Can Sun
email: can.sun@infineon.com

Thomas Rose
email: thomas.rose@fit.fraunhofer.de

Hans Ehm
email: hans.ehm@infineon.com

Stefan Heilmayer
email: stefan.heilmayer@infineon.com

Complexity Management in the Semiconductor Supply Chain and Manufacturing Using PROS Analysis

Keywords: supply chain complexity, change management, process model, complexity assessment, semiconductor industry

Supply chain complexity is a rising problem, especially in the semiconductor industry. Many innovative activities occur in the daily supply chain and manufacturing, and these changes inevitably bring in the complexities to the organization. But not all of them are valuable to the business goals. Decision makers want to keep value-added complexity and reduce non-value-added complexity. To manage the complexity, we propose a framework with four steps from changes identification towards the final decision making. The core solution of this framework is PROS (process, role, object, state) idea, which provides an understandable and structural way to describe the complexity. A simplified small real example from semiconductor supply chain is used to demonstrate this approach. The results indicate that the PROS idea is able to analyze complexity from different aspects and extract most key information; however, how to measure the structural complexity of a large complex system without complete information is still under investigation.

Introduction

The semiconductor industry is considered to be one of the most complex industries. From the raw material of silicon to the advanced semiconductor chips, there are more than 500 processing steps involved in the manufacturing. It also faces a highly volatile and turbulent market due to economic cycles, which bring the challenge to manage dynamic production environments with the pace of change in the industry [START_REF] Uzsoy | A Review Of Production Planning And Scheduling Models In The Semiconductor Industry Part I: System Characteristics, Performance Evaluation And Production Planning[END_REF], [START_REF] Bauer | Mastering Variability In Complex Environments[END_REF], [START_REF] Emami-Naeini | Control in Semiconductor Wafer Manufacturing[END_REF].

The semiconductor supply chain is characterized by long throughput times, high levels of stochasticity, non-linearity in the manufacturing process [START_REF] Wang | Model Predictive Control For Tactical Decision-Making In 5. Semiconductor Manufacturing Supply Chain Management[END_REF], and short product life cycles. These all lead to complexity to be managed in the supply chain. It is reflected as: network complexity (e.g. multiple production sites and global distribution centers), process complexity (manufacturing and business processes), product complexity (e.g. about 10,000 Stock keeping units and 500,000 order line item buckets), organizational complexity (e.g. many geographic regions with various tax and customs regulations), and information complexity (data structure and information flow) [5]. And all of them are interlinked. Managing complexity in the supply chain adds value to business. According to A.T. Kearney's report, companies can increase their Earnings before interest and tax (EBIT) by 3 to 5 percent on average through systematic complexity management [START_REF] Christopher | The Agile Supply Chain: Competing In Volatile Markets[END_REF]. Many changes via innovations are ongoing in operational, tactical and strategic supply chain activities and thus complexities are added but not all of them are valuable to the business goals. Therefore, we need to distinguish: the "good" complexity which adds value to the supply chain whereas the "bad'' one does not. Value-adding ("good") complexity offers ways to meet customer demands and create a real competitive advantage; while value-destroying ("bad") complexity dissatisfy customers and sends the company into chaos and confusion [START_REF] Christopher | The Agile Supply Chain: Competing In Volatile Markets[END_REF], [START_REF] Scheiter | How Much Does Complexity Really Cost? A.T. Kearney[END_REF]. These two different categories of complexity require companies to employ distinctive strategies. The value-adding complexity should be controlled efficiently to create value; for the value-destroying complexity, the part that does not add value needs to be eliminated, reduced and minimized [START_REF] Etheredge | Getting A Handle On Complexity[END_REF], [START_REF] Heywood | Cracking the complexity code[END_REF], and avoided in the early phase of generation. In reality these two types of complexity often occur together and thus a strategic balance is demanding, e.g., lead firms increase complexity by placing new demands on the value chain and in parallel adopt strategies to reduce the complexity of these transactions [START_REF] Birkinshaw | Putting organizational complexity[END_REF]. This brings the challenges to detect the complexity-added part and then to evaluate them in order to get rid of the non-valuable parts and support decision making.

Research Question

My research aims to manage the complexities from the computer science view. By tracking the changes on the system level, the complexity drivers can be identified and described in a systematic way. After all the key information related to complexity being captured and structured, we can assess the complexity through selected instruments and categorize it as a value-added complexity or not. In the end, the results should be validated and thus can support decision making by applying corresponding strategies (e.g. reduce complexity, avoid complexity, etc.).

Status of problem domain and related solutions

Much relevant research has been done on complexity management. Literature shows that most analysis is on the theoretical level based on an abstract model instead of operational excellence on the practical level [11]. However, the mapping process from "a real complex problem" to "a defined model for complexity" is not much explored. Research on change management is mostly analyzed from the organizational view [START_REF] Aelker | Managing complexity in supply chains: a discussion of current approaches on the example of the semiconductor industry[END_REF], small amount is viewed from the system engineering field, which is more related to the business process re-engineering and process management [START_REF] Todnem By | Organisational change management: A critical review[END_REF] and provides certain process meta-models or patterns for change management [START_REF] Kettinger | Business process change: a study of methodologies, techniques, and tools[END_REF].We are more interested in the latter direction, however, the connection between model of system change and the complexity management is not obvious. Complexity in a supply chain is often viewed from three aspects: product, process and organization [START_REF] Weber | Change patterns and change support featuresenhancing flexibility in process-aware information systems[END_REF], [START_REF] Elmaraghy | Manufacturing systems configuration complexity[END_REF], [START_REF] Deger | Managing Complexity in Automotive Engineering[END_REF]. Research on the complexity analysis usually focuses on certain aspects, e.g. product variety, while it is not common to consider the complexity from a holistic view. Considering the inter-dependencies of different aspects of complexity, we prefer to use a comprehensive approach to capture all the important features of a complex system. Regarding the methods and instruments of complexity assessment, much research is on the strategic level and only provides qualitative evaluation; some quantitative methods are available but still lack practicability and tools [11], [START_REF] Weber | Change patterns and change support featuresenhancing flexibility in process-aware information systems[END_REF], [START_REF] Lindemann | Facing multi-domain complexity in product development. The future of product development[END_REF], [START_REF] Shannon | A Mathematical Theory of Communication[END_REF].To support decision making, we are also interested in the implementation details, such as, formal indicators and structural measurement. From above analysis, it is seen that there is a gap between the existing approaches to handle complex problems and our objective. Therefore, we bring in a framework including 4 steps to manage complexity: 1) Identify complexity caused by changes 2) Represent complexity 3) Assess complexity via developed instruments 4) Evaluate and support decision making. In this paper we address the first three steps on a real problem from semiconductor industry, which are also expected to be beneficial in the last stage of decision making. And in the second step a proposed conceptual model called PROS to describe complexity is highlighted.

Proposed approach 2.1 Identification of changes and complexity

Change is one of the main reasons to cause the complexity, so our research starts from the change analysis. The goal of this step is to capture the complexity caused by changes on the detailed level. Two parts related to changes should be considered: the change itself and its impact to the system. The change itself, also referred to as the initial change or one-time-change, means the "effort to implement a change", which normally only execute once. For the impact of change, it is "the potential consequence of a change on a system or what needs to be modified of a system in order to accomplish a change" [START_REF] Schuh | Complexity-based modeling of reconfigurable collaborations in production industry[END_REF]. This often requires executing affected processes regularly in order to maintain the change of system. Both change related parts usually lead to increased complexity. The output of this step is the added processes during the initial change phase; and the affected processes during the maintenance phase.

