Dalia Kriksciuniene
email: dalia.kriksciuniene@vukhf.lt

Sandra Strigunaite
email: sandra.strigunaite@vukhf.lt

Multi-level Fuzzy Rules-based Analysis of Virtual Team Performance

Keywords: E-leadership, virtual team performance evaluation, fuzzy rules, fuzzy signature

The article presents model for evaluation of virtual team performance based on the intelligent methods of Multi-level fuzzy rules and Fuzzy Signature. The hierarchical system of parameters for virtual team performance evaluation is elaborated by applying expert survey. The aggregated measure of performance of virtual project team is derived from twelve parameters assigned to three categories (team, task and interaction). The experimental research is based on fuzzy analysis of interaction data of virtual teams which worked on implementation of three software solution projects. The research results provide evidence for the feasibility of using the proposed method as the tool for virtual project managers seeking to improve their leadership techniques, and to derive parameters for performance evaluation based on intelligent computing methods.

Introduction

Management activities of any project are often distinguished to project administration and leadership. This applies for project teams working in the real or virtual environment. The need for e-leadership in virtual project teams has become increasingly relevant as businesses move toward more non-traditional work [START_REF] Hartog | Limits to leadership in virtual contexts[END_REF]. The leadership of virtual work management and coordination is much more complicated not only because of the communication restrictions of the virtual working environment, but also because of inability of the manager to be aware of the moods and informal communication context within the team. Managers in virtual and other "organic contexts" are indeed less able to exercise the same influence [START_REF] Cascio | E-Leadership and virtual teams[END_REF]. Lee [START_REF] Lee | E-leadership for project managers: A study of situational leadership and virtual project success[END_REF] indicates a gap in the body of knowledge while applying situational leadership theory to virtual project management. Konradt and Hoch [START_REF] Konradt | A work roles and leadership functions of managers in virtual teams[END_REF] state that eleadership requires a different type of leadership techniques than the traditional project management.

The differences of conducting real and virtual projects are especially vivid from team member collaboration perspectives. The integration and change of fast developing technologies for project / task management and collaboration processes among team members is challenging for search of effective analytical techniques which could improve insightfulness of a project leader and his ability of adequate performance evaluation. Application of intelligent analytic techniques for processing team collaboration records can be used as the effective tool for project managers.

Human interaction management theory (HIM) analyses modelling principles of the human work [START_REF] Harrison-Broninski | Human Interactions: The Heart and Soul of Business Process Management[END_REF]. It emphasizes that the performance of the project work can be designed not only as the workflow of tasks and processes, but it should take into account the interaction processes among project members as well. The work models based on HIM theory should be designed from the role interaction stance by applying special notation for defining interactions related to the project tasks. By applying main concepts of this theory we research core parameters for virtual teamwork evaluation.

In most cases of observing the ways the project managers evaluate teamwork situations we could state that they apply transcendental and linguistic parameter values, for example "the task is complex" or "the experience is low". The output parameters denoting features and outcomes of the project tasks are imprecise as well. Although all project leaders apply their experience and leadership qualities for making decisions and actions in certain situations, the rules and desciptions of these situations are rather difficult to define. The efforts to define the quantitative values for the input, output parameters of the project work and their interrelationships are rather complicated, though the communication data of the project team members is extensively available from the virtual project environment. The imprecise and ambiguous characteristics of the project work imply that the methods suggested by fuzzy computational methods are appropriate for deriving necessary parameters and rules for analysis. These methods find their application in process analysis-in Fayek and Zhuo [START_REF] Fayek | A fuzzy expert system for design performance prediction and evaluation[END_REF] the investigation of fuzzy expert system for design performance evaluation is presented.

In this article we propose the method for virtual team performance evaluation by applying methods of multi-level fuzzy rules and fuzzy signature.

The article is organised as follows. In section 2 the virtual team performance parameters are defined and their measurement is suggested by applying expert survey. In section 3 the application of multi-level fuzzy rule and fuzzy signature methods is substantiated for further research. In section 4 the procedures of experimental research for virtual team performance evaluation are explained, the interpretation and insights of the research results are overviewed. In the section 5 we conclude of the outcomes and present key challenges for further research.

Virtual Team Performance Measurement Criteria

The performance measurement criteria of virtual teamwork were researched by conducting expert survey. Possibility to extract appropriate data from team collaboration environment, definition of evaluation criteria, and their quantitative measurement problems were discussed during survey of fifteen experts. The participants of the discussion were project managers of highest experience and technical consultants of JIRA Agile and JIRA Confluent solutions. The in-depth analysis of this research is presented in [START_REF] Kriksciuniene | Virtual Team Tasks Performance Evaluation Based on Multi-level Fuzzy Comprehensive method[END_REF].

By applying concepts of HIM and situational leadership theories, the survey aimed to discuss the topics: "What criteria can be used for evaluating parameters of three dimensions (task, team and interaction) characterizing project implementation in the virtual environment?" and "How these criteria can be derived from the team collaboration data, registered in the virtual environment?". According to the suggestions and insights of the experts, the hierarchical list of measurement criteria was elaborated and refined. The criteria list, their descriptions and data source types for defining their value are presented in Table 1.

Team evaluation criteria are of two types (Table 1):

(1) Parameters that describe team as unit, (2) Parameters for describing individual team members.

In Table 1, the team evaluation criteria that characterize team as the organizational unit include its size, role variety and hierarchy level. These parameters are important for adequate evaluation, as different task/team settings require respective organisational level. The team evaluation criteria that describe individual members provide compound measures aggregated from individual evaluations of each team member. These criteria include experience and characteristics, which jointly form the team maturity criterion. Task evaluation criteria are strongly based on project specifics; therefore, they can be evaluated by applying Computations, Compromise, Experts judgement or Inspiration decision processes, suggested in [START_REF] Pmbok | A guide to the project management body of knowledge: PMBOK guide[END_REF]. As not all task implementation circumstances can be known in advance, one of the recommendations of the expert survey was to include parameters denoting task intelligence level and its difficulty. The compound characteristic of task "difficulty" is derived from the phase and result clarity criteria (Table 1). The criteria, which belong to the task category, are designed to show if implementation of particular task needs team with a high experience or high level of team interaction capabilities. The third group of criteria related to interaction evaluation describes expected interaction activeness level among team members during the specified task implementation period. The evaluation of criteria, denoting questioning and information sharing levels summarize amount of various types of messages, records in blog and wiki areas, exchanged by team members.

The compound evaluation criteria, which describes the meetings held during implementation of particular task, depends on evaluation of questioning and information sharing.

Punctuality shows if the interim or final results of a task are presented on time or are reported to be done within an acceptable time.

All project management experts agreed that possibility to observe communication of team members in virtual surrounding is as much necessary as in real environment. The patterns of team behaviour, characteristics of communication situations can provide important insights about task implementation process.

The possibilities to use virtual communication data for criteria measurement were explored by analysing the collaborative software application ComindWork [START_REF] Comindwork | Manage people online[END_REF]. In Table 1 it is shown, that the values of the parameters can be set as quantitative values (Value), computed from the appropriate data from project environment (System) or defined by project experts and leadership (Expert). In either case the values of the lowest level criteria have to be quantified.

The hierarchical structure of the criteria set implies that the criteria of higher level can be computed as compound characteristics. The parameter list is designed for characterizing situation of task fulfilment by the project team. The experienced leader of the project management is expected to define the possible outcomes of task fulfilment based on evaluation of input criteria. Three output value descriptions are chosen for further investigation:

(1) Well -if task implementation process is performed well;

(2) Chaos (Delay) -if there is a problem of non-understanding and chaotic communication;

(3) Bad -if work is delayed or stagnated.

Our goal is to present method how to evaluate the hierarchical criteria, to derive rules for defining interrelationships of the input and output criteria, and assign the output values describing task fulfilment situation. The imprecise and expert-based origin of the performance evaluation criteria implies application of fuzzy methods for their further processing.

Multi-level Rule Base Method with Fuzzy Signature approach

Multi-level fuzzy rule method and application of fuzzy signatures aggregation techniques was chosen for the design of model for evaluation virtual teamwork performance.

Fuzzy signatures are used for constructing hierarchical structures of fuzzy characteristics. They can be applied for modelling the complex structure of data in a hierarchical manner (bottom up). The Fuzzy signatures can reduce complexity with slightly more complicated aggregation techniques in huge fuzzy structures. Fuzzy signature can be considered as a special kind of multi-dimensional fuzzy data, where some of the dimensions are formed as a variable sub-group and determines features of a higher level parameter or group [START_REF] Mendis | Fuzzy Signatures: Hierarchical Fuzzy Systems and Applications[END_REF]. This means that instead of assigning a single membership grade to each element X, as it is done when defining original fuzzy sets, a set of quantitative features are assigned to each element X which can have a structure of another nested vector, this way providing additional information about that specific element of the domain. This structure can be continued and finally form a signature with finite depth m [START_REF] Koczy | Fuzzy Signatures[END_REF].

