams in support of process design and evaluation[END_REF]) have proposed that to scientifically support cost control and modelling, especially in complex and dynamic organizations or industries, there is the need to develop well structured enterprise models to form the baseline for process analysis. Such models represent organizations as fairly independent sets of processes with interacting entities and flows which can be (re)designed to meet corporate objectives [START_REF] Ajaefobi | Human Systems Modelling in support of Enhanced Process Realisation[END_REF][START_REF] Cen/Iso ; Chatha | Combined Enterprise & Simulation Modelling in support of Process Engineering[END_REF]. In specific terms, some researchers in Cost Engineering [START_REF] Johnson | Relevance Lost -The Rise and Fall of Management Accounting[END_REF][START_REF] Beltramo | Beyond parametrics: the role of subjectivity in cost models[END_REF][START_REF] Son | A cost estimation model for advanced manufacturing systems[END_REF][START_REF] Asiedu | Simulation-based cost estimation under economic uncertainty using kernel estimators[END_REF]Curran, Raghunathan et al. 2004;[START_REF] Agyapong-Kodua | Process cost modelling in Manufacturing Enterprises[END_REF][START_REF] Caputo | Parametric and neural methods for cost estimation of process vessels[END_REF] have proposed and tested several cost estimating, production monitoring, cost calculation and evaluation and cost modelling techniques which are currently being used in academia and industry. The following sections provide a detailed review of some of these techniques.

A formal classification of cost modelling methods was provided by Boehm [START_REF] Boehm | Software Engineering Economics[END_REF]. In his extensive research on the economics of software engineering, he classified and described 7 cost modelling techniques as: 1) Parametric; 2) Expert judgement; 3) Analogy; 4) Parkinson; 5) Price to win; 6) Top down; and 7) Bottomup. Later researchers such as Hughes (Hughes 1996) and Curran (Curran, Raghunathan et al. 2004) can broadly be classified as intuitive, parametric, variant-based and generative.

However from a methodological point of view, cost estimating techniques may be based on qualitative or quantitative approaches [START_REF] Layer | Recent and future trends in cost estimation[END_REF][START_REF] Foussier | From Product description to Cost: A practical Approach[END_REF]. Cost models based on qualitative methods adopt expert judgement and heuristic rules as means of estimating cost [START_REF] Caputo | Parametric and neural methods for cost estimation of process vessels[END_REF]. Gray [START_REF] Gray | Factors systematically associated with errors in subjective estimates of software development effort: the stability of expert judgment[END_REF] Rush [START_REF] Rush | Expert judgement in cost estimating: modelling the reasoning process[END_REF] indicated that, in general terms, cost modelling requires a combination of high skills and extensive knowledge of multiple disciplines and relies on the accurate understanding of design and manufacturing capabilities of companies and their suppliers. This is illustrated in figure 1.

Figure 1: Skills and knowledge required for cost modelling

Some research work in supply chain cost control [START_REF] Fitzgerald | Best practices in procurement[END_REF][START_REF] Handfield | Avoid the pitfalls in supplier management[END_REF] has shown that in general terms cost models can provide enormous benefits when:

• eliciting active support from top management

• integrating and modelling processes

• attempting to understand cost drivers in appropriate detail

• measuring the performance of suppliers, production systems and employees

• developing cooperative supplier relations

• delivering and establishing a culture of continuous improvement

• facilitating a cross-functional approach linked through cost

• managing and reducing cost across the whole business structure

• developing integrated data management systems and 2000), Aeronautic Industry [START_REF] Sanchez | A methodology for assessing manufacturing cost due to tolerance on aerodynamic surface features on turbo fan nacelles[END_REF]) and Component

•
Part Manufacturing Industries (Curran, Raghunathan et al. 2004). In the Construction Industry, parametric cost estimation has featured well in the determination of project cost, based on historical data [START_REF] Akintoye | A survey of current cost estimating practices in the UK[END_REF]. In the Aeronautic A number of researchers [START_REF] Beltramo | Beyond parametrics: the role of subjectivity in cost models[END_REF]Hughes 1996;[START_REF] Briand | An assessment and comparison of common software cost estimation modelling techniques[END_REF][START_REF] Shepperd | Predicting with sparse data[END_REF] have reported that the major limitation to parametric cost modelling is the availability of data of adequate quality. With this observed limitation, Gray [START_REF] Gray | Factors systematically associated with errors in subjective estimates of software development effort: the stability of expert judgment[END_REF]) indicated that in real life situations, poor and inadequate data is always the case, hence expert judgement is sometimes necessary. Quite critically, Beltramo [START_REF] Beltramo | Beyond parametrics: the role of subjectivity in cost models[END_REF]) has indicated that parametric cost models are unable to predict cost of projects or products outside the scope of CER databases. This is a major limitation and hence the Parametric Handbook (DoD 1999) shows that, to make good use of parametric models:

1. Parametric models should not be used outside their database range 2. they should be used only after they have been verified and validated 3. should be constant adjusted to reflect changes in requirements 4. they should not be used until a realistic data corresponding to cost drivers can be obtained

