Felix Friemann
email: ffriemann@ethz.ch

Matthias Wandfluh

Paul Schönsleben

Robert Alard

Improving the Application of Financial Measures in Supply Chain Management

Keywords: supply chain management (SCM), financial measures, metrics

Many companies (especially SMEs) still feel poorly prepared and notice a deficiency of financial know-how when facing situations such as limitations in working capital. To reduce the amount of capital employed, close linkage of financial measures to the daily operations within the companies is required. Yet, supply chain performance measures are often not directly linked to overall financial targets (e.g. cost of capital vs. service level). This paper proposes taking financial parameters into consideration when making supply chain management decisions. It outlines supply chain finance (SCF) solutions available to bigger corporates, analyses current financial metrics for supply chain management and proposes concepts for a greater linkage between finance and supply chain performance measures. Finally, this paper will also reveal gaps where current concepts and metrics have limitations and future research is needed.

Introduction

Motivation

Within the last decades Supply Chain Management (SCM) gained enormous attention. It is no secret that it gives many companies great competitive advantage or even decides over success or failure of a product. That is why countless research efforts could be noted within this sector and it is an inherent part in the education of logistics managers. Even though progress in terms of optimizing and synchronizing material and information flows in SCM has been made, financial flows are insufficiently elaborated in practice by supply chain managers and their impact is not clarified. Since the targets are not aligned, finance managers limit supply chain operations in a sometimes unfavorable way and supply chain managers primarily focus on operational targets neglecting their financial impacts. Many companies (especially SMEs) still feel poorly prepared and notice a deficiency of financial know-how when facing situations such as limitations in working capital after the upturn following the latest financial crisis. After the production capacities and assets were reduced, the need for investments in new production assets and financing raw materials to serve the increased demand led to difficulties. Another example are the increasingly turbulent fluctuations in the currency and raw material markets that make it more difficult for global companies to forecast the financial flows. Deeper knowledge integration of financial concepts in the decision-making process of supply chain managers is expected to be a major competitive advantage allowing to create more robust and better performing supply chains.

Problem statement

A current study in Germany shows that many medium-sized companies rely on traditional solutions when financial resources are needed. The vast majority (84 %) asks for loans from a bank and only 31 % of the medium-sized companies work on reducing their working capital [START_REF]Stärken und Schwächen mittlerer und grosser Unternehmen im Vergleich[END_REF]. This paper shall serve as a starting point for making supply chain finance (SCF) concepts more accessible for practitioners especially in SMEs. This will specifically be done by a closer linkage of financial know-how to the supply chain management measures. Until now, financing concepts are mainly implemented by the finance department of a company. The target values of finance managers are (beside others) to reduce the cost of capital within the supply chain. However, supply chain managers are primarily rated for performance measures like delivery reliability, fill rates or their own costs. A closer linkage between these different target values is needed to improve overall performance. This paper will outline a recommendation and reveal gaps where current concepts have deficiencies and future research is needed.

Methodology

This research is based on a literature research as well as on interviews with representatives from Swiss banks and industry. The methodology follows the following three steps. First, an overview about current application of SCF concepts is presented. Second, approaches for linking financial to supply chain performance measures are analyzed. In a third step, the potential gap between existing metrics and desired requirements are deduced and a new approach is outlined.

Application of financial measures within SCM

In this chapter, a short overview regarding the usage of financial methods within the SCM discipline will be given. For this reason, a common understanding of the term SCF will be provided in the first subchapter. Then, the cash-to-cash cycle as an important measure for the net working capital will be explained. At the end, an overview over existing SCF solutions in the market will be developed.

2.1

Definition of supply chain finance (SCF)

Unfortunately, there is no distinct definition of SCF in the literature. By the banks, it was often used as a term for buyer-centric solutions and reduced on specific tools (reverse factoring1 in specific). Lamoureux and Evans define SCF as a sub-set of trade finance (meaning both the supplier and the buyer side). This means a combination of technology solutions and financial services that closely connect global value chain anchors, suppliers, financial institutions and, frequently, technology service providers [START_REF] Lamoureux | Supply Chain Finance: A New Means to Support the Competitiveness and Resilience of Global Value Chains[END_REF]. This definition is wider, but still not wide enough since SCF doesn't e.g. necessarily need financial providers or technology service providers. Moreover, in this paper SCF will be defined in a more general way as a concept encompassing any financing solution that supports the buyer or seller side of the supply chain to a considerable extent (accordingly to [3], [START_REF]Treasury Today: Supply chain finance: the next generation[END_REF]). This includes for example all concepts a supply chain manager applies that influence the financial measures of the buyer, seller or his own company.

In the next subchapter, the application of the cash-to-cash cycle as an important metric as well as its strengths and weaknesses will be explained.

Net working capital and the cash-to-cash cycle

On average, the working capital accounts for 25 % of the turnover for companies listed in the Swiss Performance Index (SPI) [START_REF] Wagner | Working Capital reduzieren[END_REF]. Consequently, reducing the working capital has been on the agenda of many companies for a long time. Working capital is defined as the current assets of a firm minus its current liabilities [START_REF] Schneider | Adding enterprise value[END_REF]. Wagner and Locker specify the assets as accounts receivable plus inventory [START_REF] Wagner | Working Capital reduzieren[END_REF]. One key focus of SCM in the last years consequently is to reduce inventories (e.g. by just-in-time deliveries). The impact of decisions on accounts payable or receivable is not a key interest for many supply chain managers even though the accounts payable are directly influenced by e.g. vendor Managed Inventory (VMI) concepts where the supplier maintains the customer's inventory.

Looking for measures for the working capital, the cash-to-cash cycle has been often used as an indicator / measure for the net working capital that is needed by a company [START_REF] Farris | Cash-to-cash: the new supply chain management metric[END_REF]. It bridges inbound material activities with suppliers, manufacturing operations and outbound sales activities with customers [START_REF] Farris | Managing the Supply Chain Using the Cash-to-Cash Metric[END_REF]. The cash-to-cash cycle can be calculated by Days Sales Outstanding (DSO) plus Days Inventory Outstanding (DIO) minus Days Payables Outstanding (DPO). Measures to improve the cash-to-cash cycle are therefore to reduce DSO and DIO and extend DPO.

This concept has been very successful for specific companies. One of the most prominent examples is the Dell Computer Corporation. In 2001, Dell had four days of inventory supply, 32 days of sales in accounts receivable, and 66 days in accounts payable adding up to a negative cash-to-cash cycle of 30 days [START_REF] Farris | Cash-to-cash: the new supply chain management metric[END_REF]. For comparison:

European companies had a positive cash-to-cash cycle of 58,6 days in the same year [START_REF] Losbichler | Der Cash-to-cash Cycle als Werttreiber im SCM-Ergebnisse einer europäischen Studie[END_REF].

But using the cash-to-cash cycle as the only metric has some drawbacks. The risks are e.g. rising costs and a higher probability of disruptions along the supply chain. This is due to the fact that while the stronger supply chain partner (which generally has the better credit rating) is able to e.g. reduce its DSO and therefore the needed working capital, the less powerful supply chain partners face worse conditions and their working capital employed is going up. When this moves on along the supply chain, it can lead to rising costs and serious problems at some point for smaller players. The effects of using the cash-to-cash cycle as a main metric for SCM measures are analysed by e.g. Losbichler and Rothböck [START_REF] Losbichler | Der Cash-to-cash Cycle als Werttreiber im SCM-Ergebnisse einer europäischen Studie[END_REF] or Seifert and Seifert [START_REF] Seifert | Financing the Chain[END_REF].

Due to these reasons, other measures to improve the financial situation of a company need to be analysed. In the next subchapter a brief outline over the range of available SCF solutions is given. It must be noticed that these solutions are mainly offered to bigger corporates since a critical turnover and market position is often essential to benefit from an implementation and recover the implementation and administration costs.

Range of commercial SCF solutions

The benefits for larger companies implementing SCF concepts with their suppliers or buyers include: 1) Reduced risks (by stabilizing their supply chain partners), 2) reduced costs along the supply chain (by e.g. lowering the working capital) and 3) enhanced capabilities of their supply chain (by e.g. providing cash to their supply chain partners that they can invest in new assets). That is why most major manufacturing and retail companies, for example, have a high degree of familiarity with SCF programs and are either considering or already using such a solution [START_REF]Treasury Today: Supply chain finance: the next generation[END_REF]. Therefore, different vendors offer various solutions to exploit these potentials (see e.g. [START_REF]World's best supply chain finance providers[END_REF], [3]). Among others, Yunqi especially mentions the advantages of online supply chain finance systems [START_REF] Yunqi | Online Supply Chain Finance: Profound Changes in Financing of SMEs[END_REF]. Banks traditionally marketed the term SCF and are offering a wide range of solutions. Beside others, these encompass factoring solutions (by selling the accounts receivable to a factor at a discount [START_REF] Davies | Show me the money[END_REF]) resp. reverse factoring, inventory finance, commodity finance or receivables finance.