The method of fuzzy signature was introduced by Koczy (1999) [START_REF] Koczy | Fuzzy Signatures[END_REF]. It is the generalization of vector valued fuzzy sets (VVFS). It means, that each element is assigned by matching A to each element x X or vector component of another VVFS (branch) or atomic value (leaf) [START_REF] Koczy | Fuzzy Signatures[END_REF]. It can be specified as in formula (1):

     k i i k i i a a x A 1 1 ] [ : , (1)
here  denotes the Cartesian product, and

       leaf if branch if a a i k j ij i ; ] 1 , 0 [ ; ] [
1 Fuzzy signature can be charted as the nested vector or hierarchical tree structure (see Fig. 1a and Fig. 1b) The whole structure of fuzzy signature looks like a tree graph. The lowest level elements of this fuzzy signature denote leaves, the middle -branches.

                                                                              
In the Fuzzy Signature structure (Fig 1 (b)) leaves [X 11 ,X 12 ] are sub-group of the higher level compound joint X 1 , the leaves [X 211 , X 212 , X 213 ] form higher level compound X 21 , which compounds X 2 in a conjunction with X 22 . Therefore X 2 can be expressed as

[[X 211 , X 212 , X 213 ],X 22 ] or [X 21 , X 22 ].
In the highest level of fuzzy signature it can be abstracted as X = [X 1 , X 2 , X 3 ] or as vector showed in Fig. 1 (a). The underlying general concept of fuzzy signature is a nested vector [START_REF] Koczy | Fuzzy Signatures[END_REF].

The connections between higher and lower levels are constructed by fuzzy set aggregations. The most common aggregation operations are the maximum, minimum and arithmetic mean. The possibility to select the method of abstraction allows to modelling particular situations of performance evaluation, where some of the parameters can be assigned different weights or even lose their importance due to specific situations of task fulfilment.

Fuzzy signatures are used for constructing Fuzzy Rules. In general fuzzy rule is described as the following structure: "If x is then y is ", where is the rule antecedent and is the rule consequent, x is the observation and y is the conclusion.

The rule antecedent can be a fuzzy signature set or fuzzy signature singleton. The signatures have the same arbitrary structure, and the corresponding aggregation operators are uniform for every rule. The consequent parts of the rules remain fuzzy sets [START_REF] Tamas | Inference in Fuzzy Signature Based Model[END_REF].

The method is applied for processing the variables and criteria included to the model characterizing virtual teamwork and its performance.

4

Analysis of Multi-level Fuzzy Rules Method Application for Virtual Team Performance Situation Evaluation

Hierarchical Evaluation Criteria Structure

The results of expert survey and analysis of virtual team performance measurement criteria, as presented in section 2, were processed by applying fuzzy signature concept for designing the hierarchical virtual team performance evaluation model. The hierarchical set of criteria is presented in Table 2. The scheme refined by the participants of the survey is arranged in four levels. The lower level criteria have the lowest level of fuzziness and can be assigned values by using interaction data of the virtual space or determined by project leader. Three possible values are selected as situation output. The criteria of the higher level are computed by applying fuzzy signature method. The hierarchical virtual team performance evaluation scheme is explored by the experimental research, discussed in the following section.

Experimental Research Setting

The goal of the experiment was to test if the suggested parameter hierarchical structures can help to identify task implementation situations. The data of the experimental research was derived form three IT software implementation projects, where the team members communicated in the virtual space during the most part of the projects. The logs of virtual teamwork collaboration system were used. The team leader had possibility to observe all the communication instances of the team members related to task fulfilment during the project work. All projects had teams with different experience and organizational structures, and different working styles. Brief descriptions of projects are presented in Table 3. Task was defined as a work package for certain functionality implementation. The shortest tasks lasted from two days, but majority had duration from one to two weeks. If a task was implemented on time then its outcome was marked as Well, if the task was delayed without clear outcome, then it was denoted as Chaos, and if the task planning was changed or redone, then it was marked as Bad. Limitations of the research were related to data evaluation: the virtual communication data could be used for evaluation of small part of parameters, the remaining part were expert evaluations and had high level of uncertainty.

Application of Fuzzy Signature and Fuzzy Rules

Multi-level Fuzzy rule applying Fuzzy Signatures method is suitable for this type data analysis because of the possibility to apply bottom-up fuzzy parameter evaluation and aggregation techniques.

The Fuzzy Signature structure for Hierarchical virtual team performance is presented in formula (4). For parameter aggregation the arithmetic mean was used. The Fuzzy Signatures for Fuzzy Rule construction is identified by three parameters [(C1)Task, (C2)Team, (C3)Interaction]. Each parameter has several possible value intervals. These parameter value interval ranges and their clarifications are presented in Table 4.

                                                                                                                               

Table 4 Third level parameter value intervals and their clarifications

Criteria value name

Abr .

Value range

Value get in these circumstances

Team evaluation

Formula :

)) , ( Output values is parameter Situation (C) with value intervals defined as {Bad}, {Chaos} or {Well}. The ranges of each value interval is [0;0.3] -Bad, [0.3;0.7] -Chaos and [0.7;1] -Well. By using Team/Task/Interaction parameter interval ranges sixty different parameter combinations (fuzzy rules) are constructed and assigned to one of the possible Outcomes.

Fuzzy rules are constructed by using MatLab software application. The results are plotted as the three-dimensional diagrams where the interrelationships of three categories-team, task and situation-are further interpreted.

The insights are provided by analysing the fuzzy rules derived of interrelationships of input variables plotted on X and Y-axes of the diagram and output variable plotted on Z-axis.

The insights on Situation outcomes by analysing Team and Task input variables are derived from the surface diagram presented in Fig. 2. The patterns of various combinations are presented by using categories of fuzzy values form Table 4. Five Situation patterns are identified: The results presented in surface diagrams and describes as insights for project evaluation can be used for forecasting of the situation outcome and for defining strategies aimed to strengthen particular parameters in order to avoid project risk. The advantage of the presented method is its ability to derive values of the situation evaluation parameters which have the highest level of abstraction and risk from the values of lowest level parameters which can be easier evaluated by even less experienced project leaders or computed from the interaction data of virtual communication space. The methods of fuzzy signature and fuzzy rules solve the problem of the fuzziness of parameters values and their hierarchical structure.

The aims of further research include refinement of criteria evaluation methods and implementation of fuzzy signature based model to the virtual teamwork environment.

Conclusions and Further Research

The analysis of scientific research related to project leadership techniques and their application to virtual teamwork analysis revealed lack of effective performance evaluation methods. The methods based on subjective judgement and direct observations of team members fail in the virtual environments.

The proposed method for evaluation of virtual team performance aimed to refine the system of parameters and apply computational method for their quantitative evaluation.

The expert survey was applied for designing model consisting of twelve fuzzy parameters arranged in the hierarchical structure that characterize dimensions of Team, Task and Interaction, leading to evaluation of virtual team work performance situation. The list of parameters and can be refined by further research.

The fuzziness of the input and output variables and their interrelationships led to applying the methods of fuzzy rules. The hierarchical structure of the parameter set and the "bottom-up" approach used for evaluation of higher level criteria implied using the methods and fuzzy signature. The criteria enlisted in the lower level of the suggested model can be not only evaluated by experts or project leaders, but by deriving their values from the interaction and log data stored in the virtual teamwork environments. The fuzzy rule set and their interpretation was designed by analysis of three dimensions: Task, Team and Situation. The applied principles can be refined for creation of expert database for project and task evaluation purposes with higher accuracy of recognizing problematic or chaotic virtual team work performance situations.

The insights and interpretations of the research results can be useful for virtual teamwork evaluation and to reduce risk of direct evaluation of project situation by the inexperienced project leaders without taking into account the underlying lower level criteria.

Fig. 1 .

 1 Fig. 1. Fuzzy Signature structures



  P1-W1 Strong Team [0.8;1] reaches situation outcome which belong to the value area Well [>0.8] almost with any type of task.  P2-W2 Experienced team in a range [0.7;0.8] with task type Difficult [0.4;0.6] reaches situation Well [0.8]. Noticeable that with Routine task [0;0.4] and Intelligent task [0.7;1] evaluation of situation is lower.  P3-W3 Growing Team [0.4;0.5] can perform task that requires lower level of intelligence (routine type), as it was assigned Situation value [0.75] for the Task simple/routine [0;0.3].  P4-C1 Growing team [0.4;0.5] and Difficult/Intelligent [0.4;1] task lead to situation assigned to Chaos [0.4;0.5].  P5-B1 Weak Team [0;0.3] with difficult/intelligent [0.4;1] task lead to Situation value in a range [0;0.3] that means Bad. Even if low intelligence tasks can be dedicated for this team type, good situation can't be expected.