Analogous cost modelling method

The analogous cost modelling technique identifies a similar completed product, process or project and reuses cost information associated with this entity to estimate the cost of the new entity, taking into consideration adjustments for the differences between the two. The effectiveness however depends on how accurate the historic data is and how accurate the difference between the two cases are established (Asiedu and Gu 1998). It has been reported that analogous costing is the best-established method of costing in many industries although normally it is applied in an ad hoc manner (Hughes 1996;[START_REF] Shepperd | Effort estimation using analogy[END_REF]. A survey conducted by Curran (Curran, Raghunathan et al. 2004) revealed that best industrial analogous cost modelling process can be classified into six stages:

1. Definition of the entity that requires costing. This involves defining the project or product in terms of characteristics such as design parameters, production requirements, operation and support attributes; reliability and maintenance.

2. Identification of data sources. This requires identifying sources of data related to the two entities under consideration. Most often data will include quantities, design and performance characteristic 3. Actual data collection. Data is collected in two folds, qualitatively and quantitatively. This is done for as many historical cases as possible. Where possible, inputs from specialist who are familiar with historic patterns will be required at this point.

4. Generating a range of factors that characterise the product in terms of features. These factors are used to define cost ratios with the underlining assumption that performance and design ratios influence cost ratios. Three unit ratios are often derived. These are complexity, miniaturisation and productivity.

5. Generating the actual cost estimates. This is based on the product of historic cost of the case and the ratios for complexity, miniaturisation and productivity.

6. The derivation of the total programme cost which involves the addition of profits, and any adjustments management may deem fit.

Typical examples of the use of analogous cost modelling can be found in [START_REF] Shepperd | Effort estimation using analogy[END_REF][START_REF] Shepperd | Estimating Software project effort using analogy[END_REF][START_REF] Taylor | Cost Engineering-a feature based approach[END_REF][START_REF] Bashir | An analogy-based model estimating design effort[END_REF]Curran, Raghunathan et al. 2004)

F

Generative-analytical cost modelling technique

As proposed by Caputo [START_REF] Caputo | Parametric and neural methods for cost estimation of process vessels[END_REF], generative cost modelling is one of the quantitative methods of estimating cost of projects, products and processes.

Caputo [START_REF] Caputo | Parametric and neural methods for cost estimation of process vessels[END_REF] In practice, analytical cost modelling techniques support concurrent engineering approaches especially in domains of 'design-to-cost' and 'design-formanufacture' projects [START_REF] Evershiem | Design-to-cost for production systems[END_REF][START_REF] Boothroyd | Product Design for Manufacture & Assembly[END_REF]. Further examples of the application of generative-analytical cost models can be found in the literature [START_REF] Pengelly | Performance of estimating techniques in current development environments[END_REF][START_REF] Shing | Design for manufacture of a cost-based system for moulded parts[END_REF][START_REF] Shehab | A design to cost system for innovative product development[END_REF][START_REF] Tang | Qualitative and quantitative cost analysis for sheet metal stamping[END_REF]; Agyapong-Kodua 2009)

Feature based cost modelling technique

Feature based cost modelling is a product design approach for linking the cost of products to their design features. This approach rests on the premise that (Wierda Derivation of process cost modelling technique 1991): 1) functions that describe cost can be derived for classes of similar objects and 2) factors which affect cost can be influenced by design decisions. Based on these assertions, feature drivers are derived and used as basis to estimate product cost. For most manufacturers, significant data on historic geometrical data exists which can be used to estimate cost of designs [START_REF] Bronsvoort | Multi-view feature modelling for design and assembly[END_REF][START_REF] Ou-Yanang | Developing an integrated framework for feature based early manufacturing cost estimation[END_REF]. In recent times, many researchers are using feature based cost models to integrate design, process planning and manufacturing. This is considered possible because Rush and Roy (Rush and Roy 2000) argue that the growth of CAD/CAM and 3D modelling helps both the designer and manufacturer to relate to common features such as holes, faces, edges, etc. Although many Design and Manufacturing Engineers seem to understand the concept of features, Curan (Curran, Raghunathan et al. 2004) reports that feature-based cost modelling is not fully established in Industries. Another observation reported by these same authors is that features differ from one industry to the other and for a given industry several features might be required to fully describe the product. In reality the major challenge with feature based cost modelling is that as products change, companies have to cope with re-defining product features. This can be very tedious considering the amount of new product changes that may be required in a dynamic manufacturing environment.