Information Extraction and Representation -PROS idea

The purpose of this step is to represent the complexity in a structural way without losing any important information. System models are employed to formalize the complexities receiving from the 1 st phase using modeling language such as SysML. The premise to accurately describe supply chain complexity is to define the boundary of the complex system and its environment. We adopt a system delimitation technique from a generic Systems Engineering (SE) methodology to define the environment and intervention system [START_REF] Bohner | Software change impact analysis[END_REF], [START_REF] Haberfellner | Systems Engineering: Methodik und Praxis[END_REF]. Some similar approaches, e.g., a knowledge representation language called Telos [START_REF] Alard | ETH Chair of Technology and Innovation Management[END_REF] can also be used to distinguish the environment in a later stage. Once the investigation area is reduced, we can identify the elements and their relationships using the system consideration of SE. Then we develop a conceptual model called PROS (Process, Role, Object, State), which defines the basic elements and relationships in a complex system. The idea of PROS originated from Object Process Methodology (OPM) [START_REF] Mylopoulos | Telos: Representing knowledge about information systems[END_REF], [START_REF] Dori | Object Process Methodology: A Holistic Systems Paradigm; with CD-ROM[END_REF]. OPM defines three basic entities: objects with states and processes. Among them objects and processes are higher-level building blocks, while states are always associated with objects and cannot be state-alone. It can be used to model the complex dynamic systems and embedded into other models for specified application [START_REF] Dori | Object-process analysis: maintaining the balance between system structure and behaviour[END_REF]. Also we notice that supply chain is similar to economic, ecological, and social systems, which are characterized by interactive "agents'' (roles) [START_REF] Sharon | A model-based approach for planning work breakdown structures of complex systems projects[END_REF], [START_REF] Berry | Adaptive agents, intelligence, and emergent human organization: Capturing complexity through agent-based modeling[END_REF].Therefore, we assume role is as important as the object and process, while OPM only handles human as an instance of object. Comparing with OPM, PROS also considers the human behaviors and their initiatives. PROS model is characterized by entities, relationships and constraints. Entities. A Process is a pattern of transformation that an object undergoes; A Role is a person to execute a process. This definition can be extended to: A role could be a person, a department, a customer, a supplier or any other group of persons or a software tool to execute a process. An Object is a thing that has the potential of stable, unconditional physical or mental existence. A State is a situation or position at which the object can exist for a period of time. Relationships. We customize the OPM relationship set [START_REF] Mylopoulos | Telos: Representing knowledge about information systems[END_REF] for our purpose and define 6 relevant pairs of relations: Process-Process, Process-Role, Process-State, Process-Object, Object-Object, Object-State. For each pair, there are one or more subrelationships. E.g., there are several different types of Process-State relationships. The attributes of these relationships are also defined: name, direction, symbols, dynamics, etc. Constraints. Two constraints are highlighted: Cardinality and Relationship rule. Cardinality defines 3 types of data structure: one-to-one relationship, one-to-many relationship and many-to-many relationship. Relationship rules imply that all the relationship definitions should follow the rules of the above 6 pairs strictly. The cardinality constraints and relationship rule can be used together. PROS Diagram and Prototype. In working with complex problems we found out that representation is an important goal for PROS. Thus we design a PROS diagram to visualize the entities and their relationships, which can be viewed as the integration of the use case and object diagram of UML notations. We also developed a prototype as shown in Fig. 1. The layout divides the canvas into 5 areas, and each contains one independent diagram. In the area marked with 1, the navigation of the whole object diagram is shown. Area 2 shows the navigation of the complete process diagram. Area 3 shows the dynamic object and state diagram for a running process. It reflects the details and changes of the objects during the processing. Area 4 shows the roles involved in the process. Area 5 shows the running step for the process. Area 1 and 2 do not change during the whole process analysis, only the analyzed area of processes and objects is highlighted. Other areas change with the process step in analysis. PROS analysis normally starts with the process aspect, similar to other system modeling languages like BPMN and UML. Besides this process-oriented analysis, the human-oriented analysis can also be applied. Agent-based modeling and simulation is a widely used technique to formalize the human (agents in broad definition) behavior and their interactions [START_REF] Holling | Understanding the complexity of economic, ecological, and social systems[END_REF]. Another technique is goal-oriented modeling, e.g., i-Star approach can analyze the agents from the view of their personal goals and what activities could be done in order to achieve these goals [START_REF] Helbing | How to do agent-based simulations in the future: From modeling social mechanisms to emergent phenomena and interactive systems design[END_REF]. The results of the PROS analysis contain most key information from a complex system and which can be used as an input for the assessment step.

Structural complexity measurement using PROS

Structural complexity is about the complexity resulting from physical interconnection of components. It belongs to the physical domain and can be directly calculated from the elements and the relationships among them [START_REF] Weber | Change patterns and change support featuresenhancing flexibility in process-aware information systems[END_REF], [START_REF]Social modeling for requirements engineering[END_REF]. Since this information can be received from the step 2, we can at least calculate the complexity oriented from elements (states of a system) and the complexity oriented from relationships (number of all connections). A further step measure is to calculate the entropy of statistical complexity based on the Shannon information theory [START_REF] Lindemann | Facing multi-domain complexity in product development. The future of product development[END_REF]. Besides the basic quantity (size) information, we assume that the structural complexity is also decided by the attributes of each individual element, such as category, importance or diversity, and whether it is interrelated to the rest of system. We also need to highlight the impact of roles (often humans), as their behaviors can lead to uncertainty and thus complexity of the system. To be able to distinguish the complexity impact of different roles, we added a weight value for each role by considering the number of involved processes [START_REF] Salado | The Concept of Problem Complexity[END_REF].

Case Study

Shared reticle vs. mono reticle

We select a case from semiconductor manufacturing to explain how complexity is generated. A set of reticles (up to 35) is needed to produce a wafer. In this paper we call the reticle set ''reticle'' for simplicity. Comparing with the as-is solution with mono reticle, an alternative solution using shared reticle could produce more products on one wafer, and thus reduce the quantity of reticles required. The reduction of reticle costs decreases manufacturing costs substantially. There is certain degree of truth that, shared reticle technology is cost beneficial, but the flip side of the coin is that the change process from mono reticle to share reticle is not that simple. For example, certain processes need to be updated, people need to be motivated to accept the changes, etc., which leads to increased complexities. Before making decision to adopt the shared reticle solution or not, it is necessary to assess its increased supply chain complexity and evaluate whether the reduced reticle cost offsets the increased complexity. The cost saving from the economic view is given on monetary values; however, the change process and its increasing complexity are not systematically assessed. Current Business Process Management (BPM) solution cannot reflect all aspects of the complex problem, while other supply chain process models are not detailed on the operational level. This gap hinders the making of high-quality decisions.

Results achieved so far

By following the framework provided in section 2, we have achieved some intermediate results, which are mainly centered on the changes and complexities identification and measurement. Changes and complexity identification and presentation. The change management can be analyzed from the aspects of process, organization (roles) via PROS. The process analysis follows the supply chain operations reference-model (SCOR) model, the most widely accepted framework for standardization in supply chain management, developed by the Supply Chain Council1 . It defines the first three levels of supply chain processes. The top level has 5 processes: Plan, Source, Make, Deliver and Return. Each level-1 process has 10-20 level-2 processes and spans multiple level-3 and 4 processes. Processes below level 3 are defined by the companies themselves. Following the SCOR model, the major processes of shared reticle up to level 4 can be identified.

Considering around all 500 steps of Produce and Test Process (sub-process of Make) related to wafer manufacturing with mono and shared reticle, it can be roughly said that 480 steps are not changed. Complexity is mainly added in the Test process (for simplicity step 480 to 490) and the Optical Control process (for simplicity step 490 to 500). For the Plan Process, the overall planning including short-term plan and midterm plan need to be changed; and Front End Plan needs to be rescheduled. The main affected processes and their added complexities are listed in Table 1. It is important to highlight which types of change the complexity belongs to, as this would be part of assessment on the next stage. We also notice that the stakeholders' attitudes towards these affected processes may influence the new solution and thus lead to complexity. Research shows people may not like change or may not adopt changes [START_REF] Sun | Complexity Measurement in the Semiconductor Supply Chain[END_REF], [START_REF] Bakker | Why people don't change[END_REF].Therefore, we need to consider the human goals in order to measure complexity accurately in the next step.

Based on the interviews and process analysis, we identify the key stakeholders involved in the change project and assess their interests. Here a goal-oriented modeling approach is employed, e.g., i-Star can be used to analyze personal goals and behaviors of alternative solutions [START_REF] Helbing | How to do agent-based simulations in the future: From modeling social mechanisms to emergent phenomena and interactive systems design[END_REF]. For each stakeholder, first we analyze their goals and corresponding actions, and then we can check how these actions benefit or hurt their goals. By doing that the relationships among stakeholders are detected too. One part of our result shows that, test engineer does not like to accept the change as it hurts his goal while the development engineer is motivated for this change.

The main object involved in this change is wafer and its states are related to the different stages of manufacturing process steps. PROS approach can be used as a guide to obtain the key elements of processes, roles and objects, as well as different relationships. We could gain this information:

 Description about the stakeholders and their goals  Description about the changed process  Description about the objects and their states involved in the processes  Partial information about the dependencies network Complexity assessment. We can get statistic information from above analysis, e.g., the change includes 4 processes and 10 sub-processes, 7 roles and 2 objects with 10 states. Using the measurement methodology proposed in section 2.3, we can calculate its element complexity. However, for the relationships among these elements, it is not easy to detect all dependencies within a large complex system. Besides that, we should measure the different types of process changes separately. Table 1 shows two types of changes: the one-time-change needs only to be calculated once, while the regular maintenance needs to be calculated periodically. To evaluate whether the benefits of a new solution outweigh the added complexity, we could calculate the deviated complexity from two solutions (the changes part) and compare it with the saved costs. For example, if the cost of added complexity is smaller than the saved reticle benefits, we can identify "switch to shared reticle" as a value-adding complexity, otherwise, it is the value-destroying complexity.

Discussion

It is seen from above analysis, PROS approach helps to analyze from different aspects: the processes and their required changes, people and their conflicts. However, for a large complex system, it is not feasible to use an exhaustive method to detect all relationships between elements. How to estimate the relationship intelligently (sufficiently accurate within a given time) is still a challenge for us. The lessons learned focus on two areas: 1) each aspect of a complex problem can be detailed and deeply analyzed by following a certain model or method -e.g., process analysis with SCOR, role analysis with goal-oriented mode. For large systems the accuracy within a given time is a challenge. 2) The qualitative analysis is not sufficient for decision making, to make better decision we need to quantify complexity oriented from all aspects of a system. The PROS approach is promising but a formula ending up with a complexity number is still missing.

Conclusion and Future Work

This paper introduces a framework to manage supply chain complexity from computer science view, which sets up a connection between change management and complexity management. We conclude that complexity should be managed from a systematic view instead of the single aspect. The core part of this framework is the PROS conceptual model, which represents and visualizes the complex system by capturing its important elements and relationships. It can supplement the quantitative complexity measurement by separating it into the elements and relationships part. Calculating the numerous relationships in a large system requires more sophisticated methodologies.