Fig. 2 .

 2 Fig. 2. Team and Task surface diagram Insights on Situation outcome by analysing Task and Interaction combination showed that mostly chaotic situations were identified. This indicates the Team parameter has the highest influence on final situation outcome. By analysing Team-Task combination results presented in the surface diagram (Fig.3) the following Situation patterns were identified:  P6-W4 then task is Intelligent [0.8;1] and Interaction rate is High [0.9;1] Situation is evaluated as Well [0.8]. In is the best possible situation.  P7-W5 if task belongs to Routine type task range [0;0.3] and Interaction rate is Low [0;0.2] the situation assigned value of Well [0.7];  P8-C2 Task is Difficult [0.4;0.8] and Interaction belongs to range [0.4;1] then Situation value is Chaos [0.5;0.6]. Analysing these type situations is possible to state that value of parameter Team plays the decisive role for defining situation outcome.  P9-C3 Interaction range is in Middle [0.5] and Task is strongly intelligent [0.9;1] then situation is assigned to Chaos [0.4;0.5].

Fig. 3 .

 3 Fig. 3. Task and Interaction surface diagram Some additional insights of Situation outcomes are derived by analysing Interaction and Team combinations. Four strong patterns are identified (Fig.4 ).

Fig. 4 .

 4 Fig. 4. Interaction and Team surface diagram

Table 1

 1 The criteria list for virtual team performance evaluation

	Criteria	Description		Source type
	Team evaluation criteria
	Size	Number of performers assigned to the task during whole task	System / Value
		implementation period
	Variety	Number of different roles assigned to task	System / Value
	Experience	Level of team experience	Expert
	Characteristics	Cumulative measures of personal characteristics: attitude to	Expert
		work/task implementation of the performer
	Hierarchy	Level of team hierarchy (the rate of high, middle, junior	System / Value
		experience within a particular role)
	Task evaluation criteria
	Phase	Expert judgment /manager evaluation, parameter rate from a	Expert / System
		particular interval (beginning, middle or end of a particular
		project phase or iteration)
	Task	Expert evaluation of the necessity of human driven effort,	Expert
	intelligence	necessary to implement particular task
	level
	Result clarity	Expert / project team evaluation about quality criteria and	Expert
		clarity of the expected result
	Interaction evaluation criteria
	Meeting level	Number of meetings and their type, topic, average duration	System/Compo
	Questioning	Number and types of questions sent to team members and	und value f(t)
	level	requests for information to team leader and senior members
	Information	Eagerness	of team and individual members to share
	sharing level	information
	Punctuality	Parameter describing team punctuality level	System / Value
	level			Yes / No set

Table 2

 2 Hierarchical virtual team performance evaluation scheme

	Input criteria (leaves)	Middle criteria (branches)	Output
	(C121) Result clarity {Low; High} (C122 ) Phase {Low; High}	(C12 ) Task difficulty	(C1) Task
	(C11) Task intelligence level {Low; High}
	(C222) Characteristics {Low; High} (C221) Experience {Low; High}	(C22 ) Maturity level		(C)
	(C211) Size {Low; High} (C212) Role variety {Low; High} (C213) Hierarchy level {Low; High}	(C21) Organisational level	(C2) Team	Situation {Bad; Chaos;
	(C311) Meeting level {Low; High}			Well}
	(C312) Questioning level {Low; High} (C313) Information sharing level {Low; High}	(C31) Activity level	(C3) Interaction level
	(C32 ) Punctuality level {Low; High}

Table 3

 3 Experimental data description

	Parameter		First project	Second project	Third project
	Duration			2 year	6 month	1 year
	Phases			9	3	6
	Number	of	team	9 -12	2 -4	12 -20
	members
	Hierarchy		High	Low	Middle/High
	Role variety		Middle / High	Low	Middle / Low
	Analysed number of	144	48	480
	tasks (work packages)
	Majority of task types	Mix	Intelligent	Difficult/Routine
	Majority	of	task	Mix	Well	Chaos
	Situations identified
	Working style		One big group	Individual work	Working in small /
						individual groups
	Main	reason	of	Experience	Lack of Time	Weak Structure
	problems


Nineta Polemi
email: dpolemi@unipi.gr

George Pentafronimos

Theodoros Ntouskas
email: tdouskas@unipi.gr

IMP2.0 Migration Collaborative Platform and e-Services

Keywords: legal immigration, collaborative technologies, e-migration services

Legal immigration is a complex, multi dimensional issue and the European Commission (E.C.) project ImmigrationPolicy2.0 (IMP2.0) [1] considered it as such by studying its legal, societal and policy implications before proposing and implementing holistic e-migration services contributing towards participatory governance and the harmonization of existing policies and practices. This paper outlines the IMP2.0 social, policy and legal research results which led to the design and implementation of targeted e-migration collaborative services by presenting the identified requirements and describing the services provided by the IMP2.0 web platform.

Introduction

IMP2.0 [1] is a technological project driven from the needs arising in the migration policy field. Social Integration, Social Cohesion, Security, Privacy and Interoperability are the most important European Union (E.U.) policy objectives that IMP2.0 directly addresses. It adopts a bottom up approach by analyzing all aspects (legal, societal, policy) of the complex migration employment problem (the most important part of a Social Integration Policy) and provides e-services which contribute towards harmonizing the efforts for establishing a common E.U. migration employment policy.

It provides an innovative IT instrument to both migration related communities (policy makers and legal immigrants), using new technologies and opens new research areas (visualization, collaborative modeling and graphics, governmental process management systems, collaborative decision making). In contrast to the present situation of IT governmental tools, IMP2.0 paves the way for a new research area in "Innovative migration electronic systems".

In this paper we outline the IMP2.0 social, policy and legal research results which led to the design and implementation of targeted e-migration collaborative services and it is organized as follows: In Section 2, the E.U. policy and legislation harmonization efforts related to employment migration are outlined and open problems and gaps at practical level are identified. In Section 3, the user requirements as reported in the IMP2.0 survey involving four hundred and sixty eight (468) stakeholders (policy makers and legal immigrants) in the migration employment community are presented. Considering these requirements, IMP2.0 designed and implemented targeted e-migration services, in order to contribute effectively towards the efforts in harmonizing E.U. migration employment policies as described in Section 4. The paper concludes with Section 5 in which the main results of the paper are outlined and further research propositions are provided.

Migration Employment Policies and Legislation

European Union Efforts

IMP2.0 performed a detailed desk study on migration policies at national and European level. In this section the main results of the European level desk study will be presented (for detailed analysis the reader is referred to [START_REF] Pentafronimos | D2.1 User and Service Classification[END_REF]).

The European Union (EU) Council acknowledges that migration employment issue, by its very nature, can be better addressed at European rather than at national level. It emphasizes the importance in harmonizing migration policies [START_REF] Kate | Guide to Locating Migration Policies in the European Commission[END_REF] starting its efforts towards this direction from 1999 with its three main policy Programmes, Tampere, Hague and Stockholm, [START_REF] Rodríguez | D1.2 Stateof-the-art and advances in European migration policies[END_REF]: The Tampere program (1999)(2000)(2001)(2002)(2003)(2004) in which the E.U. leaders at the 1999 E.U. Council in Tampere (Finland) agreed upon that a comprehensive approach to migration addressing political, human rights and development issues in countries and regions of origin and transit is needed. This requires improving living conditions and job opportunities, preventing conflicts and consolidating democratic states and ensuring respect for human rights, in particular rights of minorities (women and children). Partnership with third countries concerned is also a key element for the success of such a policy, with a view to promoting cooperative development. From a legislative point of view, the main achievements during the period of implementation of the Tampere program have been the following:  Family reunification -The Council Directive 2003/86/EC [START_REF]Council Directive EC 86/2003: On the right to family reunification[END_REF] (2006) 892] which provides an overview of migration trends in the E.U. In May 2007, the second edition of the 'Handbook on Integration for policymakers and practitioners' was issued focusing on mainstreaming immigrant integration, housing in an urban environment, economic integration and integration governance. In September 2007, the Third Annual Report on Migration and Integration (COM (2007) 512) depicts the continued monitoring process of harmonized policy developments on admission and integration of third-country nationals in the EU. The 2008 E.U. Council endorsed the Global approach to migration. Its purpose is, to create a coherent policy approach in the area of migration: Development policy, measures to encourage legal migration and fight illegal immigration, as well as managing demand for skilled labor in a framework of dialogue, cooperation and partnership with countries of origin and transit.