Non-bank solution providers also exist and offer highly automated electronic platforms. These platforms involve several banks (or investors) that can provide the cash needed for various solutions. The relationship to the financial institutions is often not as strong, but a company might benefit from a greater competition between the funding providers.

Beside these platform solutions, concepts that do not involve a bank at all complement the portfolio. One example is dynamic discounting where a company enables its suppliers to choose when to receive the payment on outstanding invoices. The earlier the payment is received, the greater the discount the supplier has to accept [START_REF]Treasury Today: Supply chain finance: the next generation[END_REF]. In case the buyer has better access to capital, this might be a beneficial solution for all parties involved. This chapter covered the definition of SCF, the introduction of the cash-to-cash cycle as a common metric to measure the net working capital and a short overview regarding the range of SCF solutions that larger businesses can choose of. The next chapter will now deal with solutions applicable to SME and especially implementable in the performance metrics of supply chain managers.

Linking finance and supply chain performance measures

An implementation of before mentioned solutions often requires powerful market players who want to tighten their supply chain by supporting their buyers or suppliers. Even for them, onboarding suppliers can be difficult (see e.g. [START_REF] Alferink | Buyer initiated non-recourse factoring of confirmed payables: A major global corporation case study[END_REF]). Within the supply chain, only a limited amount of information is shared due to several reasons (e.g. lack of trust, transparency). But especially SMEs with more restricted resources might have difficulties to participate when no larger player is interested in such a program. In these cases, the broad range of solutions that banks or platform providers offer is remarkably narrowed down. Still, it can be beneficial if the SCF solutions are directly implemented in the SCM operations. Selected examples will be shown below. After that, a path is outlined to improve the application.

Financial measures in inventory management

Existing approaches for a greater linkage between finance and supply chain performance measures exist e.g. in the area of inventory management. In 2004, Buzacott and Zhang stated that the financial situation impacts optimal inventory decisions when using asset-based financing (a lender loans money to the customer based on his assets) [START_REF] Buzacott | Inventory management with asset-based financing[END_REF]. This is because the amount of money a company can borrow for financing inventories depends on the value of the inventory itself (only a specific percentage of the inventory-value depending on various factors will be provided by e.g. the bank). The variables are the following. A bank must decide the interest to charge and the loan limit whereas the retailer needs to decide the amount of capital to borrow within the limit and the amount of inventory to order. Buzacott and Zhang model the available cash dynamically in each period. A deterministic model is developed to understand how asset-based financing influences inventory decisions and the ability to grow for a company. Besides, a stochastic model analyzes the motivation of assetbased financing and impact of demand uncertainty. The demand uncertainty is important because it is one reason why the lender might not be able to pay back the loan (when the demand is smaller than expected). They state that their model is especially useful for start-ups facing financial restrictions. This argumentation follows the proposition of this paper that especially smaller companies might benefit from innovative SCF solutions. With asset-based financing, Buzacott and Zhang focus on short-term debts. Protopappa on the other hand considers long-term interrelations [START_REF] Protopappa | Interrelating operational and financial performance measurements in inventory theory[END_REF]. She states that payment delays impact profit margins and motivates a joint consideration of financial and operational objectives since financial flows are often treated separately from the physical product flow nowadays. Therefore, a model is presented to understand the trade-off between operational and financial parameters in order to answer questions like how working capital targets affect ordering policy and the trade-off between financial and operational measurements. She analyses the interrelation between inventory level, service level, return on working capital investment, cash flows and working capital requirements. In short, operational and financial performance measures. The analysis is done by a mathematical model within various environments (single / multi-product, various product characteristics, multi-echelon supply chain with joint working capital restrictions, etc.). She concludes that offering more tight payment delays on the customers may have counterproductive outcomes on the performance of the SC due to increased costs on the customers.

These examples proof the positive performance when inventory decisions depend on both operational and financial measures. Still, the supply chain manager must be perfectly equipped with the needed financial know-how and information. Besides, financial measures must be included in his personal objectives. Since this is often not the case, other ways are elaborated to directly implement these measures into the supply chain metrics. This will be outlined in the next subchapter.

Implementing financial measures within supply chain performance metrics

In this subchapter, a way is outlined for implementing financial measures within the supply chain management department. For this being successful, metrics that are already common in this discipline have to be used. A widely accepted model within the supply chain management discipline is the Supply Chain Operations Reference (SCOR) model created by the Supply Chain Council (SCC) [START_REF][END_REF]. It provides an extensive framework and is organized around five primary management processes plan, source, make, deliver, and return and details them so that the processes of most supply chains can be described by standardized elements. Within every management process there are three levels of detail. A fourth level is left empty for organization-specific processes. For the purpose of this paper, the SCOR model is used to show where the financial parameters are needed to be taken into account in a greater way in order to improve the overall situation.

Performance is one component of the SCOR model besides processes, best practices and people. Performance contains the attributes reliability, responsiveness, agility, costs and asset management efficiency. Attributes cannot be measured and are used to set a strategic direction (e.g. for specific products or markets). Attributes are groupings of metrics. Metrics can be measured. This paper proposes using a new attribute that describes the financial situation 1) in the market, 2) within the supply chain and specifically 3) for the company. As shown in the previous chapters, these parameters have turned out to directly influence overall performance when included in the decision making process.

For example, in the current setting it would nearly always be beneficial to increase the accounts payable (payables outstanding) and reduce accounts receivable in order to increase the return on working capital (hierarchical structure in the SCOR-model: asset management -return on working capital -accounts payable). As shown before, this can negatively impact the situation of the suppliers which might therefore lead to higher risks of failure of a supplier. A new strategy might be to strengthen the overall supply chain and therefore reduce risks. This could have its reasons in the market situation (e.g. many smaller suppliers in a low-wage country). The strategy would make use the new "financial supply chain" attribute which encompasses e.g. a risk factor at the first level. At a second level, this risk factor is detailed in e.g. a combination of the days sales outstanding (DSO) and other factors. Balancing the DSO with the other factors would now lead to an optimal situation (whereas otherwise it would be beneficial to just increase the DSO). At the end, this could lead to a more robust supply chain. Another example is the start-up scenario Buzacott and Zhang [START_REF] Buzacott | Inventory management with asset-based financing[END_REF] mentioned before where access to capital is limited. Following the strategy of taking "financial supply chain" attribute more into account would also lead to better inventory decisions in that case.

These are just a few examples. In the next step, the attribute would have to be elaborated in a greater detail considering various levels and analyzing the impacts and interactions. After that different case studies might have to be conducted.

Conclusions

The research problem has been brought to academia by several companies (in particular SMEs) who stated that they do not feel well prepared regarding financial measures within the supply chain management operations. SCF represents a powerful tool to improve supply chain performance (e.g. by releasing working capital). The paper therefore illustrates this need and creates a common understanding of SCF. It also shows current solutions in the market. In the third chapter, concepts for integrating financial concepts into the daily operations are introduced and an approach to link them to the SCOR model is outlined. Nevertheless, SCF concepts are not easy to implement. This might be due to the fact that it is an interdisciplinary topic with several departments involved and it might have complex impacts on other measures or supply chain partners that are not always easy to foresee. Also, different objectives among the supply chain players, limited capabilities or lack of trust and transparency in the supply chain might lead to some implementation difficulties. Nevertheless, it is important to develop profound concepts that can be implemented in the daily operations. Structuring the requirements for a successful implementation of these concepts might be an important future research topic.

Also, until now an outline of the background and the need for financial measures is provided. An approach to include financial measures into the SCOR model is also given. In future research efforts, a structured catalogue of supply chain finance concepts might be developed. After that, the suggested approach has to be further detailed and case studies have to be conducted to prove positive overall performance. At the end, decision makers would be enabled to find suited metrics for their specific supply chains by selecting them from the overview according to their strategies and the indication from the SCOR model.

With reverse factoring (RF), early payment is provided by a bank or factoring company to a supplier against a rate based on the buyer's creditworthiness by selling confirmed invoices from the supplier to the factor. After the payment term the buyer pays the invoiced amount to the bank or factoring company[START_REF] Alferink | Buyer initiated non-recourse factoring of confirmed payables: A major global corporation case study[END_REF].