An industrial case from the semiconductor industry with two alternative solutions is analyzed from different aspects and the measurement of added complexity is discussed in order to select the optimal solution. The framework is not limited to the semiconductor industry or supply chain field and could be extended to a broad area: project management, organization changes, government policy analysis, etc. In future research we optimize the PROS approach to larger systems and improve the quantitative measurement of complexity. Two aspects will be addressed: 1) Understand and track the dynamic interaction between elements. 2) Investigate the weight value of human behaviors and their impact, and other components leading to uncertainties and thus complexity of the system.

Fig. 1 .

 1 Fig. 1. Visualization Prototype for PROS

Table 1 .

 1 Shared reticle: added complexity (CT means Change Types, O is one-time-change and R is regular maintenance)

	SCOR	Process Changed	Added complexity	CT
	Model
	Layer
	1.1.2	Make-Front End-Test	Equipment reprogramming in order to	O
			manage the changes
	1.1.2	Make-Front End-Test	For shared reticle, in testing at least	R
			every second product is different and
			thus the testing process needs to be
			switched too.
	1.1.3	Make-Front End -Optical	Equipment update	O
		Control
	1.1.3	Make-Front End -Optical	Training the operators	O
		Control
	1.1.3	Make-Front End -Optical	More operators are allocated to work	O
		Control	with optical inspections systems
	1.1.3	Make-Front End -Optical	Monitor the optical inspection systems R
		Control
	2.1.1	Plan-Production Program Overall planning processes are changed O
	2.1.1	Plan-Production Program Execute the changed planning process-	R
			es
	…	…	…	…

http://www.apics.org/sites/apics-supply-chain-council


Jing Li
email: jingli@bjtu.edu.cn

Xin Zhu

Dan Chang
email: dchang@bjtu.edu.cn

Simulation on Resident Individual Trip Choice Decision Making: Based on Modeling of Rough Set and Genetic Algorithms

Keywords: Travel decision, Rough Set, Genetic Algorithms, Modeling

Urban Residents are the evaluation subjects for the transportation policy. It is very important for the scientific development of transportation policy to research on the travel behavior from the perspective of quantitative modelling. Urban residents scientific of individual travel decisions are the prerequisites for group urban residents travel behaviors. This paper analyses the general population travel behavior based on the basis of the actual survey data and uses rough set theory to reduce the residents travel decision influencing factors. The univariate weight matrix and the corresponding weight matrix could be obtained. On this basis, the genetic algorithms objective function and fitness function could be optimized. Finally, an example simulation is given in this paper to verify the validity of the travel decision-making simulation model.

Introduction

Citizens are the most important parts of urban transportation formations. The choice of citizen travel mode will be influenced by the individual competency and preference; meanwhile, it will be influenced by the transportation environment. The aim of the urban transportation policy is to allow the majority of the population could reach their destinations with a faster, safer, more comfortable and more affordable travel mode. Moreover, both the localized and the whole domain liquidity established by the citizens traveling activities should be taken into consideration. A valid transportation policy is determined by the social satisfaction, economic benefit and level of environmental protection. Scientific and rational analysis on various citizen travelling behaviors, such as choosing public transport or non-public transport will help to find the problems in the existing transport policy system and give fair recommendations. At the present stage, research on resident individual trip mainly involves following fields: commuter and structure of urban space, character of commuter behavior basing on traveling investigation, character of trip chain and trip behavior modelling.

The researches on resident individual trip behavior theory are very fresh and mainly focus on several fields.

The first field is how to confirm factors that influent individual trip behavior. Iseki Hiroyuki and Smart Michael (2012) invested 2122 residents and analyzed the factors such as age, sex, income, race, religion, private car travel mode and frequency of public facilities using. They found that security is the most important factor for all the residents and individuals with different background will have different attitudes to different factors which will be changed with trip experience.

The second field is to develop the individual trip rules. Abou-Zeid Maya and Ben-Akiya Moshe (2011) proposed a framework basing on dynamic selection to catch the society influence on trip choice. They defined comparison of happiness and proved that comparison of happiness rising from comparison of the individual and others. Hence, the overall satisfaction or utility commute would be increased.

The third field is about the resident individual trip information. Son Sanghoon and Khattak Asad (2011) comparatively analyzed the university students' access and use of information about travel. The results showed that the internet and a wide range of information have great impact on the students' trip choice.

Although research on individual trip behavior has been carried out for several years, the theory supports and application explorations are still weak which could be formulated as following:

In the aspect of subject investigated: there is few study on simulation of individual trip decision. They always focus on degree of satisfaction more than personal preference.

In the aspect of research method: They are always qualitative and learned from other existing results. Most studies focus on the travel factors of specific travel groups and only extract the importance of factors even if using the quantitative methods. Moreover, the method always is a statistical analysis of the factors. The application of modern mathematics is only a minority. Meanwhile, the comparison and analysis of different methods basing on results is lack.

Therefore, this study hopes to achieve a breakthrough in the above areas. The research content focus on the simulation of travel decisions basing on personal preference. In the research methods, combined with statistical theory, the modern mathematical theory, accurately extracting of certain population preferences through rough set theory to establish individual travel decision model based on genetic algorithms and simulation analysis.

Methodology

The travelers are considered absolutely rational in the traditional transportation trip model. However, more and more research and practical experience shows that the assumption of absolutely rational is incorrect. Hence, the conception of bounded rationality in Behavioral Economics provides new ideas for research on individual trip behaviors and decisions. Bounded rationality means that the travelers will not chase the best travel utility those are always affected by the factors such as trip experience and travel habits. They want to guarantee the difference between actual travel utility and best travel utility to be in an acceptable range. The conception of bounded rationality is of course accepted in this paper. However, this paper is still taking conception of absolutely rational as foundation in order to carry out the research procession. The assumptions are as following,

1. The decisions are at least 2 when a resident will start travel. That is

2  d n ; 2.
The residents confirm all the decisions before one travel, ignoring all the second decision on the road;

3. The travel utility d U is different for individual preference. Each resident is always chasing their best travel utility. The best travel utility is marked as opt U . 4. The resident decision set D is the independent variable. Travel utility U is the dependent variable. The merits of the decision-making travel decide the effectiveness of travel utility. 5. In this section, the resident decisions set are divided into two categories: good set and bad set. At the same time, more vivid examples could be used to illustrate the relationship between residents travel decisions and travel utility. To make:

     2 1 G B D D ,      2 1 opt d U U
However, it is necessary to cost for resident making travel decision, for example time costs and experience costs. Therefore, d is the explanatory variables of C . Good decision-making cost should be higher than the cost of inferior decisions because the merits of the decision-making will lead to changes of the decision-making cost. Therefore, to make:

     d C d C G B D D * 2 / 1
Residents are always wandering between the worst decision and the optimal decision. They do not want to make the worst decision; Meanwhile, they are also likely unable to make optimal decisions. The reason lays in the uncertainty of complex travel environment. Therefore, residents who have bounded rationality are always making decision between optimal and worst. It is an acceptable decision set for residents. However, this paper only focuses on the personal preference because of the travel environment's uncertainty and complexity. The assumption in this paper is the resident is absolutely rational and chasing best travel utility.

Therefore, this paper will start with the resident individual travel behavior. Firstly, rough set theory will be applied to research on travel decision affecting factors and the contribution of each factor weight or the contribution weight of any two factors could be confirmed. Secondly, simple genetic algorithms will be used to simulate individual residents travel decisions and each genetic operator specific parameters and corresponding fitness function will be confirmed. Finally, modified single urban resi-dent travel decision model basing on rough set and simple genetic algorithms will be established, compared and explained.

Hutchison individual residents y, individual resident's travel decisions affecting factors x supposing there are n factors affecting the individual a trip. The complete factor set which are affecting individual resident trip decision could be defined as

  n x x x x X , , , , 3 2 1  
. The travel utility of individual y is d U . Individual y is always chasing the best travel utility opt U . Therefore, y may choose a group of feasible decisions D. He could achieve the best travel utility through the comparative analysis. At the same time, the assumption above for the residents travel decisions here is still applicable.

Pre-processing the model based on rough set theory (1) Select important factors.

There are some other factors may influent the individual decision expect for some common factors such as safe, comfort, cost and time which are always influencing the trip decision because of the differences in individual preferences, the inequality of individual travel decision quantity and the difference in purposes. Those factors could be defined as  Define the decision

       2 1 f Xc f X f D    . c
X is common factor. Meanwhile, c X and  establish the complete factor set. That is . That means there are P important factors selected.

       c c X X X ,
(2) Expression of knowledge System. Generally speaking, a knowledge system could be expressed as an ordered quad

} , , , { f V R U S  among which, } , , , , { 3 2 1 n x x x x U  
is on the field. It is the set of whole samples.

D C R  
is the set of attributes, among which sub set C is condition attribute set reflecting the characteristics of an object and D is decision attribute set reflecting the categories of objects.

r V V  
is the set of attributes values. r V represents the range of attributes.

V R U f   :
is an information function to confirm the attribute of every object

X in set U . That is, if x i U r R   , , then r i V r x f  ) , ( . Hence, R is a rough set. ( ) R X
 could be considered as the accuracy which is approximating the set X under the equivalence relation R.

The original data could be filtered and the invalid data and the inapplicable data will be deleted. Furthermore, a two-dimensional decision information table will be established to describe urban travel choice factors knowledge expression system. The correlation factor weighting matrix could be obtained by the univariate weighting matrix,

               pp p p p p w w w w w w w w w R        2 1 2 22 21 1 12 11
Meanwhile, R is a p p  real symmetric matrix. The weight value on the main di- agonal equal the corresponding weight values in the univariate factor matrix, which is

p pp w I w R w I w R w I w R . . , , . . , . . 2 22 1 11    
. The univariate factor matrix and correlation factor matrix will be explained and analyzed. The Genetic Algorithms will be introduced after the confirmation of univariate factor matrix and correlation factor matrix.