In 2009, the Commission adopted a directive on the admission of highly-skilled third country nationals, the so-called EU-Blue Card, a fast-track procedure for issuing a special residence and work permit under more attractive conditions. It is the only directive derived from the Policy Plan on Legal Migration from 2005 adopted to date.

The Stockholm Program (2010-2014) approach differs from its predecessors (Tampere Program and Hague Program) with regard to several aspects. For example, the Hague Program emphasized harmonizing migration and asylum policies across Member States, where the Stockholm Program prioritizes initiatives promoting cooperation between the Member States to find practical solutions [START_REF] Collet | The European Union's Stockholm Program: Less Ambition on Immigration and Asylum, But More Detailed Plans[END_REF]. It also seeks to use soft law such as guidelines and stand-alone E.U. agencies, rather than the hard law envisioned in the Maastricht Treaty.

The program sets out the following priorities in the area of immigration, in which the relevance of labor migration is curtailed compared to the Hague Program:  Global Approach to Migration: The need to identify common interests with third countries is highlighted.  Migration and Development: Facilitating remittances, cooperation with diaspora groups, and promoting circular migration constitute EU's priorities in the migration development nexus.

 Labor Migration: The need for improved information and data on skills needs, skills recognition and development as well as skills matching with third countries were highly considered for further actions.  Rights for third-country nationals: Third-country nationals shall be endowed with "rights and obligations comparable to those of E.U. citizens" by the end of the program's period.  Integration: Within the program several ideas in the area integration are proposed, e.g. the development of common European modules, as well as E.U.-wide indicators to monitor the results of harmonized integration policies.  Illegal Migration: The need for a sustainable return policy supplemented by encouragement of voluntary return, and renewed efforts to sign readmission agreements with more countries of origin and transit.  Unaccompanied Minors: Unaccompanied minors, not addressed in the previous programs, are included in the Stockholm Program.

In April 2010 the Commission adopted an action plan on the Stockholm Program (COM (2010) 171 final) to implement the political priorities set out in the program.

The third edition of the Handbook on Integration for policy-makers and practitioners was published in April 2010 and the Commission presented an agenda for new skills and jobs entitled "A European contribution towards full employment" (COM (2010) 682 final). In 2011 a New Agenda for Integration of third country nationals will be launched, to provide improved structures and tools to facilitate the exchange of knowledge, collaboration and the mainstreaming of integration priorities of the Member States.

Harmonization in Practice -The IMP2.0 Experience

Despite the above mentioned collaboration efforts at European level, the adopted national employment migration policies are still divergent and they do not comply with the E.U. Council directives. As a result the processes and documents followed to implement common E.U. migration employment procedures (e.g. issuing of work permits) at national level are neither cross-recognized nor cross-accepted [START_REF] Fleischmann | The effects of social and labour-market policies of EU-countries on the socio-economic integration of first and second generation immigrants from different countries of origin[END_REF].

During the IMP2.0 project the five E.U. countries involved (Germany, Italy, Spain, Greece and Estonia) found that the processes followed to carry out their three common employment migration procedures (Issuing residence permits; Recognition of qualification achieved in non-E.U. countries; Estimating the number of residence permits that will be issued annually) were all sustainably different [START_REF] Pentafronimos | D2.1 User and Service Classification[END_REF]. These procedures were based on particular national laws that they were not harmonized with the E.U. directives.

For example, regarding the first common migration employment procedure, Issuing residence permits for dependent employment; the five IMP2.0 involved countries exert different processes for granting legal access to the labor market for third-country nationals. With respect to documents type (e.g. individual work permit, residence permit for employment), involved agents and governmental level, legal conditions, order of consecutive process-steps etc. the national processes vary considerably [START_REF] Pentafronimos | D2.1 User and Service Classification[END_REF] (see e.g. in Figs. 1,2 the different processes followed in Greece and Germany).

Greek Employer

Employment contract with a remuneration at least equivalent to the monthly salary of unskilled workers.

Applicant

Certification that they have fulfilled their tax obligations;

Taxation Service

Third-country nationals who have obtained a visa for dependent employment in Greece Examination of applications

Regional Agency for Aliens and Migration

Municipality/Community of place of domicile/residence

The third-country national submits an application and documentation showing:

1. That they have fulfilled their tax obligations; 2. That the requirements of employment are met;

Residence permits for dependent employment The variation of heterogeneous processes, different types and formats of documents involved result to the non-cross border recognised procedures not allowing the free-movement of legal residents (e.g. legal immigrants, second generation immigrants) in the European continent; damaging the common efforts to control the increasing migration employment wave throughout the European continent, to better balance the European labor marker and to enhance the European competiveness in a holistic way.

IMP2.0 finally concluded that the increased number of decision makers and stakeholders involved in migration policies, increased and diverged legislations and implemented migration procedures, different organizational structures, large and inhomogeneous legacy systems involved, cause a "chaos" in the monitoring of national policies and the harmonization of procedures, processes and data formats. Traditional decision making instruments (e.g. face-to face meetings, workshops and conferences) at political level need to be supported with new innovative governmental IT tools (e.g. for policy modeling, business process management, visualization, collaborative decision making) in order to accelerate the harmonization efforts.

Societal Aspects -The IMP2.0 Requirements' Analysis

The two migration communities (stakeholders and legal immigrants) need to be involved in the processes of drafting and adopting harmonized realistic policies. IMP2.0 used an explorative multi-methodological approach to realize their requirements and needs consisting of a workshop [START_REF]First ImmigrationPolicy2.0 Workshop[END_REF], desk research (results are outlined in the previous section), and questionnaires for both communities in various languages. In this section we will present the European level analysis of the IMP2.0 questionnaires (for the national level analysis and more details the reader is referred to [START_REF] Bosswick | D1.1 End User Requirements[END_REF]).

IMP2.0 integrated an open-source software tool (based on the PHP framework Symphony 1.0-www.symfony-project.org-) that enables the design, development and deployment of on-line questionnaires. The IMP2.0 questionnaire tool comprises two main modules: One is responsible for the management of online questionnaires while the other undertakes the collection of answers, extraction of results and the generation of statistical data and related reports. The privacy of the responses as well as the effective management of all users' interactions with all the systems, components and software tools, in terms of security, privacy and trust, in the IMP2.0 web platform is undertaken from an advanced, standards-based (e.g. WS-Federation, WS-Trust), centralized and federated Identity and Access Management (IAM) system, which is based on the open source implementation of OpenSSO [START_REF] Ilyas | [END_REF].

Two types of questionnaires [1] were generated in order to capture the requirements of both migration communities and they were translated in the native languages of the above countries and also in Turkish, Albanian and Russian (the mother tongue of the majority of legal immigrants in Germany, Greece and Estonia respectively).

Altogether four hundred and sixty eight (468) stakeholders and legal immigrants participated in the IMP2.0 questionnaire process from the five participating countries (see Table 1). The European level IMP2.0 requirements are summarized in the next subsection (for the extensive IMP2.0 requirements analysis the readers is referred to [START_REF] Bosswick | D1.1 End User Requirements[END_REF]).

Legal Immigrants Requirements

Information: Migrants need more and better quality information about the practices and procedures in migration/ integration/ employment field. Information has to be clear and simple (less bureaucratic), comparable (between different countries) and presented in more languages. Access to information via electronic channels, especially web, is desired. But it is important to keep in mind that in addition to electronic media, more conventional means for providing information (such as press for example) have to be used in parallel. Most needed information is about employment/ business opportunities, job/ business regulations and migration/ labor market legislation. Collaboration: Immigrants are interested in participating and collaborating among them and with the policy makers in the policy making process. The goal to include migrants in the policy formulation process could be further promoted by focusing topics of special concern such as registration and recognition of skills and qualification, restrictive regulations of work and residence permit. Migrants are interested to propose their ideas and suggestions to improve the practices and policies in the migration/ integration/ labor field, i.e. to participate in more collaborative policy-making, so possibilities for providing feedback to migration organizations have to be created. Areas for action are for example: registration and recognition of skills and qualification, restrictive regulations of work and residence permit, lack of information and communication, high bureaucracy.

To increase the migrants' participation in policy-making and improvement of procedures, room for debates and discussions should be created, where migrants/ migrant groups/ Non Governmental Organizations (NGOs) could interact with each other as well as with public administrators and policy makers exercise a two-way communication.