Fuzzy logic cost modelling method

The fuzzy theory was first introduced by Lotfi Zadeh in 1965 as an artificial intelligence tool which formulates the human thought when dealing with uncertainty and imprecision [START_REF] Kishk | An integrated framework for life cycle costings in buildings[END_REF][START_REF] Nachtmann | Fuzzy activity based costing: a methodology for handling uncertainty in activity based costing[END_REF] Shehab and Abdalla [START_REF] Shehab | A design to cost system for innovative product development[END_REF] noted that several steps are required to develop a fuzzy theory-based cost model. Three main procedures have been reported [START_REF] Mamdani | Fuzzy reasoning and its application New York[END_REF][START_REF] Klir | Fuzzy logic foundations and industrial applications[END_REF]Curran, Raghunathan et al. 2004). These are:

1. recognition of physical conditions that need analysis and control 2. processing of inputs according to fuzzy 'if then' rules 3. averaging and weighting the outputs from all individual rules into a single defuzzyfied output that provides the solution for the system

In general terms Kishk [START_REF] Kishk | An integrated framework for life cycle costings in buildings[END_REF] is of the view that fuzzy logics are most applicable when: 1) models of processes or products are highly complex and understandings about them are limited or 2) when there are processes for which human decision making is inextricably linked.

A key advantage in the use of fuzzy logics in cost modelling is indicated by Curran (Curran, Raghunathan et al. 2004) as:

1. The mathematical concepts deployed are transparent and traceable 2. It posses the ability to match sets of input-output behavioural data

It can be integrated with traditional techniques

Although these advantages are recorded, it is however evident that fuzzy logic cost modelling is not fully established in industries [START_REF] Joumier | Fuzzy numbers as a tool for measuring imprecision in cost estimating: a pragmatic implementation example[END_REF]Curran, Raghunathan et al. 2004). It remains limited to experts of 'fuzzy sets' and artificial intelligence [START_REF] Blattberg | Database models and managerial intuition: 50% model + 50% manager[END_REF].

Neural networks based cost modelling method

Neural network cost modelling techniques constitute a form of artificial intelligence that is used to derive cost as an effect associated with some cost drivers [START_REF] Zhang | Feature-based cost estimation for packaging products using neural networks[END_REF]. Neural network cost models are based on cost attributes which relate to the product or system under consideration. They possess unique advantage in the field of statistical cost modelling because they can model cases where functional relationship between case data cannot simply be expressed in polynomial form [START_REF] Caputo | Parametric and neural methods for cost estimation of process vessels[END_REF]. Caputo [START_REF] Caputo | Parametric and neural methods for cost estimation of process vessels[END_REF] indicated that basically artificial neural network cost models 'accept as input shape-describing and semantic product characteristics' and generate outputs in the form of product cost.

Key research contributions in neural network cost models were provided by: Seo [START_REF] Seo | Prediction of the life cycle cost using statistical and artificial neural network methods in conceptual product design[END_REF] for the life cycle costing in conceptual designs; Zhang and Fuh [START_REF] Zhang | Feature-based cost estimation for packaging products using neural networks[END_REF] for estimating packaging cost based on product dimensions;

Shtub and Versano [START_REF] Shtub | Estimating the cost of steel pipe bending, a comparison between neural networks and regression analysis[END_REF] for processing operations and Cavalieri [START_REF] Cavalieri | Parametric vs Neural Network models for the estimation of production costs: A case study in the Automotive Industry[END_REF]) for the estimation of manufacturing cost of disk brakes. Other authors have compared the effectiveness of artificial neural network cost models with parametric cost models in engineer to order industries [START_REF] Shtub | Estimating the cost of steel pipe bending, a comparison between neural networks and regression analysis[END_REF][START_REF] Cavalieri | Parametric vs Neural Network models for the estimation of production costs: A case study in the Automotive Industry[END_REF][START_REF] Caputo | Parametric and neural methods for cost estimation of process vessels[END_REF], and in general terms [START_REF] Bode | Neural networks for cost estimation: Simulation and pilot applications[END_REF]. A study of the above literature shows that artificial neural that in some cases neural network models are limited in terms of accuracy, variability, model creation and model examination [START_REF] Smith | Cost estimation predictive modelling: regression versus neural network[END_REF]. Elhag [START_REF] Elhag | Statistical analysis and cost models development[END_REF]) also noted that neural network cost models are not suitable for highly innovative products which deviate largely from historic precedents.

Analysis of literature

The foregoing literature on costing (engineering, estimating, and modelling) shows that whilst there have been a number of stepwise developments in the principles of costing; these have not translated holistically in to working practices. Case studies reported by a number of authors have all been towards highly specialised and bespoke solutions that have not then been generalised for wider application domains. This is a reflection of practice seen and experienced by the authors of this paper. Generally, the widely reported cost modelling techniques can be classified as shown in figure 3. This figure shows there is no indication of integration of cost modelling methods and most of the methods described in the literature are 'product based'.

Figure 3: Classification of cost modelling methods

A compilation of literature on costing and their years of publication (not shown) revealed that developments in costing saw increased activity from the 1990's to 2000 (see figure 4). In terms of cost modelling and estimating, techniques exist as discussed, but it is noted that their application is of limited scope i.e. neither has it been holistic nor integrated. Methods, that is to say instances of techniques, are often isolated and consider cost on a piecemeal basis e.g. by product, sub-product, business Cost models can be scrutinised for accuracy, utilising statistical uncertainty in conjunction with cost estimation to produce a cost risk methodology. These do however remain largely qualitative and depend on the subjective opinions of experts to decide upon risks and their associated likelihoods and severities. Another factor to consider is that not only do we have uncertainty related to the biases of experts; there is another dimension of the product build configuration. As this is prone to change through the development phases, additional levels of risk and uncertainty are introduced. This implies the need for enhanced openness and sharing of information between various parts of an organization throughout lifecycle phases. The objective of modelling and estimating costs is to improve design through making cost information available further upstream in the realization of products and processes. Such decisions can then be documented and design rules created, as the early design stages are where the majority of costs are built into a product.