Nikolaos A Panayiotou
email: panayiot@central.ntua.gr

Ilias P Tatsiopoulos

Supporting the Design of a Management Accounting System of a Company Operating in the Gas Industry with Business Process Modeling

Keywords: Business Process Modeling (BPM), Management Accounting System, Activity-Based Costing (ABC), Cost Center Accounting, ARIS

Traditional cost accounting systems are rarely capable to fully support management decision making in organizations. The design of innovative costing systems like Activity Based Costing (ABC) can offer a valuable alternative, however, their design proves to be very challenging. Although the use of business process modeling in cooperation with Activity Based Costing and Activity Based Management (ABM) has been extensively covered in the literature, few articles can be found that refer to the design of a full costing system with the use of a modeling architecture. This paper presents the use of a proposed business process modeling architecture for the design of a full hybrid traditional accounting and Activity Based Costing system of a company operating in the gas industry. The results of the study suggest that business process modeling can enhance the design of a costing system, minimize errors and maximize the acceptance level of all the stakeholders of the system.

Introduction

A typical traditional cost system accumulates costs by classifying them into certain categories such as labour, materials and overhead costs and then assigns these costs to cost objects [START_REF] Drury | Management Accounting for Business Decisions: 2 nd Edition[END_REF]. Although the above approach is adequate for financial accounting purposes, it cannot always fully satisfy the needs of top management that is concerned with identifying, presenting and interpreting information for formulation strategy, planning and controlling activities, decision taking, optimizing the use of resources, disclosure to stakeholders and safeguarding assets [START_REF] Rama Gopal | Accounting for Managers (Starting From Basics)[END_REF]. Traditional accounting also involves the establishment of an accounting-oriented organizational view which is reflected in the organization evaluation structure [START_REF] Scheer | Business Process Engineering: 3rd Edition[END_REF]. This is a typical situation where accounting data only hardly reflects process-oriented organizational structures. For organizations striving to become more process-oriented, it would be both desirable and necessary to also reflect process structures within an organization's accounting model [START_REF] Scheer | Business Process Engineering: 3rd Edition[END_REF]. Business Process Modeling (BPM) has been extensively used by companies to improve their business process understanding [START_REF] Laakso | Performance Evaluation and Process Interventions: A Method for Business Process Development[END_REF]. A qualitative model that provides a graphical interpretation of the process captures the structure of a business process. The objective of qualitative process modeling is to visualize the process and to achieve a commonly agreed view of the process structure. Graphical process presentation facilitates communication between people and helps in developing a common conceptual model of what goes on in the studied process [START_REF] Tornberg | Activity-Based Costing and Process Modeling for Cost-conscious Product Design: A Case Study in a Manufacturing Company[END_REF]. Many researchers have described objectives associated with the adoption of Business Process Management and Business Process Modeling within organizations [START_REF] Davenport | Process Innovation. Reengineering Work through Information Technology[END_REF][START_REF] Hammer | Reengineering the Corporation: A Manifesto for Business Revolution[END_REF][START_REF] Harmon | Business Process Change. A Guide for Business Managers and BPM and Six Sigma Professionals: 2nd Edition[END_REF].One popular application covered by many articles is the use of modeling in Activity Based Costing (ABC) and Activity Based Management (ABM) systems [START_REF] Tornberg | Activity-Based Costing and Process Modeling for Cost-conscious Product Design: A Case Study in a Manufacturing Company[END_REF], [START_REF] Tatsiopoulos | The Integration of Activity Based Costing and Enterprise Modeling for Reengineering Purposes[END_REF][START_REF] Schulze | Applying Activity-based Costing in a Supply Chain Environment[END_REF][START_REF] Baykasog | Application of Activity-based Costing to a Land Transportation Company: A Case Study[END_REF][START_REF] Sonnenberg | Linking Accounting and Process-aware Information Systems -Towards a Generalized Information Model for Process-oriented Ac-counting[END_REF]. However, few [START_REF] Sonnenberg | Linking Accounting and Process-aware Information Systems -Towards a Generalized Information Model for Process-oriented Ac-counting[END_REF] emphasize on the design of a full costing system with the use of a business process modeling architecture.

The hypothesis of this paper is that Business Process Modeling can substantially assist the design of a costing system in an organization providing a number of benefits such as rational and systematic identification of cost activities, minimization of errors, improvement on the compatibility of traditional and innovative accounting concepts and maximization of acceptance from all the stakeholders of the costing system The Architecture of Integrated Information Systems (ARIS) has been used as the basis for the development of the proposed architecture, since it originates from academic research, it is well documented within the literature, and in particular it has proven its applicability and usefulness for practice. ARIS provides a framework to help dealing with the complexity of designing and implementing business processes and process aware information systems [START_REF] Scheer | ARIS -Business Process Modeling[END_REF]. ARIS recognizes different views that provide a holistic perspective on business processes by describing "who" does "what", "how", "when" and "why". Moreover, the aspect of cost is taken into account in the framework permitting the interrelation of accounting concepts with business processes and activities. The proposed architecture is demonstrated through a case study of a company operating in the gas industry.

A Case Study

The company under discussion operates in the gas industry and is the leader in the national market where it operates. Among its strategic objectives is the continuous natural gas supply at competitive prices, maintaining its leading position in the domestic market, while enhancing its presence inside and outside of the national territory by developing new applications and natural gas services. The company is the immediate natural gas supplier of electricity producers, large customers with annual consumption of over 10 million m3, gas supply companies, end users in regions where gas supply companies have not yet been established and gas-powered vehicles.

The importance of costing for the company is high, as it affects important decisions concerning the procurement mix, capacity reservation in the national natural gas transmission system, scheduling, pricing of different customer categories and future investment initiatives.

Problem Definition

The existing accounting system of the company was covering the minimum needs for financial reporting but it was not adequate for the support of decision making. As a result the Sales and the Planning Divisions felt the need to maintain custom-made information systems in order to keep data needed for decisions made at a short-term and medium-term level. The existence of more than costing systems (one formal and some others informal) caused problems in management reporting and led to inconsistent information provision to the different company divisions. In order to cover its unsatisfied needs, the company decided to design a complementary management accounting system, without affecting its existing financial-oriented accounting system. The objectives set by the new system can be summarized as follows:

• Management view of cost with accurate and adequate data in a unique way for all the divisions of the company. • Full compatibility of the cost provided for financial accounting and management accounting.

• Rational allocation of cost to the final cost objects (customers) with the use of the appropriate cost drivers and beyond the traditional volume and turnover drivers.

• Use of the concept of cost activities in order to provide meaningful information to management.

• Improved and more detailed analysis of the sales and distribution functions.

• Cost allocation to each sector and sub-sector of the existing customers.

The design of the new system should confront with some challenging issues such as the recognition of all costing activities, the selection of the appropriate level of detail, the "bridging" of diverting views of cost provided by different departments, the identification of the existing hierarchies in the different costing dimensions and the guarantee of compatibility between the new and the old system. Taking these into account and in order to support the successful design of the new management accounting system, the adoption of an appropriate business process modeling architecture was decided.

Methodological Approach

The hybrid traditional costing and Activity Based Costing system was based on a four level hierarchy which is depicted in Figure 1. According to this, cost accumulation takes place in four levels: cost center, activity, sector/ sub-sector and cost object (customer). All four levels accumulate the same amount of cost. For example, the cost of a cost center equals the cost of activities it includes. Cost data entry must at least in-clude the information of the corresponding activity or cost center. If cost data entry does not take place on a cost object level, cost allocation to the lower levels of the hierarchy is based on predefined cost drivers. In order to support the design of the new costing system, a business process management architecture was constructed based on selected methods of the ARIS framework. In this framework each modeling object is defined through different perspectives (organization, function, data, process and output view). Six ARIS methods were selected for the construction of the modeling architecture covering the four of the five views of the framework. The selected methods, which are depicted in Figure 2, were interrelated and connected through the process view.

Design of the Management Accounting System

The first step in the design of the costing system was the definition of cost centers.

Cost center analysis is in fact an organizational issue, as in the majority of organizations, cost centers coincide with organizational units. In the case study under discussion the cost centers coincided with divisions and ARIS Organizational Chart was used for their modeling.

The final cost objects of the company were customers and not products as in most of the cases. Customers are part of a hierarchy (its last level) which starts from the sector and sub-sector and continuous with customer categories. This hierarchy was modeled with the use of Service/ Product Diagram.

The definition of cost elements is a classification used by traditional accounting systems in order to describe the nature of a cost entry. Typical cost elements are salaries, wages, material cost, taxes, financial expenses, amortization and other costs. In order to model cost elements, the ARIS Cost Category Diagram was used.

The central concept of the designed costing system was the costing activity. The costing activities were defined in such a way that they were in fact a hierarchical decomposition of the existing cost centers in order to guarantee compatibility between the traditional accounting system and the management accounting (activity oriented) system. In order to model the activity model, the simplified Event-driven Process Chain (EPC) diagram was used. For each identified activity, a corresponding Function Allocation Diagram (FAD) was assigned in order to connect each activity with other objects necessary for the design of the costing system, such as the cost center, sector/ sub-sector where this costing activity is relevant, business function (production, sales, distribution, research and development, finance), cost element and cost driver.