Genetic Algorithms modeling

The decision is not always single when the individual resident y is travelling. fore, the set of decision variables is } , , , , { 1. The value of fitness is the larger the better. The larger means the individual travel utility is better and the adaptability is better. 2. The individual travel optimal effectiveness could be selected by selecting the superior individual fitness.

The best travel utility

  D U U opt max 
is the maximum value of the objective function and it is positive number.

Data modelling, calculation and analysis

The knowledge expression of urban travel factors and weight calculation

As seen from Table 1, urban travel choice factors are not only including time, piece and other factors known to public, but also including comfort, safety and other factors.

The resident survey questionnaire orders could be used as research object collection according to the rough set theory. The invalid data and inapplicable data are deleted. The remaining data set is  

 5 4 3 2 1 `, , , , x x x X x U  , e d c b a , , , ,
represents the importance of the accuracy of the time, the importance of the travel expense , the importance of the total travel distance, the importance of travel safety, and the im- The decision attribute collection set D is established by the chosen travel mode. Hence, the corresponding figures are used to represent the items in condition attribute as following, {1=very unimportant;2=relatively unimportant;3=general;4=more important ;5=very important} Similarly, in the decision attribute, the corresponding set is {0=bicycle;1=bus;2=underground;3=taxi;4=car} Therefore, dimensional decision information table could be established to describe the urban travel choice influencing factors knowledge expression system. As shown in Table2 (Experts):

Rough-Genetic Algorithms Modelling

The cost (C), distances (L), comfort (C, F), time accuracy (T) as well as cost and time accuracy combination(C, T), time accuracy and distant (T, L) are selected as parameters according to the calculation result basing on rough set theory.

In the formula,  represents the additional satisfaction. It is the utility value of other factors  . These factors are generally classified as one group due to the unobserved character.

The objective function is transformed into the fitness function.

A specific fitness function could be given according the univariate weight matrix and the corresponding weight matrix which are confirmed basing on rough set theory.

Examples of simulation, results and analysis

The model in this paper is for individual. The data is randomly selected from actual questionnaire in order to fit the simulation results more realistic. This questionnaire is answered by a lady living in Beijing. The average monthly disposable income is 2000 to 3000 RMB. The average monthly transportation expense is from 200 to 300RMB. And she did not have a car. The simulation follows the travel situation: (1) the travel aim is tourism; (2) no bulky items; (3) no travel this line before. A calculation shows that the cost of travel traffic scope of its disposable income is [6.7%,15%]. The proportion of expenditure is relatively high.

The trip will be converted to a travel decision model based on genetic algorithms. The decisions that should be confirmed including (1) Travel satisfaction should achieve highest; (2) Line i select sub way, bus or taxi? (3) Line ii select subway, bus or taxi? Conventions decision variable D is taken from [START_REF] Hiroyuki | How Do People Perceive Service Attributes at Transit Facilities? Examination of Perceptions of Transit Service by Transit User Demographics and Trip Characteristics[END_REF][START_REF] Kim | Hit-and-Run Crashes: Use of Rough Set Analysis with Logistic Regression to Capture Critical Attributes and Determinants[END_REF]

. If the value of D is [1, 2)the selection is bus. If the value of D is [2, 3)the selection is underground; if the value of D is [3, 4] the selection is taxi. ] 4 , 1 [ , 2 1  d d
, which are two decision variable. Matlab tool box is used to do program. The following figures are the results of the operation. Therefore, the lady is advised to choose taxi both on line i and on line ii according to the results given by the rough-genetic algorithms. The final prediction is that the lady should choose a taxi directly on this trip and she will achieve the optimal effectiveness.

                      L T V W T C P W T G W F C Q W L K W C H W WX D U L T L C T F C L C , ) , ( , ) ( ) ( ) ( , , , ] ) , ( ) , ( ) , ( ) ( )
( ) ( [ ) ( , , , 1 j j j l t j j t c j j f c j l j c j n t j d d l d t v w d t d c p w d f d c q w d l k w d c h w d t d d g w D f          2 1 2 1 3 2 3 1 2 2 2 1

Conclusions

In this paper, the single factor weight matrix and various factors related to weight matrix are brought out by analyzing the factors of individual residents travel behavior and decisions which are restricting their travel. Furthermore, this paper utilizes the advantage of Genetic algorithm to simulate the individual residents travel decision behavior. An example simulation is given in this paper to verify the validity of the travel decision-making simulation model.

It is contributing for improve the accuracy of the study by combining the rough set and genetic algorithm together in this paper. However, most of the residents could not make the best travel decisions during the travel time. They would choose a group of satisfaction with the decision-making under common situation. That is to allow the difference of travel utility and optimal utility in the acceptable range. Therefore, in process of the genetic algorithm modeling, the objective function and fitness function should be changed. This is the further research contents.

.

  The factors and other factors influence the individual y's decision. However, they could not decide the decision combination of y . The final decision of y could determine the individual travel utility d U in the end. Define are n factors in the complete factors set X . There are k factors in common factors set c X . Of course, n k  . The function of rough set is to reduce the original complete factors set to get an important factors set. Hence, the important factors set is basing on common factors set. The important factors set could be marked as I X ,

( 3 )( 4 )

 34 Calculate the univariate weighting matrix. The univariate weighting matrix could be obtained by extending the reduction important factors set. Calculate the correlation factor weighting matrix.

.

  Define the trip objective function of individual resident y is   It represents the best travel utility that y is chasing. The fitness function could be marked as fitness and

  portance of travelling comfort. It is the public factors set the condition attribute set of urban travel choice influence factors

Fig. 1 .

 1 Fig. 1. rough-genetic algorithms simulation results

Fig. 2 .

 2 Fig. 2. the average distance among individuals in rough-genetic algorithms model

Table 1 .

 1 The survey subjects covered all sectors of society in Beijing as entirely as possible including different ages and different occupation. The survey locations covered the major urban areas in Beijing including bus stations, railway stations, shopping street, business office, park attractions, transit hub, as well as subway cars and other places. The questionnaire questions reflected the urban travel choice influence factors. These factors constituted the index system of urban travel choices, as shown in Table1.The five factors were travel time, travel prices, travel distance, travel safety, traveling comfort. index system of urban travel choices

	3.1	Research data sources
	Data in this paper is obtained by questionnaires. Questionnaires were issued in Sep-
	tember 2010 to about 1000 and recovered 486 valid questionnaires. The investigation
	time covered three daily time paragraphs: 7:00~11:00, 11:00~13:00 and 15:00~19:00.
		Aim	Factors	Index
				Age
				Sex
				Occupation
			Characteristics	Travel options
				The average monthly disposable income
				The average monthly transport expenditure
				Car or not
			Travel time accu-racy	The accuracy of the destination arrival time Peak or off peak Waiting time
	Analysis on urban travel options factors	Travel costs	Ticket price Parking price Fuel costs
				tolls
				Total distance
			Travel distance	Transfer distance
				Number of transfers
			Travel safety	Driving safety Property security
				Seat or not
			Traveling comfort	Crowded or not Facilities convenience
				Bulky items or not

Table 2 .

 2 urban travel choice influencing factors knowledge expression system

		No. x1		Time accuracy 1		Cost 4		Condition Attributes Distance 4	Safety 5	Decision Comfort Travel mode attribute 5 2
		x2				1						5		4	5	3	1
		x3				2						3		2	3	3	2
		x4				2						4		3	3	3	1
		x5				3						1		3	5	4	1
		x6				3						2		3	5	4	1
		x7				3						2		5	5	5	0
		x8				3						3		2	5	5	3
		x9				3						3		2	4	2	4
		…				…					…		…	…	…	…
		The	univariate	weight	matrix	could	be	calculated	result	as
	I		 4	/	8 , 27	/	7 , 27	/	, 27	2	/	6 , 27	/	 27	according to the rough set theory. And the correspond-
	ing			weight				matrix		could	be	calculated	result	as

Acknowledgments: This paper is supported by the National Natural Science Foundation (No. 71103014) and Beijing Philosophy and Social Science Fund (No.14JGC095).


Ziyi Wang

Jingti Han

Visualization of the UK Stock Market Based on Complex Networks for Company's Revenue Forecast

Keywords: Complex networks, FTSE100 index, WS small world property, Revenue forecast

As an emerging research field, the complex network theory is able to depict the most daily complex systems' topologies, but in terms of financial market analysis, it still needs more attention. We can apply this theory to construct financial networks and detect them both from macro level and micro level to support a company in forecasting its revenue. This paper aims to explore the macro-characteristics of the UK stock market. We examine the properties of return ratio series of selected components in FTSE100 index, adopt the Kendall's  rank correlation coefficient between series to write adjacency matrices and transform these matrices into complex networks. Then we visualize the networks, analyze features of them at different thresholds and find evidence of WS small world property in the UK stock networks. All these work follow our research framework proposed at beginning of this paper. According to the framework, more future work needs to be done to achieve the goal and make decision support in a company.

Introduction

The function of the stock market is to provide a public platform for trading businesses and raise capital for companies. Various information technologies and statistics methods have been engaged in analyzing its dynamics, such as Internet, portable computers, regression analysis and so on. However, the interactions between companies are rarely taken into account, but undoubtedly they play an important role to impact the markets. From inside perspective of a company, forecasting its revenue through the stock market's behavior could be one way to support decision making. In order to achieve this research aim, we propose utilizing complex network theory to visualize and analyze the complexity of the interactions in this paper.