Cost models are largely seen as a means to determining absolute figures for product or process within certain degrees of confidence, through structured methods.

The behaviours of costs are often neglected in terms of the 'cause and effect' issues associated with change decisions. In this respect, it is evident from the literature that, performance indicators that were once traditionally the onus of managerial and accounting functions, are now filtered down in such a way that they are the concern of every element in value and supply chains. This is to the extent that non-accountants are assuming a much more direct responsibility for, and interest in, the financial (and non-financial) outcomes of their performance. However, this has occurred without the necessary methods, approaches, and techniques to support modelling and analysis.

Cost engineering not only encompasses monetary expenditure during the realisation of objectives but also other aspects such as time, material and resources. It can therefore be seen that cost engineering is not just confined to the control of monetary costs. The remit of the cost engineer is to facilitate and inform design such that products that are cost effective during production and later lifecycle stages are produced. There is therefore an increased need to make design considerations based on appropriate lifecycle drivers, some of which are easily quantified, whilst others less so.

The literature has shown that, in general terms, some of the problems faced by most design and manufacturing industries can be rooted to the phenomenon of complexity which stems from the complexities involved in current markets. The

Future trends

Based on the analysis of literature; observed current cost modelling practices and the general trend of advancement in MEs, the authors are of the view that as a result of the dynamics associated with most MEs, there is the need for a comprehensive modelling methodology which satisfies the following requirements:

• The modelling methodology must suitably capture all different product types in a ME with the view of linking products to respective process routes. This is because a study of trends in MEs shows that most MEs need to realize multiple products to remain competitive, hence there are significant product mixes, shared resources with unsteady changes in information or material flow, as well as control. Thus there is the need to deploy cost modelling methods with capabilities to reflect the changes associated with multiproduct flow properties. Because of the varying range of products many MEs need to realise, coupled with external factors which invariably impact on their operations, process changes may be required over a short time. A cost modelling methodology which depicts the impact of process changes is • Also the cost modelling method should enable enhanced traceability of costs to specific products and processes to enable improved management of cost distortions whilst supporting the accurate estimation of process cost due to the deployment of alternative business process configurations.

• Because of changes, risks and dynamics associated with MEs, a virtual executable cost model experimentation tool will be useful if it enables design options, business ideas, production systems reconfiguration and process improvement suggestions to be tested before their implementation. This will save MEs from implementing decisions; in fact design decisions that have great impact on the business. System dynamics and discrete event simulation tools can help model and control some aspects of dynamics associated with current manufacturing systems

• Generally, a decomposition of enterprise requirements ensures that complex problems are characterised and modelled in modular forms, so that analysis and understanding becomes easier. The consistent utilization of appropriate cost modelling constructs will enable the contextual reuse of models.

  Derivation of process cost modelling technique

  Derivation of process cost modelling technique

  justifying investment Detailed explanations of the SOA cost modelling methods are provided in the next sections.

  Derivation of process cost modelling technique2.1.1 Parametric cost modelling techniqueParametric cost models are generally associated with cost estimates or techniques which deploy 'Cost Estimating Relationships' (CERs) together with mathematical algorithms or logics to establish cost estimates[START_REF] Dod | Parametric estimating handbook[END_REF]. The origin of parametric cost models is often attributed to the early works of Wright[START_REF] Wright | Factors affecting the cost of Airplanes[END_REF] when he first determined the unit cost of an aircraft as a function of the number of aircraft produced. Wright's work was extended by Stanford Research Institute and later by the Rand Cooperation (Crawford 1985). In general terms, Rand Cooperation is accredited with the following advancements in parametric cost modelling (Crawford 1985; Curran, Raghunathan et al. 2004): 1. Developing Cost Estimating Relationships (CER) 2. Merging CER with the learning curve to form the foundation of parametric estimating 3. Deriving CERs for aircraft cost as a function of speed, range and altitude 4. Observing statistical correlation in checking CERs 5. Developing families of curves data for different aircrafts According to RAND (RAND 1995), the three most important factor relationships worth considering when developing parametric cost models are: 1. Performance and physical attributes are measures of technical capabilities 2. Technical risk and design maturity attributes of a part are measures of relative difficulty of developing and producing the part 3. Programmable parameters describe ways in which programs are operated. Many industries have adopted parametric estimation as the main means of cost estimation for their design, development and production or implementation phases of engineering projects. Major users include the Construction Industry (Akintoye and Derivation of process cost modelling technique

Fitzgerald

  Industry, parametric cost estimates play key role in bidding and target cost estimation, whilst for most component manufacturing industries, parametric cost estimates are used to determine the cost of components manufacture. Quite recently, parametric cost models have gained popularity through the support work of organizations such as International Society of Parametric Analyst (ISPA), Society of Cost Estimating and Analysis (SCEA) and Space Systems Cost Analysis Group (SSCAG)(Curran, Raghunathan et al. 2004).The activity diagram shown in figure2was created to provide an overview of the approaches adopted by Quin and Ben-Arieh[START_REF] Qian | Parametric cost estimation based on activitybased costing:A case study for design and development of rotational parts[END_REF] and Curran(Curran, Raghunathan et al. 2004), which collectively provide a methodology for developing parametric cost models..