Training: Training in the language and culture of the hosting language and culture is among their main concern. The available training channels are either inadequate or very expensive and time consuming requiring high bureaucracy.

Migrants are not well aware and feel confused about the possibility of processing their migration related documents online. Therefore more information, guiding and trainings need to be offered to popularize these services as well the services need to be simplified. Migrants are most interested in residence and work permit procedures.

Stakeholders Requirements

Migration policies (political level): With respect to economic/labor Migration policies stakeholders revealed a general demand for a comprehensive strategic approach for managing economic immigration. For instance, a lack of knowledge on political programmes to manage labor migration can be assessed as an indicator for the absence of a comprehensive strategic approach: Solely 25% of the stakeholders know a past, running or planned labor migration Programme in their home country. Also, it was found that stakeholders identify the need for enhancement of labor migration monitoring and means to efficiently match labor demand and supply. With respect to integration policy requirements a general demand for exchange on and further development of integration policies was identified.

Practical work (practical level), Institutional cooperation requirements:

Stakeholders in all participating IMP2.0 countries require internet-based structures for cooperation or dialogue with international organizations and EU-institutions, especially on labor migration. The conclusion, inter alia, is based on the finding that almost unanimously, stakeholders in all IMP2.0 participating countries ascribed high importance to international cooperation in the area of labor migration. It was found that the vast majority of stakeholders do not participate in joint projects addressing labor migration. Stakeholders require cooperation on a wide range of issues. The two most important once seem to be labor migration and exchange of good practices. Further issues of cooperation are: harmonization of policies, practices and procedures, legislation, statistical and analytical data, recognition of qualifications, migration technologies, national procedures, migration projects, illegal employment, labor market and entrepreneurship, residence and work permits, social security issues, education, problems and priorities of political intervention, integration supporting programmes, monitoring of migrant employment, monitoring of migrant self-employment, targeted training on migration issues, simplification of documents. Process requirements: Stakeholders require communal and regional networks linking different migration and integration agents for instance, communal and regional promotion and coordination of local policies, participation of citizens, and dissemination of good practices. They also revealed that these processes would need to be enhanced by fostering networks throughout all different governmental levels also including civil society agents. Administrative procedures requirements: Stakeholders would appreciate an infrastructure for electronically processing of administrative migration related issues such as application or renewal of civil status documents related to employment (e.g. work permits, residence permits, family reunification documents).

Information requirements referring to the information provider: A clear claim of stakeholders in three out of five countries included is not to "reinvent the wheel". They rather require an "umbrella portal" for information sources instead of another source presenting single information. As stakeholders said, the umbrella, of course, should not solely apply for information also for other online services, such as service for matching labor demand and supply. Specific requirements: Political areas for which stakeholders see a need for action are: the development or enhancement of a comprehensive national strategic approach for managing economic immigration; the enhancement of labor migration monitoring; efficiently match labor demand and supply; exchange on and further development of policies addressing the integration of migrants into the economy. The IMP2.0 requirements' analysis revealed the design of the IMP2.0 new emigration services described in the next section.

The IMP2.0 Collaborative e-Migration Services

Based on the IMP2.0 user requirements analysis described in the previous section IMP2.0 project defined a number of advanced and highly-sophisticated e-migration services [START_REF] Pentafronimos | D2.1 User and Service Classification[END_REF] that aim to support both legal immigrants and migration stakeholders in their difficult efforts for effective integration and collaborative policy making and harmonization respectively. The main services to be piloted and offered by the IMP2.0 web platform [START_REF] Pentafronimos | ODYSSEUS: An Advanced, Collaborative and Trusted Framework for the Provision of Migration Services[END_REF], [START_REF] Pentafronimos | OPSIS: An Open, Preventive and Scalable Migration Information System[END_REF], [START_REF] Karantjias | Participatory Immigration Policy Making and Harmonization Services based on Collaborative Web 2.0 Technologies[END_REF] are depicted in the following figure along with the identified user requirements for each target group: As depicted in the figure above, in order to satisfy the identified requirements IMP2.0 designed and implemented the following e-migration services:

Information Management Services (IMS): IMP2.0 integrated a user-friendly and robust content management system serving as a vehicle for educating end-users with respect to existing policies and regulations, as well as other valuable but distributed information. Specifically, both groups of IMP2.0 end-users (i.e. legal residents, migration stakeholders) will benefit from ubiquitous and user-friendly web interfaces in order to contribute their valuable information sources (i.e. electronic documents, press reports, web links, digitalized migration-related civil status documents, etc.). Also they will be able to search and access these information assets and efficiently classify them based on a properly designed IMP2.0 taxonomy (see [START_REF] Rodríguez | D1.2 Stateof-the-art and advances in European migration policies[END_REF], Section 2.3.1.1). It will provide seamless access to a sustainable, scalable, structural and searchable inventory, focusing on migration related topics (e.g. National migration policies/legislation/best practices).

This service provides an intuitive and simple interface that enables users to upload their contributions by providing a set of valuable and required (through the use of appropriate control mechanisms) metadata which describe each insertion based on a number of indispensable characteristics. This set of metadata includes the title and description of each information asset, a web-link when applicable as well as a number of indices that characterize the content of each contribution tagged through the integrated tree structure that represents the IMP2.0 taxonomy. The taxonomy has been defined based on the knowledge and experience in migration issues of IMP2.0 partners and has been developed using XML and javascript technologies so as to provide the desired levels of flexibility, extensibility and ease of use when accessed by the end-users for semantically tagging the content they contribute to the IMP2.0 digital library. Knowledge Harvesting and Content Extraction Services (KHCES) (Fig. 4): will integrate advanced data collection technologies and tools as well as interactive front-end user interfaces in order to collect "Open Intelligence" and exploit the "wisdom of the crowds". Specially, it will provide the means for collecting unstructured information and gathering different opinions, views and experiences on migration policies, national practices and procedures regarding civil status documents. This will be achieved by developing a trusted collaborative environment composed by web 2.0 tools like wikis, blogs, etc. or through graphic models thus enabling open participation, direct and multidimensional feedback, Open discussions, as well as the opportunity for gaps identification and proposal of adequate solutions.

Open Surveys Support Services (OSSS): On-line questionnaires, surveys, polls, collaborative documents, and open debates will be used to compose and provide this service to both groups of end-users (i.e. legal residents, migration stakeholders). By accessing and consuming this type of services, IMP2.0 users will be able to exchange diverse proposals, support controversial ideas, positive and negative opinions, answer multiple choice questions and provide both open and structured reasoning as well as their valuable knowledge and experience.

This will be achieved by integrating open-source software tools and specialized Web2.0 components which will enable distributed information acquisition and centralized data management and provide capabilities for statistical analysis and production of reports. The online IMP2.0 questionnaire tool has already been as described in the previous section.

Migration Policy Synchronization and Homogenization Service (MPSHS): This service enables migration policy and decision makers, public administrators, politicians and experts to work and collaborate towards harmonized E.U. migration policies and procedures. Specifically, the objective of this service is to support migration stakeholders in posting and drafting migration policy text, developing and testing policy models, evaluation scenarios ("what-if process") and accessing valuable and efficiently processed statistical data. Migration stakeholders (notably decision and policy makers) will be able to benchmark national practices, policies, procedures and studies as well as to perform assessments in terms of legislation, organizational, political and security characteristics, identify penetration/acceptance rates and effectively forecast, in order to overcome existing obstacles with respect to E.U. directives and best practices.

To achieve these, the ImmigrationPolicy2.0 workplan takes provision for technical implementation activities, which are mainly focused on the integration of readily available R&D open source and free-license components. The main objectives of the technical implementation and integration tasks of the project are two-fold:  To establish a highly agile automation environment, that could boost both the reengineering and the integration of migration related processes. This environment will facilitate changes in the migration related processes and services, through enabling the flexible re-composition of complex policy-making and/or harmonization migration services.  To compose and deploy the services and processes required to operate the project's pilot services. The composition will leverage the SOA environment and BPM tool of the ImmigrationPolicy2.0 platform.