All the designed algorithms for the allocation of cost in the defined four levels (depicted in Figure 1) were modeled with the use of ARIS Program Flow Charts (PF).

The interrelation of the modeling objects used in the six methods described in the above paragraphs permitted the generation of a report fully describing the designed costing system (including the information of cost center, business function, sector, cost element and cost driver for each activity).

Conclusions

The use of a developed business process modeling architecture in the case study presented in the paper demonstrated some of the benefits that can be achieved in the design of management accounting systems. Management accounting has the important task to communicate both financial and non-financial information to the stakeholders of an organization, relating to its activities, in order to enable them take better decisions and improve the efficiency and effectiveness of existing operations.

The relation of management accounting with the performed activities in order to give full meaning to numbers is an important reason that increases the need of business process modeling. The proposed architecture based on the ARIS framework is definitely not the only way to cover business modeling needs. However, it proved to be very effective in the connection of different views of an accounting system satisfying all the stakeholders of such a system. Its effectiveness was proved, firstly by the fact that stakeholders' costing needs were satisfied (something that could not be achieved before the use of the suggested approach). Taking into account that the penetration of formal and primary activity based costing systems in Europe is very low due to existing difficulties in their acceptance, this is a good indication that the approach used for the design of the new system was effective. Secondly, it can be argued that the approach was effective because it offered useful costing functionality such as cohesively integrated views, activity orientation without losing the traditional desirable functionality and decision making support through the meaningful and flexible calculation of cost guaranteed by the integrated methods of the approach.

The most important of the benefits realized in the case study can be summarized as follows:

• Connection of the accounting view with the sales and operation view in a consistent way.

• Provision of meaningful information for decision making related to processes and activities as well as to organisational units and functional structures.

• Support of the design phase of the management accounting system enabling emphasis on the aspects that mattered.

• Generation of accurate functional specifications for the implementation of the costing system in a software.

• Provision of a structured approach for the control of the designed system and the critical review of the developed business rules for cost allocation.

• Improvement in the degree of acceptance of the new accounting system by all the stakeholders.

• Facilitation of future maintenance and improvement of the costing system in such a way that reflects real business changing practices.

The application of the suggested BPM approach for the design of other management accounting systems in the future (in the same or other sectors) is necessary in order to justify the positive results achieved in the case study presented in this paper. The design of a pure activity based costing system with the use of the suggested approach will be even more didactical and will better help in the expansion of the modeling architecture with the potential use of a larger number of views and modeling objects. Finally, the expansion of the modeling architecture in order to support the implementation phase will enhance its practical use.

Fig. 1 .

 1 Fig. 1. Suggested Costing Approach

Fig. 2 .

 2 Fig. 2. Business Process Modeling Architecture


M Zied Babai
email: mohamed-zied.babai@bem.edu

Ziad Jemai
email: zied.jemai@ecp.fr

Yves Dallery
email: yves.dallery@ecp.fr

Base stock inventory systems with compound Poisson demand: case of partial lost sales

Keywords: base-stock, compound Poisson, queuing system, service level, lost sales. adfa, p. 2, 2011

In this paper we extend earlier work that analyzes a single echelon single item base-stock inventory system where Demand is modeled as a compound Poisson process and the lead-time is stochastic. The extension consists in considering a cost oriented system where unfilled demands are lost. The case of partial lost sales is assumed. We first model the inventory system as a Makovian M/G/∞ queue then we propose a method to calculate numerically the optimal base-stock level. A preliminary numerical investigation is also conducted to show the performance of our solution.

Introduction

Inventory control policies have been discussed extensively in the academic literature since the 1950s. A considerable amount of research has been conducted by considering the Normality assumption for modeling the demand ( [START_REF] Silver | Inventory management and production planning and scheduling[END_REF], [START_REF] Strijbosch | Modified normal demand distributions in (R,S)inventory control[END_REF], [START_REF] Zipkin | Foundations of Inventory Management[END_REF]). This is due to the fact that the Normal distribution is attractive from a theoretical perspective and it is also known to provide a good empirical fit to observed demand data. However, it should be noted that the normality assumption makes more sense in the context of fast moving items and in the case of intermittent demand items, such an assumption is judged to be far from appropriate [START_REF] Syntetos | Distributional assumption for parametric forecasting of intermittent demand[END_REF].

Intermittent demand items are characterized by occasional demand arrivals interspersed by time intervals during which no demand occurs. As such, demand is built, for modeling purposes, from constituent elements (demand arrivals and demand sizes) that require the consideration of compound demand distributions. Compound Poisson demand processes have pretty much dominated the academic literature due to their comparative simplicity and their theoretical appeal since they may result in standard statistical distributions ( [START_REF] Archibald | s,S) Policies under Continuous Review and Discrete Compound Poisson Demand[END_REF], [START_REF] Cheung | On the (S-1, S) Inventory Model under Compound Poisson Demands and i.i.d. Unit Resupply Times[END_REF], [START_REF] Eaves | Forecasting for the ordering and stock holding of consumable spare parts[END_REF], [START_REF] Teunter | Determining Order-Up-To Levels under Periodic Review for Compound Binomial (Intermittent) demand[END_REF]). For a Poisson arrival process for example coupled with Logarithmic sizes the resulting distribution is Negative Binomial [START_REF] Teunter | Determining Order-Up-To Levels under Periodic Review for Compound Binomial (Intermittent) demand[END_REF]. In addition, from a modeling perspective, the compound Poisson process may also model the demand in the context of fast moving items by considering very low demand time intervals or equivalently a high Poisson rate.

Recently, a research work has been conducted to analyze a single echelon single item base-stock system where Demand is modeled as a compound Poisson process and the lead-time is stochastic following a General distribution [START_REF] Babai | Analysis of order-up-to-level inventory systems with compound Poisson demand[END_REF]. In order to determine the optimal base-stock level, the authors have considered cost oriented inventory systems where unfilled demands are backordered. The backordering assumption is realistic and often considered by researchers in order to determine the optimal parameters of inventory policies. However, other interesting cases could also be considered for that purpose, such as the lost sales case under which the system assumes that an excess demand is not carried over but is lost and the total cost include a lost sales cost. This case constitutes the objective of our research work.

It should be noted that the lost sales inventory models have received far less attention from researchers than the backorder models. This is because in one hand lost sales inventory models are much less analytically tractable and in the other hand, most of the optimality results in the base-stock systems have been derived under the backorder assumption. The lack of attention to the lost sales case, especially for base-stock inventory systems under compound Poisson demand has motivated this research work. In this paper, we extend the work of [START_REF] Babai | Analysis of order-up-to-level inventory systems with compound Poisson demand[END_REF] by analyzing the same base-stock inventory system under the lost sales case. The optimal base-stock level is determined under a cost oriented system where unfilled demands are lost.

The remainder of the paper is organized as follows. Section 2 describes the inventory system considered in the paper and provides a method that can be used to calculate the optimal base-stock level. Section 3 presents some preliminary results of the numerical investigation. We end in Section 4 with conclusions and directions for further research.

System Analysis

System Description and Notation

We consider a single echelon single item inventory system where the demand and the lead time are stochastic. Demand is modeled as a compound Poisson process, i.e. the inter-demand arrivals are exponentially distributed and the demand size follows an arbitrary discrete probability distribution. The focus on the discrete case is motivated by the fact that it leads to solutions that are mathematically tractable. Note that if demand sizes are continuous, the same analysis holds but summations should be replaced by their analogous integral functions. The stock is controlled according to a basestock policy where each replenishment order is associated with a stochastic lead-time. The inventory system will be analyzed in this paper by considering a cost oriented system where unfilled demands are lost.

For the remainder of the paper, we denote by: λ: mean demand arrival rate X: demand size (random variable)

System Modeling and Analysis

In this paper, we assume that partial lost sales are considered, i.e. a demand can be partially satisfied from the stock on hand and the excess demand is lost. The expected total inventory cost is composed of the expected holding cost and the expected lost sales cost. It is given as follows:

[ ] [ ] ) ( ∞ 1 = + + ) ( 0 ∑ ) ( + ) ( + = ) ( S i i i i S p S X λ B X S h hSp S C E (1) which is equivalent to [ ] ) ( ∞ 1 = ∞ 1 + = 0 = ) ( 0 ∑ ∑ ∑ ) ( ) ( + ) ( ) ( + = ) ( S i i S n i S n i S p n f S n λ B n f n S h hSp S C E (2)
where , as shown in the following Markovian chain, where the state i corresponds to the number of outstanding ordered units in the system. For more details about the modeling of inventory systems by using the queuing theory, the reader is referred to [START_REF] Buzacott | Stochastic Models of Manufacturing Systems[END_REF]. S should be calculated numerically such that:

)
[ ] [ ] { } 0 ) ( ) 1 ( : min * ≥ - + = S C E S C E S S Where [ ] ) (S C E is given by (2) and ) (S i p is given by (3).
It is clear that in order to find numerically the optimal base-stock level * S ,

the function [ ] [ ] ) ( ) 1 ( S C E S C E - + should be calculated for different values of 0 1 2 3 λ 0 λ 1 λ 2 1/L 2/L 3/L ….
S (by using a dichotomy for example), which requires the calculation of the stationary probabilities

) (S i p for different values of S .
In the next section, we calculate numerically the optimal base-stock level and cost and we investigate the impact of some parameters' variation on the optimal base-stock level.