Figure 2 :

 2 Figure 2: Development of parametric cost models

  Derivation of process cost modelling technique

  claims that generative-analytical cost modelling produces the most accurate cost estimate because the technique is able to depict the actual production processes. Recent research has advanced the scope of generativeanalytical cost modelling by applying enterprise modelling and decomposition techniques to manufacturing processes[START_REF] Agyapong-Kodua | Process cost modelling in Manufacturing Enterprises[END_REF] Agyapong-Kodua 2009). This involves detailed analysis of production processes and is based on a well structured decomposition formalism previously defined as part of the CIMOSA approach to Enterprise Modelling[START_REF] Weston | A model-driven, component-based approach to reconfiguring manufacturing software systems[END_REF] Agyapong-Kodua 2009;[START_REF] Cen/Iso ; Chatha | Combined Enterprise & Simulation Modelling in support of Process Engineering[END_REF]. Here processes are decomposed to their 'elemental activity level'. At the elementary activity level, cost and values are assigned to each activity to determine the elementary cost. The cost derived through the realization of each activity depends on the resource consumed. Thus labour and machine rates, material quantities and prices are used to determine the actual direct activity realization cost. In addition to this, 'activity based costing' method is used to assign overheads or indirect cost to the various operations. After the estimation of elementary activity cost, based on the decomposition technique, respective cost of activities belonging to well defined business process are grouped together. The cost of individual business processes are further grouped together to form the total production cost.It has been reported(Curran, Raghunathan et al. 2004;[START_REF] Caputo | Parametric and neural methods for cost estimation of process vessels[END_REF] Agyapong-Kodua 2009) that common features of generative-analytical cost models are: at a detailed level within the Work Breakdown Structure (WBS).2. Cost is estimated for basic tasks such as engineering design, tooling, fabrication of parts, manufacturing engineering, and quality control.3. The cost of materials is estimated or obtained from the supplier.4. The approach requires detailed and accurate data and should be undertaken by an experienced engineer In a related work by Shehab[START_REF] Shehab | A design to cost system for innovative product development[END_REF], databases of standard times, cost rates and best practice manufacturing methods were integrated with computer-aided process planning software and knowledge based methods to derive an iterative technique for cost modelling. Also as part of a recent work by Agyapong-Kodua (Agyapong-Kodua 2009), the application of static generative cost models was enhanced via the use of system dynamics and discrete event simulation modelling tools. This has derived a flexible basis for cost modelling, suitable for analysing dynamic impacts of various causal effects on cost generation in manufacturing systems.

  Derivation of process cost modelling technique

  Derivation of process cost modelling techniquenetworks show better results than parametric cost models. However it has been shown

  Derivation of process cost modelling techniquedomain, lifecycle phase or investment decision. Additionally, cost is normally considered in relative isolation of other metrics.

Figure 4 :

 4 Figure 4: Literature according to year

Figure 5 :

 5 Figure 5: Literature lifecycle stage focus

  Derivation of process cost modelling technique

  Derivation of process cost modelling techniquestructural and dynamic complexity of markets impact on the structure and processes of the enterprise too, hence complex cost generation factors emerge. Advancing information and machine technologies have also impacted on how cost is created, measured and controlled. The development and utilization of microelectronics; CAD/CAM/CAE; computer communication networks; software engineering; object oriented database systems; distributed artificial intelligent systems; multimedia and multimodal environments as well as open systems architectures are impacting greatly on design and manufacturing industries. All these technologies influence processes and especially how cost is developed. Depending on an industry's need, automation can be very high and complex, and cost modelling methods will have to recognise this new complex dimension of production systems. Another clear observation is that, many industries are focussing on their core competences and forming partnership with other organizations which can support aspects of their. From a manufacturing point of view, the decision to either 'make' or 'buy' is crucial, if a business is to survive in current dynamic markets. The onus therefore lies on cost engineers to better develop models which can support critical decision making. The added challenge for designers and manufacturers is that cost modelling methods must be able to analyse capabilities of systems and the cost implication of management decisions. The observed need for a scientific cost estimation approach to match the ever-growing manufacturing industry is obvious. Also most process cost modelling techniques assume single flow manufacturing systems and underestimate the implication of multiple flows, resource sharing, product mix, reworks and other manufacturing dependent failures. The realization and capture of these process-related attributes is necessary because MEs Derivation of process cost modelling technique are characterised by complex systems of processes which need to be resourced with technical and human systems. These systems need to be properly coordinated and controlled to allow variety of products to be realised through them over varying periods of time. Current approaches to the identification and modelling of cost has not been adequate because most of the cost modelling techniques do not encode time dependencies related to product flows, controls, process instants and time dependent causal effects. This implies that analysis of alternative flows of product (volume and mixes) through a shared process cannot accurately be modelled by current generation cost modelling techniques.