Complex network theory is able to abstract and depict the most daily complex systems' topologies. As an emerging hotspot, this theory has attracted attention of schol-ars increasingly from various research fields and became one of the most significant tools in social network analysis. Complex network theory has been introduced since decades ago. To date, it has been widely used in the study of social relationships, transport networks, biology, ecology, emergency management, power grids, etc., and as a credible and powerful tool to characterize the markets.

Up to now, some scholars have done several researches about the major stock markets all over the world. In 1999, Mantegna [START_REF] Rosario | Hierarchical structure in financial markets[END_REF] proposed a hierarchical tree to investigate the common economic factors affecting the stocks' prices. In 2005, Boginski et al. [START_REF] Vladimir | Statistical analysis of financial networks[END_REF][START_REF] Vladimir | Mining market data: a network approach[END_REF] constructed a market graph which followed a power-law model and calculated cross-correlations to reflect the market behavior with the data from US stock markets. Till 2009, Haldane [START_REF] Andrew G Haldane | Rethinking the financial network[END_REF], the Chief Economist and the Executive Director of Monetary Analysis and Statistics at Bank of England, first convincingly explained the current financial markets with complex networks in an official speech. Caraianie (2012) [START_REF] Petre | Charaterizing emerging European stock markets through complex networks: from local properties to self-similar charateristics[END_REF] analyzed the properties of the returns of European stock markets by complex networks, and found that the networks are scale-free and self-similarity. Zhuang et al. [START_REF] Xintian | Characterizing analysis of complex network for shanghai stock market[END_REF] constructed a network of stock prices fluctuations in Shanghai stock market and analyzed its topology. Further, Zhang et al. [START_REF] Jianhua | Network topologies of Shanghai stock index[END_REF] compared the networks extracted from the original series and return series. They showed different characteristics because of different data. The former one fitted with a power law distribution and was a smallworld and free-scale network, while the latter one governed by an exponential degree distribution. For Hang Seng index of Hong Kong stock market, Li and Wang [START_REF] Ping | Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies[END_REF] found fluctuation patterns based on the network topological statistic. In these researches, networks from various databases and statistic results are visualized to make texts more visually attractive and help audience understand more effectively.

The aim of this research is to apply the complex networks theory to the UK stock market to forecast companies' revenue. The research framework is shown below (Fig. 1). The first two steps are contents in this paper and the others are the future work in our research. In this paper, we investigate the relationship between return series with observations from 2004 to 2014 in FTSE100. We find that return series show significant non-linear correlations that do not meet strict assumption of Pearson's correlation; therefore we adopt Kendall's  correlation as edges' weight to construct and analyze networks more accurately.

Methodology

FTSE100 index, being one of the most professional stock market exchange indices all over the world, has 101 components from various industries. However, not every company contributes to the market during the period we chose. Hence, an analysis of these long term running companies would give us a big picture of the network structure of the British stock market.

Data collection and pre-processing

The weighted network is able to describe the nodes and relations between them much more really and clearly than non-weighted network, therefore, a whole connected, no direction and weighted network is constructed in this paper. Within different thresholds, the research will find their macro-characteristics.

The data are extracted from "Yahoo Finance", and the timespan in consideration of this paper is from 1st January 2004 to 10th October 2014. The dates of the public holidays in UK are deleted as stock market is closed, including New Year's Day, Good Friday, Easter Monday, Early Bank Holiday, Spring Bank Holiday, Summer Bank Holiday, Christmas Day and Boxing Day in each year. To reflect facts as real as we can, companies that do not have data in full period are deleted as well. Consequently, there are 86 components of FTSE100 as the vertices in network, such as BP plc (British Petroleum), LSE (London Stock Exchange Group PLC), and LLOY (Lloyds Banking Group PLC) and so on so forth. The edges are the relationships among the 86 stocks and the correlation coefficient is the weight of each edge.

Pre-processing each company's closing price data series is needed. Denoting the original daily closing price of the stock i at time t is () i Pt . These data are calculated as

() ( ) 100 ln , ( 1, 2, , ) ( 1)
i i i Pt r t t n Pt        . ( 1
)
Then there will be the return ratio data series ( ) { ( )}, (1, 2, , 1), (1, 2, ,86

) ii R t r t t n i    
, and the number of data in one series is   The more data we have, the greater extent network can reflect the real UK stock market from results we conclude. Therefore, the components we choose have the most amounts of data during the period. Following this principle, there are 234 178 (2723 per each companies) pieces of efficient data.

Edges and their weights

Analysing the statistical characteristics of the return series is the first thing we should do to understand the basic statistic of the return series. Six random return ratio series are shown in table1. From this table, it is clear to see that the means are around 0 and the standard deviations are all over 1, that is to say, there are bigger fluctuations in these return series.

Obviously, the fluctuations are depended by the uncertainty of the stock market. Majority skewnesses of data series' distributions, in this table, are smaller than 0, and kurtoses are greater than 6 (twice of 3), which mean the return series show left skewed (thick/fat tail) and high peak distribution. Meanwhile, the probabilities of Jarque-Bera are all 0 and do not accept the hypothesis: the return series are normal distribution. Because of these characteristics, it can be seen that these six return series obey student T distribution, the same as the rest 80 series.

The Q-Q graphs below give evidence of the judgment we made above. As the graphs showed, the return series have the features mentioned above and do not accept the hypothesis of normal distribution.

To examine the correlations among the series, it is calculated the autocorrelation and partial autocorrelation of 21 period-lag of these series. The Ljung-BoxQ value is significant and the results show that there are no significant relations. Therefore, all the return series we chose are independent in the period.

According to the test results, in this paper, we employ the Kendall's  correlation as the edges' weights. A correlation coefficient is a measure of the consistency of changes between the variables. Pearson Product Moment Correlation or PPMC (Pearson's correlation, for short), which is a measure of the linear correlation between two variables, is common to see in the correlation research of the stock exchange markets since it is easier to understand and calculate than others. However, there are some limitations for Pearson's correlation. For example, the variables should be normally distributed and it is for linear relationship between the two variables. Kendall's  correlation measures the coordination degree of variables that based on the rank of random variables. Therefore, Kendall's  correlation coefficient is able to reflect nonlinear dependences better without restriction mentioned above.

With these calculations, we can write adjacency matrices. Through the adjacency matrices, we construct complex networks and analyse them with respect to degree distribution, average shortest length path and clustering coefficient.

Results and Discussion

With Pajek, a social network analysis tool, we transform the adjacency matrices into complex networks.

Network structure analysis from macro perspective

Visualising networks at a threshold of 0.36 as below: the nodes are the 86 companies from FTSE100 index and the edges are determined by the Kendall's  correlations between the series. The network is the whole connected weight network. In Fig. 3, the darker edges represent the bigger correlation coefficient between the companies. It is noticed that five companies have the strongest relationships and these five companies are formed into two clusters: AAL01 (Anglo American Plc.), BLT17 (BHP Billiton Plc.) and RIO73 (Rio Tinto Plc.); BLND16 (British Land Co Plc.) and LAND53 (Land Securities Group Plc.). The first three companies highlighted by the green are all multinational mining companies. The last two highlighted by the blue are all the property companies and they all turned into a real estate investment trust (REIT) in January 2007. British Land is the second largest REIT in the UK and Land Securities is the largest one. Undoubtedly, the companies in the same industries would be easy to have strong relations.

In order to describe a network from the macro aspect, it is usual to characterise its density and scale. Clustering coefficient and average path length are the indicators to measure these two features.

i i ii N C kk   . (2)
The overall level of clustering C in a network is defined by Watts and Strongatz [START_REF] Watts | Collective dynamics of 'small-world' networks[END_REF] as the average of all the i C :

1 1 N i i CC N    . (3)
Obviously, 01 C  . If 0 C  , the vertices in the network are independent. If 1 C  , any nodes are directly connected in a network, i.e. the network is a global coupling network.

Average path length is defined as the average number of steps for all possible pairs of network nodes. It is a measure of the efficient of information transport on a network, i.e. the scale of a network. Suppose in a network G Gthe length of any two nodes i and j is ij l , which is the shortest number of steps from node i to j . The average length of a whole network

L is 1 11 2 ( 1) NN ij i j i Ll NN        . ( 4
)
N is the number of vertices in a network. We do not consider vertices' own distance in this paper.

Clustering coefficients and average path lengths are calculated at different thresholds with data mentioned before, showing in table 2. In table 2, at various thresholds, the FTSE100 network has a small average shortest path length and a large clustering coefficient. With these two characteristics in a network, referencing the research did by Watts and Strogatz [START_REF] Watts | Collective dynamics of 'small-world' networks[END_REF][START_REF] Xiaofan | Complex networks theory and applications[END_REF]in 1998, it is a Watts-Strogatz small-world network (WS small-world network for short). With these features, the fluctuation in this stock exchange market would spread rapidly. Specifically, it is found that sharp changes of some influential companies' stocks will spread at a faster pace to a wider range. These two characteristics, small average path length and large clustering coefficient, are two indicators to measure the small-world property. WS small world network is a transition from a complete regular network to a complete random graph.