Numerical Investigation

For the purpose of the numerical investigation, we assume that the Poisson rate of the demand arrivals l is varied from 0.1 to 10, which allows us to deal with demands that characterize both fast and slow moving items as it has been done by [START_REF] Babai | Analysis of order-up-to-level inventory systems with compound Poisson demand[END_REF]. Regarding the distribution of the demand size X, in order to reduce the complexity of the of the numerical investigation, we should consider a demand size distribution that is discrete and regenerative, since in that case the distribution of the random variable X i (the sum of i discrete demand size distributions) is of the same type, so that by knowing the type of the distribution f i and the first two moments, the analysis is straightforward. For the purpose of this numerical investigation, we consider that demand sizes follow a Poisson distribution with μ X = 10. The results are presented by considering the case: h = 1, B = 10.

The optimal base-stock level and the optimal cost when l is varied in [0.1,1] are shown in Figure 1 which corresponds to the case of slow moving stock keeping units (SKUs). The optimal base-stock level and the optimal cost when l is varied in [START_REF] Archibald | s,S) Policies under Continuous Review and Discrete Compound Poisson Demand[END_REF][START_REF] Zipkin | Foundations of Inventory Management[END_REF] are shown in Figure 3 which corresponds to the case of fast moving SKUs. 2 show that the optimal base-stock level is an increasing function of the demand arrival rate l which is expected since the average demand per time unit increases which necessitates higher stock level to reduce the total cost. It should be noted that in the case of slow moving SKUs and for very low l values, the optimal base-stock level is equal to 1 even when the average demand size increases which can be explained by the fact that the demand per time unit remains relatively low and does not necessitates more than one unit to be kept in stock. Obviously, when the demand size and the demand arrival rate increase considerably in the cases of both slow and fast moving SKUs, the optimal base-stock level and cost increase considerably.

Conclusions and future Research

In this paper, we have analyzed a single echelon single item inventory system under a compound Poisson demand and stochastic lead-time. We assume that the system in controlled with a continuous review base-stock policy.

Based on a Markovian M/G/∞ queue model, the optimal base-stock level is determined under a cost oriented system where unfilled demands are lost. Some preliminary numerical results, related to the optimal base-stock level and cost, have been given in the case of both slow and fast moving SKUs. The results show that in the case of slow moving SKUs and for very low l values, the optimal base-stock level is very low. Moreover, in the cases of fast moving SKUs, when the demand size and the demand arrival rate increase considerably, the optimal base-stock level and cost increase considerably.

An interesting way to extend this research is to conduct an empirical investigation with real data to show the behavior of the optimal base-stock level and cost in such a context. Another important issue to consider is the hy-pothesized distribution when modeling the demand in the context of slow moving items (i.e. representation of demand sizes and demand intervals). This issue has been repeatedly addressed in the academic literature [START_REF] Syntetos | Distributional assumption for parametric forecasting of intermittent demand[END_REF]. A compound Erlang process would be an interesting option to consider for the demand modeling.

Xμ

  : mean of demand size X σ : standard deviation of demand size f : probability density function of the random variable X F : cumulative probability distribution of the random variable X Y : lead-time (random variable) L: mean lead-time ) (t I : inventory position at time t ) (t N : number of outstanding ordered units in the system at time t S: order-up-to-level h: inventory holding cost per unit per unit of time B: unit lost sale cost per unit k X : the sum of k i.i.d. random variables X (k ≥ 1) k f : probability density function of the random variable k X k F : cumulative probability distribution of the random variable k X (k ≥ 1) ): probability of an event x

=

  Thus, it is easy to show that in the stationary regime, The optimal base-stock level *

Fig. 1 .Fig. 2 .

 12 Fig. 1. Variation of the optimal base-stock level and cost in the case of slow moving SKUs


Walter Riofrio

Looking at the Beginnings

Keywords: evolvability, far from thermodynamic equilibrium, open-ended evolution, prebiotic world dynamics, self-organized systems

teaching and research institutions in France or abroad, or from public or private research centers.

Dynamic systems are dynamic entities that include different types of activities among their components. Depending on the type of complex system, the different forms of interrelation that exist among its components will produce certain activities that will be subject to observation and measurement [START_REF] Capra | The Web of Life: A New Scientific Understanding of Living Systems[END_REF][START_REF] Mainzer | Thinking in Complexity: The Complex Dynamics of Matter, Mind & Mankind[END_REF][START_REF] Bak | How Nature Works: The Science of Self-Organized Criticality[END_REF]. A characteristic shared by all complex systems is that, at the moment a determined activity is produced, a uniform distribution over time does not follow. In other words, the "timing" in which the determined action or activity is produced is important. Or put a different way, "when" things happen is important [START_REF] Rensing | Biological timing and the clock metaphor: Oscillatory and hourglass mechanisms[END_REF][START_REF] Carr | Timing is everything: Organization of timing circuits in auditory and electrical sensory systems[END_REF][START_REF] Bell-Pedersen | Circadian rhythms from multiple oscillators: Lessons from diverse organisms[END_REF][START_REF] Vanrullen | Spike times make sense[END_REF]. For example, it is not totally true to assume that (a) email users send their messages at uniform intervals in time, (b) an infection by a determined contagious disease can be adequately represented through the Poison distribution, or (c) molecule X, moving on a metabolic pathway, running into molecule A is equivalent, in terms of probability, to it running into molecule B. These reflections force us to face a very important issue in the study of complex systems; of particular interest is discovering the causes that produce their dynamic organization in spontaneous conditions. These issues are especially important when our research is directed to living systems. We know that biological systems are self-organized and self-reproductive, and, in this context, we also understood that the self-organizational dynamic of these systems is composed of many levels and types of processes that are interconnected and interdependent [START_REF] Fontana | The arrival of the fittest: Toward a theory of biological organization[END_REF][START_REF] Furusawa | Origin of multicellular organisms as an inevitable consequence of dynamical systems[END_REF]. One of the most characteristic global behaviors of biological systems is the one that enables an autonomous and agent behavior with respect to their environment [START_REF] Kauffman | The Origins of Order: Self Organization and Selection in Evolution[END_REF]. Another important global behavior leads us to ask whether something exists in the biological system that enables it to feature a great deal of resilience and robustness in the face of adverse conditions or of breakdowns in certain components in its processes: its incredible homeostatic capacity [START_REF] Barkai | Robustness in simple biochemical networks[END_REF][START_REF] Levin | Resilience in natural and socioeconomic systems[END_REF][START_REF] Carlson | Complexity and robustness[END_REF][START_REF] Kitano | Biological robustness[END_REF][START_REF] Stelling | Robustness of cellular functions[END_REF]). Even when the knowledge and isolation of the different molecular components in biological systems continues to accumulate on an increasing basis in the respective data banks, we are still lacking a descriptive scheme that enables us to understand -fundamentally -what the essential properties are for determining and characterizing the organizational dynamic of living systems [START_REF] Quastler | The Emergence of Biological Organization[END_REF][START_REF] Maturana | Autopoiesis: the Organization of the Living[END_REF][START_REF] Barabási | Network biology: Understanding the cell's functional organization[END_REF].

Origin of Prebiotic World

It would seem that a suitable place to consider certain explanations on this topic is at the beginning of the move from an exclusively chemical and physicalchemical dynamic towards a type of dynamic that has more in common with the evolutionary dynamics of living beings. In other words, the search for the core of cellular organization may send our research back to the very origins of biological systems, proposing an alternative approach to what currently is being considered as the only possible explanations [START_REF] Cairns-Smith | Seven Clues to the Origin of Life[END_REF], Wächtershäuser1988, Maynard Smith, Szathmáry 1999[START_REF] Hazen | Life's rocky start[END_REF]. It is possible to hypothesize that the reproductive and catalytic properties observed in all living systems would be most comprehended from other more primitive or more basic capacities. For all of that, we claim that it is still important to continue with more research that is proposing to find alternative explanations about how, in the physical reality, the emergence of biological organization is produced in ways that are self-sustained, robust, autonomous, agent, and homeostatic with the addition of possessing the potential for increasing, throughout time, its levels of structural and organizational complexity.