 To provide a number of tools facilitating citizens participation, government modelling and policy development, as well as support for Open Surveys. The first step of the integration efforts of the project involves the development of a basic backbone infrastructure for the project pilots. This infrastructure comprises a portal (i.e., consisting of Web2.0 components) enabling end-users participation and interaction, a CMS enabling the management of migration information assets and related portal content, as well as the middleware infrastructure (i.e. application servers, enterprise service bus) that will provide the SOA environment. Notably, this basic infrastructure will hold the data structures of the project including taxonomies, the XML-based and e-Gif enabled content objects, while also providing related tools for the effective collection of data and simple query execution (e.g. online forms, questionnaires etc.) as well. In addition it will provide:  Advanced content management tools such as rich text editors, live page editing and scheduling, and advanced document managers.  Web 2.0 aware technologies with their own set of authorizations, message boards for facilitating conversations around migration-based topics, blogs for allowing users to convey information and RSS feeds from the last mentioned message boards and blogs within ImmigrationPolicy2.0.  A multi-tier search engine so that end-users are able to search relevant information throughout an entire web interactive portal, within specific portlets such as Wikis, Message Boards, other Web 2.0 aware technologies and even in external integrated applications through its advanced multiple interfacing module.  Intuitive front end user interfaces that will share a set of common characteristics to promote user friendliness and accessibility: they will be multilingual, in order for users to easily toggle between different language settings and they will follow standardized best practices for accessibility (especially for special groups).  Web publishing tools so to easily create and manage content, from a simple article of text and images to fully functional web sources.

Summarizing, IMP2.0 implements a range of highly sophisticated services in order to provide a robust and sustainable IS/IT collaboration framework that is able to support decision-making in the critical domain of migration. Integrating advanced tools for collecting, analyzing and sharing diverse information and supporting policymaking decisions by providing the opportunity for all key players to work together and contribute their knowledge and experience, the proposed solution delivers an efficient synchronization framework capable to leverage existing traditional practices.

Conclusions

For more than 20 years now (from the Maastricht Treaty, 1986, to the Treaty of Amsterdam in force since 1999) the Member States have joined forces to combat international phenomena such as illegal immigration. There is an urgent, (acknowledged by the ongoing Amsterdam Treaty and the E.U. Councils' programmes) need for more effective, collaborative actions among Member States in order to harmonize national migration policies and specific migration procedures.

The technological, policy-driven, IMP2.0 project contributes directly to these needs and responds to the invitation of the E.U. Council for the development of information systems that will contribute towards a common E.U. migration policy. IMP2.0 performed a social analysis on the migration needs and requirements involving both stakeholders and legal immigrants in order to propose e-migration services considering all aspects (policy, legal, societal). Collaborative technologies are the IMP2.0 technological tools used in order to offer e-migration collaborative services hosted in its Web2.0 based-platform. The IMP2.0 user requirement analysis revealed the need for various new e-migration services.

The IMP2.0 serves as an innovative migration system able to host additional emigration services for legal immigrants (e.g. training/ consulting, employment opportunities for legal immigrants, on line applications for labor migration documents, recognition of qualifications, certifications) and stakeholders (e.g. matching employment supply-demand, labor migration monitoring, online processing of migration related documents, one-stop entrance on migration information ) serving their needs and expanding the e-society concept to all its participants.

Fig. 1 .

 1 Fig. 1. Greek Procedure[3, p.50]

Fig. 2 .

 2 Fig. 2. German Procedure [3, p.76]

Fig. 3 .

 3 Fig. 3. IMP2.0 User requirements and matching services

Fig. 4 .

 4 Fig. 4. Knowledge Harvesting and Content Extraction Services

  Students -A Directive on the conditions of admission of third-country nationals for the purposes of studies, pupil exchange, unremunerated training or voluntary service was adopted by the Council Directive 2004/114. Member States' legislation must comply with the Directive by 12 January 2007.  Researchers -A Directive for the facilitation of the admission of researchers into the E.U. was adopted by the Council Directive 2005/71. The Hague program (2005-2010) sets the objectives for strengthening freedom, security and justice in the E.U. for this period. The 2005 E.U. Council, taking into account the outcome of discussions on the Green Paper on an E.U. approach to managing economic migration (COM (2004) 811) addressing labor migration, best practices in Member States and its relevance for implementation of the Lisbon strategy, invited the Commission to present a Policy Plan on Legal Migration (COM (2005) 669). The document foreshadowed the proposal for a directive on a single application procedure for a single permit for nationals of third countries to reside and work lawfully in the territory of a Member State and on a common set of rights for third-country workers legally residing in a Member State, which was adopted by the Commission in October 2007 (COM (2007) 637 final). In September 2005, the Commission adopted the communication 'A Common Agenda for Integration -Framework for the Integration of Third-Country Nationals in the European Union' (COM (2005) 389).This Communication provides new suggestions for harmonization action both at E.U. and national level. In December 2005, the E.U. Council adopted the Global Approach to Migration, and considers migration issues as integral part of the E.U.'s external relations. In June 2006 the Commission presented the Second Annual Report on Migration and Integration [SEC

on the right to family reunification. Member States' legislation had to comply with this Directive not later than 3 October 2005.  E.U. long-term resident status -The Council Directive 2003/109/EC [13] on a long-term resident status for third country nationals who have legally resided for five years in the territory of a Member State. Member States legislation had to comply with this Directive by 23 January 2006. 

Table 1 .

 1 Sample of the Requirement Analysis[2, p.25]

	Country	Stakeholders	Immigrants	Total
	Greece	22	140	162
	Italy	14	111	125
	Germany	17	85	102
	Estonia	15	51	66
	Spain	2	11	13
	Total	73	398	468

Acknowledgments. The authors are grateful to the E.C. ICT PSP Programme for funding the ImmigrationPolicy2.0 (IMP2.0) project and all the partners for their valuable contribution. Especial thanks to Professor Wolfgang Bosswick and Verena Krobisch from EFMS for their substantial input in the societal analysis.


Nicholas Nechval
email: nechval@junik.lv

Maris Purgailis

Konstantin Nechval

Weibull Model for Dynamic Pricing in e-Business

Keywords: e-business, pricing, uncertainty, revenue, Weibull model, seller risk, test plan

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

Introduction

The benefits of dynamic pricing are twofold. First, it provides new opportunities for companies to maximize their return per customer. With lower menu costs (that is, the cost of displaying prices to customers), companies can have multiple prices for different channels and product configurations  and can change those prices more frequently. Companies able to gather information about their competition and about customer needs and willingness to pay can customize their offerings and prices. This enables them to deploy dynamic pricing through the most appropriate of many channels. With dynamic pricing, companies can give their customers exactly what they want, at exactly the price they are willing to bear. Nothing is left on the table. The second, perhaps less obvious, benefit is that dynamic pricing can also bring better returns on deployed assets. For businesses with high fixed-cost technology infrastructures, periods of low demand and, thus, low utilization are expensive. Conversely, when there are inflexibilities in the supply chain for critical components, periods of high demand can lead to shortages and can both delay purchasing and damage customer relationships. But with dynamic pricing, companies can encourage demand in slow periods and discourage it in busy periods.

Pricing in e-business is similar to that in traditional business. However, in ebusiness prices are readily available to consumers and competing organizations via the Internet. With vital pricing data readily available, organizations may be forced to reevaluate their pricing methodology and strategy to avoid being significantly undercut, while remaining competitive in their respective markets.

On Internet markets, as is the case on most traditional markets, sellers do not usually know the demand functions of their customers without ambiguity. So as to establish a reasonable theory of the way Web-stores should fix their prices on the network, it is thus necessary to take the uncertainty they face into account by explicitly introducing the process by which they acquire information on their environment. In most uncertain environments, Web-stores can only learn what the most profitable prices are by price experimentations. By its very nature, the Internet is well adapted to such a learning process. Indeed, in this electronic environment the menu costs are negligible and sellers can therefore easily experiment different prices. However, as such a learning activity is costly, the Web-stores have to make a tradeoff between charging the most profitable price according to their current information (i.e., to exploit their information) and inquiring on the profitability of the other prices (i.e., to explore the profitability of the other prices). The determination of the Web-stores' pricing strategy under uncertainty is thus an inter-temporal decision problem in which they have to make an exploration vs. exploitation compromise. Some dynamic pricing algorithms have already been proposed in the E-commerce literature.

Much recent work in dynamic pricing has concentrated on pricing perishable products, such as are typically sold by the airline, hotel, car rental, and fashion industries. Inventory levels are a critical consideration in pricing such products. A large literature has addressed dynamic pricing in the presence of inventory considerations, where it is usually referred to as "revenue management" or "yield management." A recent comprehensive review of such practices is given in [START_REF] Elmaghraby | Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices and Future Directions[END_REF]; also see [START_REF] Mcgill | Revenue Management: Research Overview and Prospects[END_REF].