Thresholds in networks

Reasonable threshold selection is a crucial step for constructing networks. If a selected threshold is too small, there would be false associations due to the random noise, resulting in the complete connected network; if the selected threshold is too large, more isolated points will make the existence of the network, the network will contain fewer vertexes, and hence lots of important related information will be lost. Under these situations, it is no need to analyse the network degree distribution and clustering coefficient any more. In addition, according to the same interval, when the thresholds change from small to large, if the number of relations among stocks decreases rapidly, the left companies are more significant than others to contribute to the national economy or local economy. Otherwise, there are no more huge differences among companies to make contribution to a nation or a region. So the research with appropriate thresholds can explore real relationship among stocks to the whole system.

In this paper, the research draws 26 complex networks at 26 thresholds respectively, and the number of edges shows in Fig. 4, which reveals a descending trend of the edges. As we all know, even with the same vertices, various numbers of edges can construct various networks. Based on the specific networks, researches for parameters could be processed, such as the adjacency matrix of networks, the cumulative distribution of degree, clustering coefficient, average nearest neighbour degree, k-core and partitions and so on so forth. For the thresholds of the financial network we construct, it is steadier to the edges' number between 0.3 and 0.4.

Conclusion and future work

As an emerging method in economic disciplines, complex networks still needs more attention. In this study, we proposed a basic framework to forecast revenue for a company to make decision support based on complex networks theory. We detected data from the FTSE 100 index and write adjacency matrices to construct networks and visualize them. Based on basic statistics of data, we explored features of networks, and found the FTSE100 index network is a WS small world network and thresholds are playing a significant part in constructing networks. We investigated the UK stock market data independently with other research data. Similarly, the WS small world properties show in US stock market, Shanghai stock market [START_REF] Jianhua | Network topologies of Shanghai stock index[END_REF], international stock markets [START_REF] Dongmei | Analysis of International stock market structure and feature from the perspective of complex networks[END_REF]and so on. Combining data analysis with visualised graphs, decision makers could do predictions much faster and more reliably to support strategies in companies. Other macro features and in-depth micro research will be conducted in the future, for example, clustering communities, detecting topology changes of networks with impacts from internal and external events in companies. Many networks from stocks markets have been studied, but there are still some important questions need to be answered: what are common features in international stock markets, what these markets differ in each country and how we can visualise them clearly to support making decision, as examples.

Fig. 1 .

 1 Fig. 1.A basic framework to forecast company's revenue using complex networks

Fig. 2 .

 2 Fig. 2. Q-Q graph of return series against normal distribution

Fig. 3 .

 3 Fig. 3. Complex Network of FTSE100 index at a threshold of 0.36

Fig. 4 .

 4 Fig. 4. The number of edges at different thresholds of financial network

Table 1 .

 1 Basic statistics of six return ratio series

	Company	Mean	Median	Std. Dev.	Skewness Kurtosis	Jarque-Bera Statistic Probability
	AAL	0.003166 0.040642 2.760246	-0.13138 10.06153 5665.449	0
	ABF	0.052881 0.062794 1.341194	-0.07136 10.78818 6884.209	0
	ADN	0.072697	0 2.347117 0.146311 10.15676	5820.97	0
	AGK	0.082391 0.063191 2.350748	-0.55548 29.70248 81038.36	0
	AHT	0.151669	0	3.27993 0.003828 14.71018 15558.36	0
	ANTO	-0.01732 0.060223 4.265728	-19.2306 719.1176 58352041	0

Table 2 .

 2 Clustering coefficient and Average path length at different thresholds

	Thresholds	Clustering coefficient	Average path length	Number of edges
	0.25	0.7848	1.6426	3104
	0.27	0.7278	1.8666	2282
	0.30	0.6463	2.1320	1206
	0.33	0.5772	2.4169	594
	0.36	0.6015	2.8870	250
	0.40	0.6744	1.3582	86
	0.50	0.8571	1.1579	32

Acknowledgments. The authors would like to thank Prof. Kecheng Liu for engaging discussion. We also thank the editor and reviewers for their insightful comments and helpful suggestions. This research is supported by (1) the Research on Control and Efficiency of Emergency Support Networks (No. 71271126), financed from National Natural Science Foundation of China; (2) Study on Control and Efficiency of Emergency Transportation Support Networks (No. 20120078110002), financed from Research Fund for the Doctoral Program of Higher Education of China; (3) the Research


David Audretsch
email: daudrets@indiana.edu

Maksim Belitski
email: m.belitski@reading.ac.uk

Creativity Filter and Start-Ups to Resolve the Innovation Paradox

Keywords: Creativity filter, innovation, knowledge management, skills, inter-organization

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

Introduction

There is an increasing interest in understanding how opportunities and new ideas are created [START_REF] Amabile | Stimulate creativity by fueling passion[END_REF], [START_REF] Audretsch | Does the knowledge spillover theory of entrepreneurship hold for regions?[END_REF]. Firms need new ideas that expand their market share and bring new products [START_REF] Taylor | Superman or the fantastic four? Knowledge combination and experience in innovation teams[END_REF]. One of the key focus of entrepreneurship is understanding why some firms are better than others to identify opportunities and bring new ideas [START_REF] Audretsch | Does the knowledge spillover theory of entrepreneurship hold for regions?[END_REF] and why employment of high level skills and knowledge may not result in greater innovation, known as an "Innovation paradox" [START_REF] Miron-Spektor | The effect of the conformist and attentiveto-detail members on team innovation: reconciling the innovation paradox[END_REF]. While there is a disagreement in the management and innovation literature about the process of creating innovation [START_REF] Agarwal | Knowledge Spillovers and Strategic Entrepreneurship[END_REF], the central components of opportunities are knowledge, motivation and skills [START_REF] Lovelace | Maximizing cross-functional new products teams' innovativeness and constraints adherence: A conflict communications perspective[END_REF], [START_REF] Bilton | Management and creativity: From creative industries to creative management[END_REF], [START_REF] Miron-Spektor | The effect of the conformist and attentiveto-detail members on team innovation: reconciling the innovation paradox[END_REF]. Fostering skills and knowledge that help to create new opportunities [START_REF] Oldham | Employee creativity: Personal and contextual factors at work[END_REF], has become the priority for new entrepreneurial firms. New entrepreneurial firms have greater abilities to innovate than established mature firms, as new entrepreneur's ability to identify opportunities is related to knowledge [START_REF] Audretsch | Does the knowledge spillover theory of entrepreneurship hold for regions?[END_REF], experience and skills. Employment of people within certain functional areas (design, software, and engineering) helps firms to shape knowledge and innovate [START_REF] Levitt | Creativity is not enough[END_REF].

Despite extensive theorizing about the importance of various external factors as predictors of new ideas and economic performance, that include education and competences [START_REF] Lovelace | Maximizing cross-functional new products teams' innovativeness and constraints adherence: A conflict communications perspective[END_REF]; team creativity and leadership [START_REF] Gong | A Multilevel Model of Team Goal Orientation, Information Exchange, and Creativity[END_REF]; cognitive styles of creativity [START_REF] Miron | Do personal characteristics and cultural values that promote innovation, quality, and efficiency compete or complement each other?[END_REF], [START_REF] Miron-Spektor | The effect of the conformist and attentiveto-detail members on team innovation: reconciling the innovation paradox[END_REF] extant empirical research misses the link between available knowledge and skills, knowledge management and innovation outcomes [START_REF] Collins | Knowledge exchange and combination: The role of human resource practices in the performance of high-technology firms[END_REF]. In understanding this link scholars have integrated goal orientation theory [START_REF] Hirst | A crosslevel perspective on employee creativity: Goal orientation, team learning behavior, and individual creativity[END_REF], the knowledge spillover of entrepreneurship theory [START_REF] Audretsch | Does the knowledge spillover theory of entrepreneurship hold for regions?[END_REF], [START_REF] Audretsch | The Theory of Knowledge Spillover Entrepreneurship[END_REF], organizational creativity theory [START_REF] Amabile | Stimulate creativity by fueling passion[END_REF], [START_REF] Levitt | Creativity is not enough[END_REF] social capital theory [START_REF] Tsai | Social capital and value creation: The role of intrafirm networks[END_REF] and social information processing and exchange theory [START_REF] Gong | A Multilevel Model of Team Goal Orientation, Information Exchange, and Creativity[END_REF], [START_REF] Miron-Spektor | The effect of the conformist and attentiveto-detail members on team innovation: reconciling the innovation paradox[END_REF].

Despite all of this knowledge, above theories have not examined availability the role of knowledge management and organizational factors that enable knowledge and skills transformation into new ideas and performance [START_REF] Shalley | The effects of personal and contextual characteristics on creativity: Where should we go from here[END_REF], [START_REF] Shalley | Interactive effects of growth need strength, work context, and job complexity on self-reported creative performance[END_REF].

In this study, knowledge is seen as availability of skills within the company or purchase external skills (e.g. design and graphics, multimedia and software, and engineering and math skills) and human capital that includes both the formal education as well as tacit knowledge from experience and practical learning. Following prior studies [START_REF] Audretsch | Does the knowledge spillover theory of entrepreneurship hold for regions?[END_REF], [START_REF] Audretsch | The Theory of Knowledge Spillover Entrepreneurship[END_REF], [START_REF] Audretsch | The missing pillar: the creativity theory of knowledge spillover entrepreneurship[END_REF], we expect that knowledge promotes innovation and economic efficiency. Motivation through a broad range of organizational and inter-organizational practices aiming in developing creativity within the organization and innovative orientation of a firm is likely to moderate the relationship between knowledge and innovation [START_REF] Gong | A Multilevel Model of Team Goal Orientation, Information Exchange, and Creativity[END_REF]. We aim to understand how characteristics of a firm, in particular skills and education effect innovation of a focal firm. What is the role of knowledge management and firm-specific internal characteristics (further -creativity filter) in the relationship of knowledge management and commercialisation?