  Derivation of process cost modelling techniquetherefore necessary to effectively describe the actual cost which is likely to be incurred on the account of changes in processes.• Although some work has been done on process oriented cost modelling techniques, literature has shown that, in the main, product based quantitative cost modelling techniques abound. Despite the strengths of the product based cost modelling techniques, it is important to be able to deploy cost modelling methods which are able to depict or translate design solutions into equivalent manufacturing processes and their associated required resources. Thus process based modelling techniques have potential to model operational sequences for different product families and can be helpful in estimating, controlling and monitoring the generation of cost at a reasonable degree of accuracy. An enhancement and combined usage of existing product-based cost modelling techniques and process modelling techniques, with a definitive view of production systems design will help measure cost and process efficiencies more accurately.

Figure 2 :

 2 Figure 1: Skills and knowledge required for cost modelling

FigureFigure 5 :

 5 Figure 3: Classification of cost modelling methods

  Derivation of process cost modelling techniquerequired cost modelling method should inherently possess decomposition formalisms and uniformly display a set of modelling constructs that facilitate model reusability in MEs. Process decomposition and integration can be enabled through the selection and appropriate utilization of enterprise modelling tools.Based on this set of modelling requirements, the authors are of the view that the integrated use of concepts and techniques from Cost Engineering, Enterprise Modelling, System Dynamics Modelling and Discrete Event Simulation Modelling, will be useful. Research is underway to fully establish how relevant modelling techniques belonging to these separate domains can be integrated and supported with relevant data to help generate a multipurpose cost model useful for decision support in designing and manufacturing.

	F o r F o r F o r F o r F o r
	P P P P P
	e e e e e
	e r e r e r e r e r
	R R R R R
	e e e e e
	v i e v i e v i e v i e v i e
	w w w w w
	O n l O n l O n l O n l O n l
	y y y y y
		Thus the
	*Corresponding author	22

*Corresponding author

http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.ukInternational Journal of Production Research


Peter J F Harris
email: p.j.f.harris@rdg.ac.uk

Structural transformation of graphite by arc-discharge

Keywords: carbon, graphite, carbon nanotubes, fullerenes graphene

Structural transformation of graphite by arc-discharge

The formation of novel structures by the passage of an electric current through graphite is described. These structures apparently consist of hollow threedimensional graphitic shells bounded by curved and faceted planes, typically made up of two graphene layers. The curved structures were frequently decorated with nano-scale carbon particles, or short nanotubes. In some cases, nanotubes were found to be seamlessly connected to the thin shells, indicating that the formation of the shells and the nanotubes is intimately connected. Small nanotubes or nanoparticles were also sometimes found encapsulated inside the hollow structures, while fullerene-like particles were often seen attached to the outside surfaces. With their high surface areas and structural perfection, the new carbon structures may have applications as anodes of lithium ion batteries or as components of composite materials.

Introduction

Interesting things can happen when an electric current is passed through graphite. In 1990, Krätschmer and Huffman and their co-workers showed that C 60 is formed, in high yield, by vaporising graphite in a simple carbon arc apparatus under an atmosphere of helium [1]. Most of the C 60 is deposited on the walls of the arcevaporation vessel, along with disordered soot-like material. A short time later, Iijima showed that multiwalled carbon nanotubes with extremely perfect structures can be produced in a similar way [2], although in this case the nanotubes form on the negative graphite electrode. In 1993 it was shown that single-walled nanotubes can be produced by arc-discharge if Co and Ni or some other metal is added to the anode [3,4].

Recently, yet another kind of carbon has been discovered in graphite samples through which a current has been passed [5]. This new carbon apparently consists of hollow graphitic shells bounded by curved and faceted planes, typically made up of two graphene layers. These structures were first found in a commercial ultra-pure graphite. It is believed that they formed during a purification process which involved passing an electric current through the graphite. Support for this idea was provided by 3 some preliminary experiments involving the passage of a current through graphite rods in a carbon arc apparatus, which produced very similar structures. In the present study the controlled production of the novel graphene structures by the passage of an electric current through graphite is described in detail. The material is characterised using high resolution transmission electron microscopy, and evidence is presented that the structures are three-dimensional rather than flat. The possible mechanism whereby graphite could be transformed into the three-dimensional shells is discussed.

It is suggested that the new carbon structures might find applications in a wide variety of areas. For example, their extremely large surface-to-volume ratio and likely high conductivity suggest that they may be useful in sensors or lithium ion batteries.

They may also have potential in catalysis or as hydrogen storage materials.