In a classic paper, Rothschild [START_REF] Rothschild | A Two-Armed Bandit Theory of Market Pricing[END_REF] investigated the nature of optimal sequential pricing strategies that experiment with two prices. He showed that under a general class of prior distributions on demand, there is a positive probability that a pricing policy that maximizes expected total discounted reward over an infinite horizon will select the revenue-maximizing price only finitely many times. Therefore, the policy may converge to the suboptimal price. This phenomenon was studied more generally by Easley and Kiefer [START_REF] Easley | Controlling a Stochastic Process with Unknown Parameters[END_REF][START_REF] Easley | Optimal Learning with Endogenous Data[END_REF], as well as McLennan [START_REF] Mclennan | Price Dispersion and Incomplete Learning in the Long Run[END_REF] and Aghion et al. [START_REF] Aghion | Optimal Learning by Experimentation[END_REF]. Several other prior studies have also described the qualitative behavior of optimal priceadjustment strategies using parametric classes of demand functions, such as those by Grossman, Kihlstrom, and Mirman [START_REF] Grossman | A Bayesian Approach to the Production of Information and Learning by Doing[END_REF], Mirman, Samuelson, and Urbano [START_REF] Mirman | Monopoly Experimentation[END_REF]. Leloup and Deveaux [START_REF] Leloup | Dynamic Pricing on the Internet: Theory and Simulation[END_REF] consider pricing strategies in a Bayesian framework.

In this paper, however, we shall consider markets where inventories are not as important to pricing and focus on the revenue implications of demand functions online. By taking a frequentist approach, our methods contrast with some line searchtype methods previously proposed for this problem in the literature, such as the "derivative following" methods proposed by Greenwald and Kephart [START_REF] Greenwald | Shopbots and Pricebots[END_REF], Dasgupta and Das [START_REF] Dasgupta | Dynamic Pricing with Limited Competitor Information in a Multiagent Economy[END_REF]. These methods resemble stochastic approximation algorithms for locating the revenue-maximizing price. While simple to implement, these methods do not incorporate prior information, nor do they make full use of the data that have been observed.

Model Formulation

Consider a seller (vendor) operating a shop where a single product is for sale. Here, a shop is understood to be any space, either real or virtual, where prices are displayed to arriving customers, who then decide whether to purchase the product. For example, a shop may be a web page or collection of web pages that display the price for a particular product, such as a software product or digital media document, and provides visitors with links to purchase the product. We assume that information about present and past prices is not available outside of the shop, as would be good practice if the seller wishes to strictly control the price of the product. In each of consecutive time periods of equal length (say, day), a random number of customers arrive to the shop, observe the posted price, and individually decide to either purchase some quantity of the product or exit the shop without purchasing. We shall further assume that the numbers of customers arriving in each period form an identically distributed sequence that is independent of past arrivals as well as both past and current prices. This assumption may be warranted in a finite time horizon if we assume that the customer base is composed, for example, of a large number of distributed Internet users, each of whom desires the good in a given period with a small probability, independent of other users and independent of past demand. We also assume that the number of consecutive time periods of equal length represents a deterministic time horizon (which may be infinite if no definite end period is anticipated). The seller may change the price at the start of any time period, always choosing from a predetermined set of prices. Given that the price is only displayed in the shop, we assume there is no cost to changing the price. A customer will buy the product if the current price is less than or equal to his or her privately held reservation price. We shall assume that the reservation prices of arriving customers also form an identically distributed sequence that is independent of past prices, the reservation prices of past customers, and past numbers of customer arrivals.

In some time period, which consists of n consecutive time periods of equal length, the seller sets a new price c for product and receives a random amount of revenue according to the number of customers arriving to the shop in that period whose reservation prices are at least as great as c. The seller can only observe a random amount of revenue, X, received in each of n consecutive time periods of equal length. Thus, he will have available a sample of observations X=(X 1 , …, X n ). It is assumed that the random variable X follows the two-parameter Weibull distribution with the probability density function

) 0 ( exp ) , | ( 1                             x x x x f         (1)
indexed by scale and shape parameters  and .

The problem is to find the sample size n of observations of the random variable X and test plan based on X=(X 1 , …, X n ) in order to determine whether or not the new product selling price c is accepted. The test plan has to satisfy the specified constraints for the seller risks of Type I and II, respectively.

Test Plan when the Shape Parameter is a Priori Known

In determining whether or not the new product selling price c is accepted, we have to use the test plan which satisfies the following conditions:

1 1 } } { | reject lly statistica Pr{     X E c (seller risk of Type I), (2) 2 2
} } { | accept lly statistica Pr{     X E c (seller risk of Type II), (3)
where

                  1 1 ) , | ( } { 0 dx x xf X E (4)
is the expected value of X, E{X}= 1 is statistically acceptable for c, E{X}= 2 is statistically rejectable for c,  1 and  2 are the specified seller risks of Types I and II, respectively.

To test for assuring  in the Weibull distribution, let n observations of the random variable X be made and the complete data sample X=(X 1 , X 2 , …, X n ) be obtained.

Then, if the shape parameter  is known a priori, the maximum likelihood estimator

of   is given by , / 1 n X n i i        (5)
and the pivotal quantity

) / ( 2      n V  (6) is 2
 distributed with 2n degrees of freedom. The n and h are determined by

       . reject , , accept , c h c h       (7)
To select n and h, we use the equations ( 2) and ( 3), which can be presented in the case when the parameter  is known as

       ; | Pr 1   h  =                      ; | 2 2 Pr 1 1 1 nh n  =   2 ; 2 1 Pr   n V  =  1 , (8)        ; | Pr 2   h  =                      ; | 2 2 Pr 2 2 2 nh n  =   2 1 ; 2 2 Pr     n V =  2 , (9) where , ) / 1 1 (       j j j = 1, 2, (10) 2
; 2 p n 
is the p-quantile of 2  distribution with 2n degrees of freedom. From ( 8) and

(9), 2 1 ; 2 2
; 2

1 2 2 1           n n . ( 11
)
Therefore, the required n is the smallest integer satisfying [START_REF] Greenwald | Shopbots and Pricebots[END_REF]. Using n based on (11), we have from ( 8) an ( 10) that the h for    is given by .

2 ) / 1 1 ( 2 ; 2 1 1 n h n                 (12)
Thus, the new product selling price c is accepted if

; h    
otherwise, it is rejected.

Test Plan when the Shape Parameter is Unknown

Preliminaries

We consider both parameters ,  to be unknown. We will give here appropriate expressions for the case of complete (uncensored) sampling. Let X = (X 1 , …, X n ) be a random sample from the two-parameter Weibull distribution (1), and let ,     be maximum likelihood estimates of ,  computed on the basis of X = (X 1 , …, X n ). In terms of the Weibull variates, we have that

, ) / ( 1      V , / 2     V      ) / ( 3  V (13) are pivotal quantities. Furthermore, let , ) / (     i i X Z  i=1, …, n. ( 14
)
It is readily verified that any n2 of the Z i 's, say Z i , …, Z n-2 form a set of n2 functionally independent ancillary statistics. The appropriate conditional approach, first suggested by Fisher [START_REF] Fisher | Two New Properties of Mathematical Likelihood[END_REF], is to consider the distributions of V 1 , V 2 , V 3 conditional on the observed value of Z = (Z i , …, Z n ). (For purposes of symmetry of notation we include all of Z i , …, Z n in expressions stated here; it can be shown that Z n , Z n-1 , can be determined as functions of

Z i , …, Z n-2 only.) The marginal distribution of , / 2     V ( 15
)
conditional on fixed z=(z i , …, z n ) is appropriate for making inference about  when  is unknown. It can be found (see Corollary 1.1 below with r = n) that the marginal probability density function of V 2 , conditional on fixed z, is given by

), 0 ( , ) ( ) | ( 2 1 1 2 2 2 2 2 2                 v z z v v g n n i v i n i v i n z z  (16) where 1 2 0 1 1 2 2 2 2 ) (                           dv z z v n n i v i n i v i n z  (17)
is the normalizing constant. The probability statement

     1 } | Pr{ 2 2 1 z q V q (18)
leads in the usual way to the (1) conditional confidence interval .

2 1      q q   (19) The marginal distribution of      ) / ( 3  V ( 20
)
is used to make inferences about , when  is unknown. It can be found (see Corollary 2.1 below with r=n) that the probability distribution function of V 3 , conditional on fixed z, can conveniently be expressed as

2 0 1 1 1 2 2 3 2 2 2 2 ) ( } | Pr{ dv z z h G z v h V n n i v i n i v i v n n i v i n                              z z  (h  0), (21)
where G n () represents the incomplete gamma integral,

. ) ( ) ( 0 1 dt n e t G t n n        (22)
For any specified value of h, [START_REF] Nechval | Improvement of Inventory Control under Parametric Uncertainty and Constraints[END_REF] can be integrated numerically to give conditional probability statements for V 3 . Then, for example, the probability statement

   } | Pr{ 3 z h V ( 23
)
leads to an  conditional confidence interval for ,

. / 1        h (24)
Main Theorems. The results can be presented more naturally, however, if we consider the distribution of the logarithm of a Weibull variate, which we denote by Y.