This study makes a discussion and contributes into open innovation and creativity literature by unpacking the role of creativity as a filter of knowledge to innovation [START_REF] Agarwal | Knowledge Spillovers and Strategic Entrepreneurship[END_REF], [START_REF] Cummings | Enhancing creativity: Managing work contexts for the high potential employee[END_REF]. We take a firm level perspective, exploring firm-level characteristics as a conduit of knowledge to innovation.

Knowledge, Creativity and Innovation

Knowledge and skills are the building blocks of creativity [START_REF] Amabile | Stimulate creativity by fueling passion[END_REF] and are important to the ability to innovate [START_REF] Cummings | Enhancing creativity: Managing work contexts for the high potential employee[END_REF]. They allow firms to deviate from their counterparts and come up with breakthroughs that may change methods of production and processing while promoting the acceptance of innovation. By generating novel ideas that require new solutions, workers with creative skills and knowledge [START_REF] Florida | The rise of the creative class[END_REF] provide their companies with new knowledge that brings new marketable opportunities [START_REF] Audretsch | The missing pillar: the creativity theory of knowledge spillover entrepreneurship[END_REF]. The most direct link is reflected in the commercialization of knowledge through the creation of a new business. This relationship lies at the heart of the 'knowledge spillover theory of entrepreneurship' [START_REF] Audretsch | The Theory of Knowledge Spillover Entrepreneurship[END_REF]. The combination of skills and ideas is not static, and may respond to changes in the firms organizational and innovation climate. Employing creative individuals and encouraging the expression of their voices increases the likelihood of identifying problems and generating new ideas [START_REF] Levitt | Creativity is not enough[END_REF], triggering new ways of thinking and modes of [START_REF] Miron-Spektor | The effect of the conformist and attentiveto-detail members on team innovation: reconciling the innovation paradox[END_REF]. Traditional measurement of knowledge by the human capital or occupations [START_REF] Florida | The rise of the creative class[END_REF] was found to be correlated with a range of other indicators capturing the formal qualifications of the workforce. Hence it was unclear whether the knowledge captures only education or more generic skills and experiences. We use a combination of skills and a proportion of workforce with scientific degrees as measure knowledge at a firm-level. Both skills and workforce qualification enable firms to change the way opportunities are defined, and be a source of these opportunities to increase innovation [START_REF] Collins | Knowledge exchange and combination: The role of human resource practices in the performance of high-technology firms[END_REF], [START_REF] Agarwal | Knowledge Spillovers and Strategic Entrepreneurship[END_REF] we assume:

Proposition 1. Firms that deploy skills and employ workforce with scientific degrees are likely to have higher level of innovation.

3

The Innovation Paradox and The Creativity Filter

Despite the importance of skills and formal education for generating new ideas previous management literature has found a neutral or even negative outcomes related to idea implementation [START_REF] Miron | Do personal characteristics and cultural values that promote innovation, quality, and efficiency compete or complement each other?[END_REF]Although firms may employ individuals within certain functional areas with the personal attributes associated with idea generation (e.g., creativity) [START_REF] Amabile | Stimulate creativity by fueling passion[END_REF] it is unclear whether these ideas and experiences will become innovation. This finding is not surprising given innovation requires out-of-the-box thinking, exploration, risk-taking and tolerance of mistakes. It requires promoting knowledge through firm organizational and managerial practices and channels, creating a conducive environment for innovation in organization [START_REF] West | Sparkling fountains or stagnant ponds: An integrative model of creativity and innovation implementation in work groups[END_REF]. Thus, if the above conditions do not hold successful implementation of ideas becomes questionable [START_REF] West | Innovation in top management teams[END_REF]. This contradiction inherent in innovation was called "The innovation paradox."

We know that workers often complain that their firms are reluctant to introduce change, and that they find it difficult to work within the existing firm strategy and practices, and so that these practices may impede new ideas to sprout out [START_REF] Miron-Spektor | The effect of the conformist and attentiveto-detail members on team innovation: reconciling the innovation paradox[END_REF], [START_REF] Cummings | Enhancing creativity: Managing work contexts for the high potential employee[END_REF]. Deploying variety of skills (e.g. IT, multimedia, design, math, engineering, graphics, etc.) within certain functional areas may not result in higher level of innovation, as positive effect of some companies will be cancelled out by the negative effects. Workers with skills are subjected to inter-organizational environment and factors that are there to motivate workers and enhance not "enforce" the implementation of new ideas [START_REF] Audretsch | The missing pillar: the creativity theory of knowledge spillover entrepreneurship[END_REF] Social information processing theory [START_REF] Gong | A Multilevel Model of Team Goal Orientation, Information Exchange, and Creativity[END_REF] and knowledge spillover of entrepreneurship theory [START_REF] Audretsch | The Theory of Knowledge Spillover Entrepreneurship[END_REF] could be used to further describe the process linking knowledge, creativity and innovation.

Within the social information perspective, firms acquiring creative for their innovation create certain types of behaviors and performance that gives rise to an environment supportive of creativity [START_REF] West | Innovation in top management teams[END_REF]. It also conveys expectations of creative performance within the firm. Empirical studies found this dimension is the only significant predictor of innovation novelty [START_REF] West | Innovation in top management teams[END_REF], as workers may or may not agree to share their idea should the benefits of doing so be uncertain and the working environment hazardous for creativity [START_REF] Shalley | The effects of personal and contextual characteristics on creativity: Where should we go from here[END_REF], [START_REF] Shalley | Interactive effects of growth need strength, work context, and job complexity on self-reported creative performance[END_REF]. A complex of organizational and inter-organizational practices work as a creative environment, which enables more efficient conversion of knowledge into innovation. This mechanism describing the link between knowledge and innovation may be described a creativity and work as a filter to knowledge. The creativity filter is a high-level umbrella construct that captures the impeding or moderating effects of a broad range of organizational as well as inter-organizational mechanisms that may hamper innovation and innovative orientation by a firm through investment in in-house R&D and other creative expenses to support innovation inhouse. According to the social information processing theory, creativity will moderate the power of knowledge. Unlike the knowledge filter, described [START_REF] Audretsch | The Theory of Knowledge Spillover Entrepreneurship[END_REF][START_REF] Gong | A Multilevel Model of Team Goal Orientation, Information Exchange, and Creativity[END_REF]47] as, "the inertia inherent in decision-making under uncertainty within incumbent organiza-tions", the "creativity filter" refers to enforcement of organizational and interorganizational mechanisms and R&D intensity that moderate or hamper innovation [START_REF] Audretsch | The missing pillar: the creativity theory of knowledge spillover entrepreneurship[END_REF]. These practices and innovation inputs pose significant constraints on the behavior of employees [START_REF] West | Sparkling fountains or stagnant ponds: An integrative model of creativity and innovation implementation in work groups[END_REF]. First, we expect more creative behavior to evolve through the new organizational and inter-organizational mechanisms (e.g. systems of employee responsibilities, teamwork, de-centralization, integration or de-integration of work, and training) when individuals can access and implement new ideas, perspectives, and knowledge. Second, the employee's creative behavior will be supported by an information exchange with external firms or public institutions (e.g. alliances, partnerships, outsourcing or sub-contracting), provides a platform through which innovation can diffuse. Both activities make up an organizational component of the filter. Another R&D component of the filter represents creative expenditure that improves innovation [START_REF] Tierney | Creative self-efficacy: Potential antecedents and relationship to creative performance in two organizational settings[END_REF] exposes workers to diverse ideas both internally and through external interactions

The creativity filter will enforce a higher flow of knowledge and deployment of skills through promoting responsibilities, teamwork, integration, and information exchange resulting in more ideas to sprout-out [START_REF] Dirks | The role of trust in organizational settings[END_REF].

Proposition 2. The creativity filter moderates the relationship between the knowledge and innovation.

Creativity and new entrepreneurial firms

The mechanism of commercialization of knowledge and ideas is new entrepreneurial start-up described in the 'knowledge spillover theory of entrepreneurship' [START_REF] Amabile | Stimulate creativity by fueling passion[END_REF]. Since knowledge tends to be 'sticky' in space, it becomes a determinant of entrepreneurial start-ups. Drawing on the knowledge spillover theory of entrepreneurship and its human capital component [START_REF] Agarwal | Knowledge Spillovers and Strategic Entrepreneurship[END_REF] we posit that knowledge needs to be enhanced by someone, whether an individual or a company, who can take a responsibility of ideas and deliver innovation to the market. Starting an entrepreneurial venture spillovers knowledge which otherwise would remain un-commercialized [START_REF] Audretsch | The missing pillar: the creativity theory of knowledge spillover entrepreneurship[END_REF]. New entrepreneurial firms are more successful than their old counterparts in enhancing innovation.

Along with the creativity filter, young businesses are better in resolving the "Innovation paradox" by outperforming their market counterparts through creative destruction. Next we consider the time period for knowledge spillovers. We assume up to three year time lag is a sufficient period for any specific information on development decisions, R&D, and new ideas to spread in the market and across all sectors. The speed of information spread and commercialization of a product could be higher for other sectors, such as IT and engineering. We suggest start-ups serve as a conduit of new ideas and as a creativity filter per se which filters out good ideas resulting in start-ups.