In this new stage in the development of scientific knowledge, we find ourselves in unsurpassed conditions for broaching, with huge possibilities of success, the problems that remained unresolved in the earlier schemes of scientific research, problems such as the origin of life, which includes that crucial dilemma of the controversy between the "RNA first" or "metabolism first" scenario. We can visualize this dilemma from Eigen's proposal (Eigen1971), which identifies the relationship between biological information and biological function, like a "chicken-egg dilemma". We now understand that this question moves beyond being just a historical problem. Before inquiring which came first, it is more important that we ask ourselves which one of them could have given rise to the prebiotic evolutionary processes. At present, we recognize that the solution for the old dilemma must necessarily pass through the stage of understanding the notion of biological information [START_REF] Wills | Does Information Acquire Meaning Naturally?[END_REF]) and of designing a definition of functions in naturalist terms [START_REF] Collier | Autonomy and process closure as the basis for functionality[END_REF], that is, without falling into epiphenomenic versions or appealing to some form of adscription. We propose an initial working hypothesis with the purpose of contributing to the discussion and improving the understanding or clarification of what more than likely happened in the distant past, in the transition that meant the step from being inanimate to being animate.

Dynamic Organization and Internal Properties

To understand the conditions that make the appearance of living forms possible is to understand that their most basic properties were present at the origin of the prebiotic world. We also want to explain that when referring to the origin of the pre-biotic universe, it is illogical to speak in terms of a Darwinian evolution since neither DNA nor RNA had appeared and neither had anything like "genetic material". These emerged long in the history of the pre-biotic world. Therefore, we cannot speak of fitness and other concepts connected with biological evolution.

There is just open-ended evolution -a type of evolution whose components are related to the idea of evolution by natural selection. Nevertheless, it is possible for us to refer to the capacities that permit the gradual building of the structure and dynamic organization of those systems in terms of their internal properties [START_REF] Bagley | Spontaneous emergence of a metabolism[END_REF][START_REF] Bak | How Nature Works: The Science of Self-Organized Criticality[END_REF][START_REF] Jeong | The large-scale organization of metabolic networks[END_REF]. Likewise, the solution for the problem sketched above (the old dilemma) has to move through a period of establishing the criteria that can differentiate the selforganizing dynamics of the systems that make up the prebiotic world from other types of self-organized systems, and perhaps, through a time of a better understanding of the new science of networks [START_REF] Bray | Molecular networks: The top-down view[END_REF][START_REF] Watts | The "new" science of networks[END_REF], which enables us to understand the transition from the inanimate world to the animate world and to understand the step from random to scale-free networks. Another aspect is the design of a new version of evolvability that could be applied to the distinct changes that were produced in the prebiotic world [START_REF] Kirschner | Evolvability[END_REF]. We are proposing a theoretical construct that visualizes the most basic properties of living systems, originating in the systems that provided the possibilities for its emergence in the universe: in the prebiotic systems. More accurate put, we consider these original properties to be autonomy, information, and function [START_REF] Riofrio | What is life? Again, is this question interesting? Paper presented at the Complexity[END_REF]. The aforementioned theoretical construct is a type of dynamic system that we defend as the one that decisively established a division in the different types of self-organized systems. On one hand, we would have the self-organized systems that would be generating self-organized dynamics with certain degrees of ordering but whose matter and energy sources -which enable them to be in the far from thermodynamic equilibrium statewould strongly depend on their exterior environment. Instead, we affirm that there might have existed a type of self-organized system that could have incorporated as part of its dynamic organization the necessary factors that provided it the ability to be and to maintain itself, by its own dynamic, in the far from thermodynamic equilibrium state. We have named this type of self-organized system the "Informational Dynamic System" and, moreover, we propose that it is this variation of a self-organized system that for the first time opened the doors of the prebiotic world. This is the one that caused the necessary and sufficient conditions to set off the succession of certain phenomena of the universe towards the possibility of the emergence of biological systems. It is also the system that might have been the driving force to the beginning of the move from the inanimate world to the animate one [START_REF] Riofrio | Informational dynamic systems: Autonomy, information, function[END_REF]. Actually, this type of dynamic system would be composed of a group of molecular compounds that are interconnected by networks of processes, where determined types of actions take place and that, on a global scale, will enable this system to maintain and sustain itself in a robust manner over time and in conditions that are far from thermodynamic equilibrium.

To visualize the organization we are hypothesizing for the Informational Dynamic Systems, we need to include the interaction and interdependence among three different groups of molecular processes. The first corresponds to a process that enables the system to behave as a self-organized system for reasons that are systemically internal to it. It has managed to keep itself far from thermodynamic equilibrium since part of its organization is constituted by the group that links the endergonic processes with the exergonic ones and the facilitation that produces the coupling of molecules with "high energy" bonds. The second is a set of processes that constitutes the protoplasmic membrane. In this portion of the system's organization, the tasks of isolating the system from its exterior are done; in addition, it is the part of the system organization that is a complete agent in where solutions to chemical problems, such as the "osmotic crisis", the management of electrochemical gradients, will be generated as well as the work associated with the problems of "recognition" and transportation of matter and energy compounds from the outside to its inside. The third group involves the processes which are linked to the tasks of reproduction, repair, and control of the internal dynamics. These processes interact among each other as well as with the ones inside the two groups mentioned above. One of the basic characteristics of the first ancestors of living systems, those that opened the door of pre-biotic world, was the capacity to generate "meaningful information" about their environment and about their dynamical internal milieu. The important thing for our idea is that the information, properly said -The Information -has a meaning (very basic semantic) that is created on the inside of the system. Any type of signal or sign can be a carrier of what might be information (or what we call "potential information"). We consider a signal or sign to be any matter-energy variation (sound wave, electromagnetism, concentration of a chemical compound, change in pH, etc.). The "potential information" carrier must be in the surroundings, on the inside, or have transmitted the information to some system component. So, we need that one sign or signal which is the carrier of potential information must have been incorporated into some process inside the informational dynamic system. Secondly, the possible information becomes information ("information with meaning" for the system) since it has the capacity to produce something (an effect). Third, the effect has a repercussion in the system, influencing its own dynamic organization. The effect of the information that has meaning for the system can be found in the maintenance or the increase of the system cohesion. Such cohesion is constituted by the group of relationships and interdependencies that exist among the processes; it is a relational and dynamic definition that encompasses the nature of the system organization [START_REF] Collier | Entropy in evolution[END_REF][START_REF] Collier | Self-organization, individuation and identity[END_REF]. As well, the effect could produce some level of interference in the system cohesion, possibly interrupting one or more processes. It is clear that meaningful information can be caused by some signal (that carries potential information) coming from the environment like a signal that is generated in the internal dynamic of the system. In all cases, whether an effect in favor of or in contrast to cohesion, the system will develop some type of response that will be correlated to that meaningful information and the process or processes related to the effect.

In the other hand, we consider the function to be located in the action that generates a determined process and what we can understand as 'what contributes' (cooperates, favors, supplies) to the interrelation and interdependence among the processes with a view to maintaining the far from equilibrium state. On the inside of the process, each component will have the mechanism that is proper to its chemical constitution, but that chemical action (or group of actions) will have its raison d'être because of the process. Then, each process that carries out a determined and particular action (made up by the causal nexuses among the component mechanisms that constitute them) will be assimilated into the dynamic organization only if this particular action is maintaining, improving, or achieving the far from equilibrium. And this action is precisely its function in this organizational logic of the Informational Dynamic Systems. Thus, a function is something that contributes or facilitates to maintaining or increasing the far from equilibrium state. A dysfunction, on the other hand, is something that does not contribute or facilitate to maintaining the far from equilibrium state. Succinctly stated, we can say that our theoretical proposal visualizes the emergence of information and biological function in a sort of coordinated origin -at the same time -in the local processes of these types of systems. This visualization of the physical emergence of Information and Function gives us to talk about the notion of "Information-Function"; each time we observe functions happening in these systems' processes, we can be sure that some type of information has been transmitted through them. Likewise, when we observe the transmission of some type of information among the process, we can be sure that some function has been produced among them.


Shigeki Umeda
email: shigeki@cc.musashi.ac.jp

A Test-bed system for supply chain management incorporating reverse logistic

Keywords: Supply chain management, Reverse Logistics, Simulation, Test-bed system

Due to environmental and ecological responsibility, enterprises are trying to reuse, remanufacture and recycle the used products to reduce the negative impact on environment. Reverse logistics is one of essential elements to implement such sustainable supply chain system. This paper proposes simulation-based test-bed system for supply chain management incorporating reverse logistics.