The random variate Y follows the first asymptotic distribution of extreme values, with density

), ( exp exp exp 1 ) , | (                             y b a y b a y b b a y f (25) where , ln   a . 1    b ( 26
)
Now, ( 25) is a distribution with location and scale parameters a and b, respectively, and it is well known that if , a  b  are maximum likelihood estimates for a, b, from a complete (uncensored) sample of size n, then

, / ) ( 1 b a a U    , / 2 b b U   b a a U   / ) ( 3   ( 27
)
are pivotal quantities, whose distributions depend only on n. That is, inferences concerning a and b here may be based on the pivotal quantities (27) as usual; however, the distributions of these pivotals should be considered conditional on the observed values of ancillary statistics. We generalize this situation and allow the original data to be possibly censored. Here the following theorems hold.

, ..., , 1 , / ) ( r i b a Y S i i      (29) where
are ancillary statistics, any r2 of which form a functionally independent set, a  and b  are the maximum likelihood estimators of a and b based on the first r ordered past observations (Y 1  ... Y r ) from a sample of size n from the first asymptotic distribution of extreme values (25), which can be found from solution of

, ) ( ln 1 / /                      r e r n e b a r i b y b y r i     (31) and , 1 ) ( ) ( 1 1 1
/ / / 1 /                             
     (32) is given by , ) exp( ) ( ) exp( exp ) ( ) | ( 1 2 2 1 2 2 2 2 2 r r i r i r i i r u s r n u s s u u u g                          s s  ), , 0 ( 2   u (33) where 1 0 2 1 2 2 1 2 2 2 ) exp( ) ( ) exp( exp ) (                                       du u s r n u s s u u r r i r i z i i r s  (34)
is the normalizing constant.

Proof. The joint density of

Y 1  ...  Y r is given by ) , | ..., , ( 1 b a y y f r                      r i i i b a y b a y b r n n 1 exp exp 1 )! ( ! . exp ) ( exp                  b a y r n r (35)
Using the invariant embedding technique [START_REF] Nechval | Effective State Estimation of Stochastic Systems[END_REF][START_REF] Nechval | Improved Decisions in Statistics[END_REF][START_REF] Nechval | Constrained Optimization in Newsboy Problems under Uncertainty via Statistical Inference Equivalence Principle[END_REF][START_REF] Nechval | Improved Estimation of State of Stochastic Systems via Invariant Embedding Technique[END_REF][START_REF] Nechval | Improved Adaptive Control of Stochastic Systems[END_REF][START_REF] Nechval | Invariant Embedding Technique and Its Applications for Improvement or Optimization of Statistical Decisions[END_REF][START_REF] Nechval | Optimization of Statistical Decisions via an Invariant Embedding Technique[END_REF][START_REF] Nechval | Improvement of Inventory Control under Parametric Uncertainty and Constraints[END_REF], we then find in a straightforward manner, that the probability element of the joint density of U

i r                                  s   u 1 (, ), u 2 (0, ), (36)
where

1 0 2 1 2 2 1 2 2 2 ) exp( ) ( ) exp( exp ) ( ) (                                        du u s r n u s s u u r r r i r i z i i r s   (37)
is the normalizing constant. Now u 1 can be integrated out of (36) in a straightforward way to give (33). This ends the proof.

Corollary 1.1. Let X 1  ...  X r be the first r ordered past observations from a sample of size n from the two-parameter Weibull distribution [START_REF] Elmaghraby | Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices and Future Directions[END_REF]. Then the marginal probability density function of the pivotal quantity

, / 2     V (38) conditional on fixed z=(z i , …, z n ), (39) where
, ..., , 1 , ) / ( r i X Z i i       (40)
are ancillary statistics, any r2 of which form a functionally independent set,   and   are the maximum likelihood estimators of  and  based on the first r ordered past observations (X 1  ... X r ) from a sample of size n from the two-parameter Weibull distribution [START_REF] Elmaghraby | Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices and Future Directions[END_REF], which can be found from solution of

, ) ( / 1 1                              r x r n x r i r i (41) and , ln 1 ) ( ln ) ( ln 1 1 1 1 1                                       r i i r i r i r r r i i i x r x r n x x x r n x x           (42) is given by ), 0 ( , ) ( ) ( ) | ( 2 1 1 2 2 2 2 2 2 2                   v z r n z z v v g r r i v r v i r i v i r z z  (43) where 1 2 0 1 1 2 2 2 2 2 ) ( ) (                             dv z r n z z v r r i v z v i r i v i r z  (44)
is the normalizing constant.

) | Pr( 3 s h U  ), 0 ( ) exp( ) ( ) exp( ) exp( ) ( ) exp( ) exp( exp ) ( 2 0 1 2 2 1 2 2 2 1 2 2 2                                                h du u s r n u s u s r n u s hu G s u u r r i r i r i r i r r i i r s  (46) where . ) ( ) ( 0 1 dt r e t G t r r        (47)
represents the incomplete gamma integral.

Prof. The proof is similar to that of Theorem 1 and so it is omitted here.

  n V V E h z                                (55)
where

. ) | ( 1 1 1 1 2 2 0 2 2 2 dv v g v V E z                                      (56)
Thus, the new product selling price c is accepted if

; h     
otherwise, it is rejected.

Conclusions and Directions for Future Research

The choice of an appropriate dynamic pricing model is a crucial decision problem because a good model not only can help sellers save testing time and reduce testing cost, but it also can positively affect the image of the product and thus attract more consumers to buy this product. Therefore often the Bayesian approach is used to solve the above problem. Unfortunately, in this case the subjectivity of investigator (a limitation of the Bayesian approach) is introduced through a priori distribution. In order to rule out the subjectivity of investigator and to consider comprehensively the relevant risks, in this paper a frequentist (non-Bayesian) decision analysis is employed. It is based on the invariant embedding technique [START_REF] Nechval | Effective State Estimation of Stochastic Systems[END_REF][START_REF] Nechval | Improved Decisions in Statistics[END_REF][START_REF] Nechval | Constrained Optimization in Newsboy Problems under Uncertainty via Statistical Inference Equivalence Principle[END_REF][START_REF] Nechval | Improved Estimation of State of Stochastic Systems via Invariant Embedding Technique[END_REF][START_REF] Nechval | Improved Adaptive Control of Stochastic Systems[END_REF][START_REF] Nechval | Invariant Embedding Technique and Its Applications for Improvement or Optimization of Statistical Decisions[END_REF][START_REF] Nechval | Optimization of Statistical Decisions via an Invariant Embedding Technique[END_REF][START_REF] Nechval | Improvement of Inventory Control under Parametric Uncertainty and Constraints[END_REF] which allows one to use available statistical information as completely as possible.

To extend the scope of our analysis, it would be interesting to explicitly introduce price competition between Web-stores. Indeed, the Internet environment may be a very competitive market and the sellers have to take the behaviors of their competitors into account in their own dynamic pricing strategy. So as to take this competition into account in our model, we can introduce a non-stationary behavior of the customers on the market. Such an extension would be a very big step towards a generalization of the pricing model proposed in this paper.

Theorem 1 .

 1 Let Y 1  ...  Y r be the first r ordered past observations from a sample of size n from the first asymptotic distribution of extreme values (25). Then the marginal probability density function of the pivotal quantity

Theorem 2 .

 2 Let Y 1  ...  Y r be the first r ordered past observations from a sample of size n from the first asymptotic distribution of extreme values (25). Then the probability distribution function of the pivotal quantity s, is given by

Acknowledgments. This research was supported in part by Grant No. 06.1936, Grant No. 07.2036, Grant No. 09.1014, and Grant No. 09.1544 from the Latvian Council of Science and the National Institute of Mathematics and Informatics of Latvia. The authors are also very grateful to two anonymous referees for their detailed comments that have helped in improving an earlier version of this paper.

Corollary 2.1. Let X 1  ...  X r be the first r ordered past observations from a sample of size n from the from the two-parameter Weibull distribution [START_REF] Elmaghraby | Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices and Future Directions[END_REF]. Then the probability distribution function of the pivotal quantity

conditional on fixed z, is given by

Test Plan

The n and h are determined by

To select n and h, we use the equations ( 2) and ( 3), which can be presented in the case when the parameter  is unknown as

From ( 51) and (52), .

Therefore, the required n is the smallest integer satisfying (54). Using n based on (54), we have from (51) and (10) that the h for   