Although new firms moderate the relationship between skills and innovation, the same role could also be performed by existing and more experienced firms operating in innovative fields, like knowledge-based companies (ICT, bioengineering, pharma-ceutics). Such firms typically hire highly educated and skilled individuals (engineers, telecommunications graduates) to implement and further develop new ideas and innovations (e.g., Sony, Apple or Microsoft). In measuring the moderation role of both start-ups and established firms, we need to take into account several possible channels of creativity to the market which allows us not to overstate the relevance of any specific type of a conduit.

Proposition 3. New entrepreneurial firms moderate the relationship between the knowledge and innovation.

Measures and approach

Innovation is measured as the percentage of a business's total turnover from goods and services that were new to the market [START_REF] West | Innovation in top management teams[END_REF]. In line with the management and economics literature [START_REF] Agarwal | Knowledge Spillovers and Strategic Entrepreneurship[END_REF][START_REF] Audretsch | The Theory of Knowledge Spillover Entrepreneurship[END_REF][START_REF] Audretsch | The missing pillar: the creativity theory of knowledge spillover entrepreneurship[END_REF]. Productivity could bhe reflected by two measures. The first measure consists of the gross value added in sales. The second measure consists of the wages and other employment benefits paid to firm's sales.

Our variables of interest are creativity and the creative environment which can either enhance or constrain the creativity. Building on what is needed for individual creativity [START_REF] George | Dual tuning in a supportive context: Joint contributions of positive mood, negative mood, and supervisory behaviors to employee creativity[END_REF], we follow [START_REF] Agarwal | Knowledge Spillovers and Strategic Entrepreneurship[END_REF][START_REF] Shalley | The effects of personal and contextual characteristics on creativity: Where should we go from here[END_REF][START_REF] Shalley | Interactive effects of growth need strength, work context, and job complexity on self-reported creative performance[END_REF] in operationalizing a firm's creativity in terms of the employment of individuals with skill at any level in the graphic arts/layout/advertising and design of objects, multimedia/web design, software/database development and management, or engineering/applied sciences and mathematics/statistics. Firms may also obtain these skills from external sources for in-house use. Usually a binary answer is obtained for each of the three types of creative skills (0 means skills were not employed, and 1 means skills were employed). We draw on [START_REF] West | Innovation in top management teams[END_REF], who originally developed the scale measuring the creative climate supportive for innovation along with [START_REF] Cummings | Enhancing creativity: Managing work contexts for the high potential employee[END_REF], [START_REF] George | Dual tuning in a supportive context: Joint contributions of positive mood, negative mood, and supervisory behaviors to employee creativity[END_REF]. The mechanism describing the link between creativity and innovation may work as a filter to knowledge and therefore termed a creativity filter. The creativity filter is a composite indicator of complex organizational systems. It consists of an organizational and innovation input (R&D) component. To be able to design and develop the creativity filter researchers jointly with the Office of national Statistics, UK have conducted phone interviews. In the sample 155 R&D managers located in various UK regions representing the manufacturing, service and R&D sectors. 130 responses were interviewed. The results were used to assign appropriate weights to organization component of the filterintroduced by three organizational and business practices (see formula 1 below).

𝐹 𝑖 = (𝑤 0.25 𝑀 1𝑖 + 𝑤 0.5 𝑀 2𝑖 + 𝑤 0.25 𝑀 3𝑖 ) + 𝑅𝐷 𝑖 [START_REF] Agarwal | Knowledge Spillovers and Strategic Entrepreneurship[END_REF] 𝐹 𝑖 is the size of the filter of a firm i in industry j. The R&D effort -innovation component of the filter is given as the choice of a firm to invest in in-house creative work undertaken within the business that increases knowledge. This can be for the purpose of developing new and improved products and processes for current or future innovation. The R&D component contributes half of the filter size, which varies between zero -no R&D expenditure -and one -in-house R&D expenditure is undertaken.

The organizational part of the filter is a composite sum of the three types of organizational strategies and practices applied by organization. It aims at raising internal efficiency and the effectiveness of approaching markets and customers. The higher the score, the smaller the size of the creativity filter and the smaller the gap between commercialized and un-commercialized creativity.

Companies that have fewer than 10 employees, have not introduced at least one method of organizing work and business practices over the period of 2008-2010 and companies that did not provide any rank of those practices were excluded. Respondents were asked to rank organizational and business practices by their importance to innovation. Most respondents (102) placed 𝑀 2𝑖 , referring to new methods of organizing work responsibilities and decision making (i.e. the first use of a new system of employee responsibilities, teamwork, de-centralization, the integration or deintegration of departments, education/training systems, etc.) as the most relevant component of organizational innovation. More than half of the respondents (70)

ranked 𝑀 1𝑖 as the first or second most important component of innovation, which refers to new business organizing procedures (i.e. supply chain management, business re-engineering, knowledge management, lean production, quality management, etc.) and constitutes a quarter of the organizational component of the filter. Finally, the rest of the group ranked 𝑀 3𝑖 as the second or third most important component of innovation, which refers to new methods of organizing an organization's external relationships with other firms or public institutions (i.e. the first use of alliances, partnerships, outsourcing or sub-contracting etc.).

We distributed the weights equally between 𝑀 2𝑖 and 𝑀 3𝑖 by assigning 0.25 of the unity of the organizational components that contribute half of the filter size. This varies between zero (no organizational strategy or practices were introduced) and one (all three types were introduced). The interview method was used in order to shed more light on the relevance of each specific organizational practice to the process of introducing new products to the market. This meant we could be flexible and precise when distributing the weights, rather than treating all new practices as equally important. The organizational and innovation components of the filter vary between zero and two. In order to test the moderating effects of the filter in linking the process of creativity and knowledge flow to innovation we included the interaction of each type of creative skill in the model. As control variables we will need to include firm size (log of the number of employees and the square of the log of number of employees), UK regions, sector dummy, an exporting dummy, the effectiveness of patent protection (0: patent protection not used to 3: high efficacy), enterprise age.

Managerial Implications

The model demonstrates firm's reliance on availability of skilled and creative employees both inside and outside a firm. Business start-ups and experienced established companies exploring new opportunities is an important factor shaping creativity into marketable products and processes. On the one hand, establishing a new business is the most efficient and quick way to commercialize creative skills. On the other hand, start-ups are on average less productive than established firms, unless they are successful in employment of individuals with a mix of creative skills to secure higher wages, and add value to their products. Our creativity filter reveals the importance of innovative and organizational effort when working on innovation. This enables more creative behavior and thereby the smaller size of the filter. The filter is something to be taken into consideration by R&D managers, as it correlates strongly with innovation output. As filter impedes the creative behavior of employees, it also constraints the development of new products. Thus, changes in organizational business strategy and R&D support are important. Managers may find it useful to foster the learning activities of their employees through lean manufacturing, introducing a system of employee responsibilities, promoting the development of team work, the de-centralization of tasks, temporary job placements, and educational systems such as Sigma 6, Invest in People and other similar strategies. Developing team-building and rewarding the implementation of new ideas will perform some conduit of creativity functions. An open exchange of information via the organizational and managerial practices discussed is critical to innovation and the creativity-filter-innovation link.

Within these boundaries, R&D and finance managers may encourage internal research and development in a number of ways, such as by financing it in-house or finding sponsors to fund creative work undertaken within the business. In particular, focus should be on the generation and implementation of new ideas employees both inside and outside of organization. To sum up, the creativity is a multilevel phenomenon, and managers should apply a systematic approach to institutionalized platforms as routines and practices inside their firm. Creativity filter is a conduit of creativity to innovation and it is about both innovation inputs and organizational practices (capabilities) that enables to commercialize creativity mix through recruitment of employees with various creative skills and experimenting to see what works best.

Conclusion

This study is the first to examine creativity filter as a conduit of creativity in innovative firms, demonstrating that creativity comes before knowledge and skills. Further integration of goal orientation theory, the knowledge spillover of entrepreneurship theory, organizational creativity theory and information exchange theory is needed to release the black box explaining the "creativity-innovation-productivity" links.

Policies targeting an increase local economic growth and tax revenues may focus on better commercialization of available creative skills at the firm level, and by providing support to new firm start-ups to spillover creativity. Developing a policy to support both extramural and intramural spillovers of creativity could increase innovation. Any increase in the gross value added in sales will accordingly affect the amount of corporate tax collected. To continue growing an entrepreneurial policy that supports both established firms and new businesses start-ups which employ individuals with creative skills at any level is important.

Government policies that enable businesses to implement new management techniques as well as major changes to their organizational structure while increasing their innovation should be further promoted. Having the creativity filter monitored by both shareholders and R&D innovation teams in organizations may help to avoid possible failures in the development and impediment to novel ideas. To enhance radical innovation, our study suggests that innovation and skills policies should encourage the employment of individuals with software, multimedia, math, applied science and engineering skills. These skills could be easily transferred into innovation and profits.

Specifically, policies may focus on setting up a scheme that enables the development of R&D teams at the firm level which are composed of both experienced entrepreneurs and individuals with a creative skills mix. The target of the creativity filter is to ensure that the gap between creativity and knowledge exchange is kept to a minimum and more ideas flow throughout the filter. In embedding the R&D teams with entrepreneurs who can see opportunities and negotiate with "attentive-to-detail" members will intensify the knowledge flow. More start-ups may take place within the organization and benefit the productivity of established firms. The failure in doing so will increase the creativity filter size and increase the number of workers leaving and starting a new business.