Introduction

Modern manufacturing enterprises need to collaborate with their business partners through their business process operations such as design, manufacture, distribution, and after sales service. A supply chain system is a chain of processes from the initial raw materials to the ultimate consumption of the finished product spanning across multiple supplier-customer links. It provides functions within and outside a company that enable the value chain to make products and provide services to the customers. Many discussions have been done [START_REF] Daniel | Supply Chain Management Incorporating Reverse Logistics[END_REF].

In the last decade, due to environmental and ecological responsibility, enterprises are trying to reuse, remanufacture and recycle the used products to reduce the negative impact on environment, especially the manufacturers of the electrical consumer products. Electrical and electronic scrap also known as e-waste or e-scrap -has increased dramatically.

Requirements for corporate responsibility and sustainability are getting more urgent. The reverse logistics in supply chains is strongly related to all stages of a product development and is also a critical problem to all level of the industry.

Reverse logistics systems require taking back products from customers and the repairing, remanufacturing (value-added recovery), or recycling (material recovery) the returned products.

The reverse logistics makes more complicated material-flows in supply chain. There are different kinds of material-flows in a chain. One is forward-flow which starts at part/material suppliers and reach customers. The other is reverse-flow which starts at customers and reach remanufacturer or recycler. Accordingly, introduction of reverse logistics in supply chain system would have profound effects on operations such as material-handling and procurement. This relationship is similar with arterialflow and venous-flow in a human body.

System design and implementation of a "supply chain system with reverse-flow" would be extremely difficult in comparison with the cases without reverse-low. This is because considerations of reverse logistics would promote many issues in both configuration design phase and operations design phase. A generic method is needed to support supply chain system with reverse logistics.

System modeling technologies often provide useful operational analysis of system behaviors. The SCOR model is the most prominent process model in supply chain system [START_REF]SCOR model[END_REF]. This model provides a set of core models, which represents business processes in supply chain operations. The SCOR model includes five core models (PLAN, SOURCE, MAKE, DELIVER, and RETURN). Individual model describes activities in detail. Such macro-level models are, needless to say, useful for generic system descriptions at initial stage.

Modeling and simulation is one of the general purpose tools to optimize designs and operations of manufacturing and logistics systems. Especially discrete-event simulation provides predictions of system's behaviors potential status by "what-if scenario". Thus, simulations have been used as a powerful solution tool for various operational management problems, such as capacity planning, resource planning, lead-time planning, supplier selection, and outsourcing planning. The disadvantage of modeling and simulation is that system analysts need to implement simulation models of their own target system. This workload is very huge.

Analysts would be able to use modeling and simulation if typical generic simulation models are provided as a simulation model library in advance. In this case, the analyst chooses proper models in library, and customizes them as the need arises [3][4].

The objectives of this paper are [START_REF] Daniel | Supply Chain Management Incorporating Reverse Logistics[END_REF] to propose a generic supply chain model with reverse logistics for product reuse, (2) to implement generic simulation models for the test-bed system by using generic models, and (3) to represent effectiveness of the proposed test-bed system by numerical examples. These models include component members, which enables to organize a supply chain system with reverse logistics. All models represent both material-processing logic and information-processing logic in the chain.

2

Reverse logistics models

Member elements model

First, we configured models that provide regular flow in a supply chain system. This feature is composed of elements, which include a Supplier, a Manufacturer, a Retailer, a Customer, and a Chain manager. Second, we also arranged components that realize reverse flow for product reuses. These elements are "Collector", "Remanufacturer", and "Recycler". A set of these elements would be a generic supply chain model with reverse logistics (Fig. 1). Data descriptions of these elements include input (information/material), output (information/material), Pre-defined information, activities sequences, and performance measurement data. The summaries of activities of these elements are as follows.

Fig. 1 represents a configuration of this model. This model is based on an analogy between arterial-venous blood flows in a human body and material-flow in a supply chain. Solid lines are production generation flow (arterial-flow), meanwhile, dashed lines are reverse logistics flow (venous-flow). Arterial-flows and venous-flow should be synchronized with each other. The system synchronizes venous flows with arterial flows. A set of simulation models represents above elements was implemented as a test-bed system for supply chain management incorporating reverse logistics.

Chain manager:

The major task of this element is to generate orders to elements which belong to an arterial flow in a chain: these are "Supplier", "Manufacturer", and "Retailer". This is a heterogeneous element in the chain. It predicts Customers' demands, and it gives orders to other members by using the predicted data. It keeps Customers' purchase data in a particular duration, and it uses them to predict demands in next ordering cycle. We developed an IDEF0-based hierarchical function model, that represents ordering process mechanisms in a chain [START_REF] Umeda | Planning and implementation of information systems in supply chain systems[END_REF]. Supplier: This element is a start point of material flows in a chain. It generates parts by a sourcing order from Chain manager. And, it sends the parts to "Manufacturer" by using a transporter. Manufacturer: It receives parts from the Supplier and keeps them. When it receives an order from the Chain manager, it starts to generate products. After predefined lead-time, it sends the products to "Retailer" by using a transporter.

PUSH-type and PULL-type reverse model

Fig. 2 represents configurations of reverse logistics models. These models are based on an analogy between arterial-venous blood flows in a human body and material-flow in a supply chain. Solid lines are production generation flow (arterial-flow), meanwhile, dashed lines are reverse logistics flow (venous-flow). Arterial-flows and venous-flow should be synchronized with each other. The system synchronizes venous flows with arterial flows. A set of simulation models represents above elements was implemented as a test-bed system for supply chain management incorporating reverse logistics.

The flow from Customer to Remanufacturer by way of Collector is a reverse logistics flow. There are two ways to control this flow: PUSH-type and PULL-type. Customer sends "used-products" to Collector, when Customer disposes them. The role of Collector is to distinguish reusable materials from the disposed products, and stores them.

One way is that Collector and Remanufacturer sends reverse products to Manufacturer in an orderly manner. This is PUSH-type flow, which is illustrated in Fig. 2 (a). Another way is that Remanufacturer regenerates reverse products as the need arises in Manufacturer. The same logic is applied in between Remanufacturer and Collector. This is PULL-type flow. The implementation of this logic needs two pull signals, which is illustrated in Fig. 2 (b). The first one is from Manufacturer to Remanufacturer, and the second one is from Remanufacturer to Collector. Collector acquires reusable materials from Customer with constant collection rate. Remanufacturer pulls materials from Collector, when it requires materials. Manufacturer also pulls materials from Remanufacturer as the need arise.

In PUSH-type, remanufactured products are sequentially pushed into Manufacturer, synchronizing with occurrence of reverse. Remanufactured product would be kept as material inventory in Manufacturer. In PULL-type, reverse products are stocked at Collector. These products stay at there, during no PULL signal from Remanufacturer. And, Remanufacturer does not work until it receives PULL signal. When high volumes of reverse products are generated, they are stopped at Collector.

When demand volume by Retailer increases, volume of used product flowed to Collector would rise. These are recycled by Remanufacturer, and are stocked as refreshed parts in Manufacturer's buffer. Meanwhile, in PULL-type, even if demand volume decreases, volume of used product flowed to Collector would move down.

Synchronized with the used product volume, the volume of spare parts and reuse materials would increase or decrease. When manufacturing order increases after low production continues, parts shortage is possibly occurred in Manufacturer.

Simulation examples

Based on the generic supply chain model described in 2.1 and 2.2, we implemented two types of model of reverse supply chain systems. One is Push-type reverse supply chain model, and another is Pull-type reverse supply chain model. In these models, Chain manager predicts market demands, and gives orders to both Supplier and Manufacturer in every week (5 working days).

Performance of reverse supply chain system depends on the "collection rate" of reusable materials from disposed products in market. In this case, we defined this value as 60%. Remanufacturer provides high performance; meanwhile Collector needs comparatively long lead-time to get reusable materials from the disposed product. Balance of these two reverse suppliers would be a key issue to determine whole of reverse supply chain system.

Other parameters of this simulation are lead-time and lot-size of chain members (Manufacturer, Retailer, Remanufacturer, Collector, and Deliverer). Chain manager generates the orders to Manufacturer and Supplier. Manufacturer and Retailer own almost same resource capacities. Meanwhile, Collector, Remanufacturer, and Retailer own almost similar resource capacities.

Operations during a hundred days are simulated, and the ordering cycle is a week (5 working days). Chain manager gives an operation order to Supplier and Manufacturer in every 5 working days. When the manager gives orders, he/she predicts demands in market by using exponential smoothing method. Each chain member gives transportation orders to Deliverer, when its operations are finished.

Figure 3 represents transitions of material volumes in the Push-type reverse supply chain. Retailer and Remanufacturer represent a steady state transition (Figure 3 Collector needs independent lead-time to collect reusable materials. Nevertheless, Collector cannot withdraw all materials that consumer used. In this simulation scenario, Collector sends materials to Remanufacturer as soon as possible. Accordingly, materials in Collector would decrease. Simulation configures considerable input materials as initial value; however, material shortage has occurred in midterm. This phenomenon is fully predictable, considering operational policy in Collector.