Experimental

The apparatus used to produce the new carbon structures was an Edwards S150B evaporation unit. This is normally used for coating scanning electron microscopy specimens with a thin layer of carbon. In this unit, the electrodes are 3 mm graphite rods, one of which is sharpened to a point and held in contact with the other electrode with a spring mechanism. High purity rods were used, with impurity content <20ppm (Agar Scientific Ltd., UK). The chamber was pumped by a rotary pump, giving a vacuum of approximately 0.1 Torr. Discharge was carried out at a voltage of 10 V, with a current of approximately 20 A, for a duration of about 2 minutes. These are the standard conditions for carbon coating, although with a rather longer duration. Following arcing, the pointed electrode was generally found to have been shortened by a few mm, and a small deposit could be observed near the point of contact of the two electrodes. This deposit was scraped from the electrodes and then prepared for TEM by dispersing in iso-propanol and then pipetting onto holey carbon

Results

A micrograph of material from the fresh graphite rod is shown in Fig. 1(a). As expected, this consists mainly of flat crystallites, ranging from a few 100 nm to about 5 µm in size, containing up to 100 layers. The crystallites were often folded and buckled, and were accompanied by small amounts of disordered material. However, nanotubes or other fullerene-related structures were not seen in the fresh graphite.

The carbon collected from the graphite rods following arcing contained some "normal" graphite, but this was accompanied by many regions which had a very different appearance. One of these areas is shown in Fig. 1(b). Here, the outline of the structure is much more irregular than in the fresh graphite, with many curved and unusually-shaped features. The material is decorated with numerous short nanotubes or nanoparticles. An area in which a number of nanotubes can be seen is shown in Fig. 2(a). These tubes typically possessed between two and four walls and could be several 100 nm in length, but tended to be less perfect than those grown by the traditional Iijima arc-evaporation method, in that they often contained sharp bends and other discontinuities. In some cases nanotubes were found to be directly connected to the larger structures; examples can be seen in this image. The observation that nanotubes are joined seamlessly to the larger regions indicates that these regions are three-dimensional rather than flat, the three-dimensional structure arising from presence of pentagonal and other non-hexagonal rings. The junctions between the tubes and the larger shell-like regions may involve seven-membered rings. be seen from this image that the graphene material is largely bilayer, but some threelayer and single-layer graphene is also present. The single-layer graphene structures were found to be very beam-sensitive, so obtaining high quality images of this material proved difficult. The bilayer spacing, determined from this and other images, was generally somewhat larger than the interplanar spacing for graphite, being typically around 0.4 nm.

The thin graphitic material exhibited many unusual features. In some areas, nanoparticles or nanotubes appeared to be encapsulated inside the large structures. This is illustrated in Fig. 3, where a single-walled nanoparticle can be seen apparently inside a bilayer shell. This provides further evidence that the thin graphitic structures are hollow. Another interesting observation is that very small particles, which appeared to be fullerenes, were frequently seen on the outside surfaces of the thin graphitic structures, as shown in Fig. 4. It is notable that the fullerene particle, which is approximately the size of a C 60 molecule, is preferentially attached to the apex of the faceted graphene structure. The interaction of fullerenes with the conical graphene structures known as carbon nanohorns has been studied recently by Suarez-Martinez and colleagues [6]. These workers have shown that fullerenes are frequently observed at the tips of nanohorns, rather than on the main bodies of the structures. Although this phenomenon is not fully understood [7], it suggests that fullerenes prefer to become attached to regions containing pentagonal rings. Therefore, observations such as that in Fig. 4 suggest that the apex of the faceted structure contains a pentagon. This is supported by the fact that the apex makes an angle of approximately 150°. This is close to the angle observed in certain MWNT caps, where a conical region

Discussion

A remarkable transformation in the structure of graphite as a result of the passage of an electric current in an arc-discharge apparatus has been described. It is believed that this involves the formation of three-dimensional shell-like structures bounded by very thin walls. In most cases these walls consist of bilayer graphene, although walls with three or more layers are quite frequently seen. Single-layer graphene structures are also occasionally observed. There are a number of reasons for believing that these new structures are three-dimensional and hollow rather than flat.

Firstly, as reported here and in the previous paper [5], carbon nanotubes are often observed to be seamlessly joined to the larger regions. It is difficult to envisage a way in which nanotubes, with their circular cross-section, could be connected to flat, few layer, graphene without being seriously distorted, at least in the vicinity of the junction. Secondly, nanoparticles or nanotubes are sometimes found encapsulated inside the large structures, as shown in Fig. 3, indicating that the structures are hollow. Thirdly, small fullerene particles, similar in size to C 60 molecules, are often found preferentially attached to the apices of faceted graphene structures, as in Fig. 4, providing evidence for the presence of pentagonal rings. Some structures rather similar to those described here have been reported in recent studies by Jia and co-workers [START_REF] Jia | [END_REF] and by Huang et al. [10]. These studies involved in situ Joule heating of graphite "nanoribbons" inside a TEM. In both papers the authors drew a different conclusion about the nature of the transformation to that given here: the process was discussed in terms of sublimation and edge reconstruction of flat graphene. It is possible, however, that they were seeing a transformation from flat graphite to hollow structures, as described in the present work, rather than sublimation.