Manager makes production plans for both Manufacturer and Supplier considering Market needs. Manufacturer would additionally own the remanufactured materials by Collector and Remanufacturer. Accordingly, materials in Manufacturer would be increased.

In Pull-type system, Manufacturer pulls materials from Remanufacturer, when it is needed, and Remanufacturer pulls materials from Collector. Accordingly Manufacturer does not own over-need material. Besides, the collected material would stay at Collector. The only way is that Manager would make plans considering predictions of recycled materials from Collector at any situation. However, it is very difficult to predict how many recycled materials in any operational phases. We would have no choice without preparing materials at suppliers' buffers, considering available materials at suppliers in a chain. Simulations based on other scenarios would be needed to discuss this issue.

Conclusion and future research

The work described in this paper is the first step in simulation researches for reverse supply chain management. Recovery, recycling, or reuse of products will be important issues in current supply chain management. A formal study of SCM incorporating reverse logistics is critical. The proposed test-bed simulation system would be a useful tool for designing supply chain incorporating reverse logistics.

There are various types of supply and reverse chain management problems. Design and planning would be the most popular scope. When a system planner designs a supply chain or a manager reviews performance of the existing supply chain, he/she would attach importance supplier selection problem. It is a significant decision since it affects the system performance for a long time. From the supply chain performance viewpoint, it affects all the problems discussed above. Mature decisions would be needed.

First of all, we should organize problems in reverse supply chain management. Design and planning problems, suppliers/venders selection problems, and outsourcing planning problem would be discussed. These problems are interlinked. Among them, discussions of Push-type and Pull-type reverse models would the most important.

Fig. 1 .

 1 Fig. 1. Generic supply chain model with reverse logistics

Fig. 2 .

 2 Fig. 2. Push-type and Pull-type reverse model

Fig. 3 .

 3 Fig. 3. Material volume at chain members


Walter Riofrio

Dynamic changes in Prebiotic Systems

Keywords: cohesion, complex systems, emergence, evolvability, far from thermodynamic equilibrium, open-ended evolution

Introduction

Understanding the origin of living systems is grasping the most basic capacities that are used in the construction of the organization of these systems [START_REF] Shapiro | Origins: A Skeptic's Guide to the Creation of Life on Earth[END_REF][START_REF] Fox | Molecular Evolution and the Origin of Life[END_REF][START_REF] Lurquin | Origins Life and the Universe[END_REF].

The prebiotic world can be conceived of as a group of systems that generated the move from the inanimate to the animate. In more precise terms, the prebiotic world must have been constituted by a series of more or less successive steps and each one of them, was represented by a specific type of dynamic system. In each successive stage, the respective dynamic system must have contained those capacities/ improvements possessed by the systems from previous steps and, in It is possible to think that in the prebiotic epoch the conditions should have existed that enabled the development of the rudiments of a dynamic organization containing the essentials for the subsequent emergence of life, a specific type of dynamic that would be associated with the variability of the different prebiotic systems.

Variability in prebiotic systems

know that two variability types exist in biological systems: one that is produced by genetic changes (mutations) and is therefore inheritable and the second, which is produced by changes in the environment and associated with the system's capacity to maintain its cohesion [START_REF]Phenotypic plasticity in the interactions and evolution of species[END_REF][START_REF] Hoffmann | Heritable variation and evolution under favourable and unfavourable conditions[END_REF]. It is associated with multiple strategies that produce homeostatic phenomena [START_REF] Marder | Variability, compensation and homeostasis in neuron and network function[END_REF]. Although this second variability type is not "inheritable", in the sense that we are accustomed to thinking of in biology, it is still possible to think about an open-ended evolution that focuses on increasing the complexity of the systems.

More important than preserving some of components that are reliably transmitted to the successive generations, it seems reasonable to claim that during the prebiotic epoch, it was crucial to maintain the cohesion of its organization at all costs. The dynamic of its organization is revealed in the fundamental properties that make its integrity and identity explicit. Therefore, maintaining the conditions that enable the stabilization of these propertiesmaintaining them robustly -is that which must have been preserved in the different systems of the prebiotic world.

To characterize the identity of the dynamic organization of these systems is to identify the most fundamental properties that define them. Once these properties are located, it is a question of widening the notion of evolution by natural

selection towards an open-ended evolution. Therefore, instead of occupying ourselves with having to follow up on the inheritable variability, we are now interested in the variability that preserves the cohesion of the fundamental properties in contexts of increasing the complexity of the networks of processes allow the expression of these properties.

If we apply this approach to the variations in the prebiotic universe, then we will inevitably arrive at the conclusion that the fundamental causes for variability in those systems were changes in its environment. In other words, since there was nothing like "genetic materials" at the beginnings of the prebiotic world, the system evolved in the face of problems generated by the environment through different ways of preserving the basic properties which characterized them. So, dynamic systems of the prebiotic world must have developed -taking into consideration that they survived these adverse conditions -strategies that enabled them to establish nexuses between the external environmental changes and the internal developments that perpetuated the dynamic cohesion of their organization.

We now realize that there are a variety of processes in the plasmatic membranes of cells that enables them, within certain limits, to suitably manage their conditions and internal requirements. Including isolation from its environment, it has a capacity that actively selects certain matter-energy components from its exterior and carries them to its interior.

We may hypothesize that the extreme complexity and sophistication of these processes correspond to the final phases of strategies developed very early by evolutionary processes in which improvements were gradually produced. Moreover, their presence is important for resolving problems that seriously place the cellular integrity at risk if they are not worked out, problems such as the osmotic balance, the electrochemical transportation, and the contribution of compounds to internal processes.

The above would reveal to us the earliest ancestor of these actions. It would be pointing out that its importance and age lie in the intimate relationship they have with the spontaneous origin of a dynamic organization of a system that will guide us -much, much later -towards the world of the living.

Evolvabilty and Inheritance

In this way, we may hypothesize that from their most primitive origins, the true ancestors of the living systems had the capacity to interact with and to express an active behavior towards their environment. If we are in right track, then, the successive systems in the prebiotic universe had as one of their most important dynamic structures a protoplasmic membrane that formed a fundamental part of their organizational composition. This structure would have been formed of molecules interacting in processes they would have simulated at very basic levels, those we can still see in the plasmatic membranes of the current cells.

Apart of to be a physical barrier, this protoplasmic membrane permits certain properties of chemistry to have a focal point of action to generate problematic circumstances which in turn produce the conditioning situations for exploring different solution strategies. And is this kind of protoplasmic membrane what the systems in prebiotic epochs with the capacity of being evolvable from its very origins.

We talk about evolvability when we are able to observe a phenotypic variation that is susceptible to being a target of natural selection or, in other words, when an organism has the capacity to generate a phenotypic variation that is inheritable [START_REF] Altenberg | The Evolution of Evolvability in Genetic Programming[END_REF][START_REF] Conrad | The geometry of evolution[END_REF][START_REF] Dawkins | The Evolution of Evolvability[END_REF][START_REF] Kirschner | Evolvability[END_REF][START_REF] Wagner | Complex adaptations and the evolution of evolvability[END_REF]. Nevertheless, when we are thinking upon the origins of the prebiotic world, we cannot establish these types of associations. It is nearly impossible to think that in those remote epochs there existed molecular entities so complex and sophisticated as nucleic acids or proteins. Hence, it is not possible to talk about evolution in terms of natural selection during those times; what we are proposing, then, is that it is possible to talk about evolvability in the prebiotic world.

Once these systems are confronted by a specific problem that the environment generates, the different possible solutions (strategies) produced in the system's protoplasmic membranes as a product of the reproduction of these systems are nothing more than the maintenance of the integrity of their dynamic organization. This sort of prebiotic "inheritance" must have been associated with a certain evolvability capacity rather than with a Darwinian type of evolution.

In other words, every time the systems reproduced we could see that inside the processes, the components could be changed, but as a whole, the system's descendents attempted to keep their most fundamental properties intact and compatible with its survival; that is, in conditions compatible with the far from equilibrium state.

To end this work, it seems feasible to propose the idea that the basis of hereditary similarity in "prebiotic evolution" depended on the way cell-like systems were embedded in their environments, rather than on internal, gene-like mechanisms. We also suggest evolution is happening at small-time scales -so it

  addition, it had the chance to explore new strategies or to improve on what was already there.

is continuous -due to that the membrane makes the cell "evolvable". Also, we consider interesting to continue the exploration of the possible consequences derived of the previous statements and proposals sketched in this article, with the ultimate goal to widen our current comprehension of evolution.