The mechanism of the transformation is not known at present, but a few comments can be made. It is possible that the key to understanding the process may lie in the edge structure of graphite planes. It is well established that graphite planes often have "closed" edges, so that the layers resemble folded sheets [11 -15], as illustrated in Fig. 5 (a). In a sense, therefore, these adjacent graphene layers already represent closed structures, and the transformations reported in this paper may simply involve an "opening" of the layers, as shown schematically in Fig. 5 (b). Such a process might be initiated by the nucleation of pentagonal rings at the closed edges: it is clear from the presence of nanotube-like structures in the carbon, and the attachment of fullerenes to the faceted structures, that pentagons are present. It also seems clear that the electric current passing through the carbon, rather than simply the high temperature, is responsible for the transformation. However, further work is needed to gain a more detailed understanding of the process.

Although two-dimensional graphene has attracted huge interest in recent years [16,17], the possibility of producing large three-dimensional structures with graphene walls has not been widely discussed. A few theorists have considered regular threedimensional networks built from small graphene patches (e.g. refs. [18 -20]), but these require three sheets to be joined along a line, usually with sp 3 -bonded carbons, rather than two sheets as in the structures reported here. In 1995 Ebbesen and Hiura published a paper entitled "Graphene in 3-dimensions -towards graphite origami", but this was primarily concerned with using scanning probe microscopy to create folds in graphene layers on the surface of highly ordered pyrolytic graphite [21]. The resulting structures were still essentially two-dimensional. It has been suggested that chemical techniques could be used to create three-dimensional structures from graphene [22], or that nanoscale water droplets might induce graphene sheets to fold up like the petals of a flower [23,24]. However, none of these ideas have yet been demonstrated experimentally. Currently, therefore, the technique described in this paper is believed to be the only method for synthesising large, hollow structures with ultrathin graphitic walls.

The new the three-dimensional graphene structures described here could potentially have important applications. One possible area might be hydrogen storage, since forms of carbon rather similar to those described here have been shown to have H 2 storage capabilities. Thus, Orimo et al. reported in 1999 that "nanostructured graphite" prepared by mechanical milling of synthetic graphite can have high H 2 uptakes [25]. Carbon nanohorns have also been shown to have potentially useful H 2 storage properties [26]. Theoreticians have suggested that "pillared graphene", a three-dimensional network constructed from graphene and short nanotubes, could adsorb 6% of its weight in hydrogen at room temperature and pressure [27]. Although the present material is a disordered rather than an ordered network, its H 2 storage characteristics might be similar to those of "pillared graphene".

The new structures may also have applications in electrical devices. Recently, it has been demonstrated that graphene can be used in electrochemical double layer [29] G.X. Wang, X.P. Shen, J. Yao and J. Park, Carbon 47 (2009) p.2049.

  A sample of a fresh graphite rod was also examined by TEM. The microscope used was a JEOL 2010, with a point resolution of 0.19 nm, operated at an accelerating voltage of 200kV. Images were recorded photographically.

5 A

 5 higher magnification image of another region is shown in Fig.2(b). It can

  part of the tube (see ref.[START_REF] Harris | Carbon Nanotube Science[END_REF], p128). It is believed that a single pentagon occurs at the point where the two regions are joined.

  ]. The high surface area graphitic shells reported here might actually have advantages over conventional "flat" graphene in this application. The flat graphene particles would have a tendency to clump together, while the faceted shells would be more likely to retain their surface area. The high conductivity of the structures, and their large internal volume might also make them potential candidates for the anodes of lithium ion batteries[29].Finally the mechanical properties of the graphitic shells might be superior in some ways to those of flat graphene. Although graphene sheets are extremely stiff in tension, they have little resistance to bending or compression. Curved or faceted structures would be expected to have much greater flexural rigidity. The new materials might therefore be useful components of composite materials.

  G.K. Dimitrakakis, E. Tylianakis and G.E. Froudakis, Nano Letters 8 (2008) p.3166. [28] M.D. Stoller, S.J. Park, Y.W. Zhu, J.H. An and R.S. Ruoff, Nano Letters 8 (2008) p.3498.

Figure 1 (

 1 Figure 1 (a) Low magnification micrograph of carbon from fresh graphite rod. (b) Micrograph at same magnification showing transformation in structure following arc-discharge.

Figure 2 (

 2 Figure 2 (a), (b) Typical structures found in carbon following arc-discharge.

Figure 3

 3 Figure 3Bilayer graphene structure, apparently hollow with single-walled nanoparticle inside (arrowed).

Figure 4 Faceted

 4 Figure 4Faceted bilayer graphene structure with enlarged region showing small fullerene particle attached to apex.

Figure 5

 5 Figure 5Schematic illustration of transformation of folded graphene sheets into hollow structure.

http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

Acknowledgement

I thank Kazu Suenaga for discussions.