Genetic learning of virtual team member preferences

Computers in Human Behavior 29 (2013) 1787–1798

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Com puters in Human Behavior

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Genetic learning of virtual team member preferences

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Parag C. Pendharkar ⇑Penn State Harrisburg, 777 West Harrisburg Pike, Middletown, PA 17057, United States

a r t i c l e i n f o a b s t r a c t

Article history:Available online 30 March 2013

Keywords:Virtual teams Inter-agent communication Genetic algorithms

Virtual team members do not have complete understanding of other team members’ preferences, which makes team coordination somewhat difficult and time consuming. Traditional approaches for team coordination require a lot of inter-agent electronic communication and often result in wasted effort. Methods that reduce inter-agen t communication and conflicts are likely to increase productivity of virtual teams.In this research, we propose an evolutionary genetic algorithm (GA) based intelligent agent that learns ateam member preferences from past actions, and develops a team-coordination schedule by minimizing schedule conflicts between different members serving on a virtual team. Using a discrete event simulation methodology, we test the proposed intelligent agent on different virtual teams of sizes two, four, six and eight members. The results of our experiments indicate that the GA-based intelligent agent learns individual team member preferences and generates a team-coordination schedule at a lower inter-agent communication cost.

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1. Introduction

There are several reasons that lead to developmen t of virtual teams in modern organizati ons. First, modern organizations are increasingly adopting distributed design structures. Under the distributed organizati onal design; management, control, coordination, jobs, and operation s are distributed among different human agent teams that work complete ly virtual, complete ly face-to-face or some combination of virtual and face-to-face (Aart, Wielinga, &Schreiber, 2004; Bélanger & Watson-Ma nheim, 2006 ). Second, the macro economic developments have led organizations to increase inter-firm cooperation (Gluckler & Schrott, 2007 ). This inter-firmcooperation often requires teamwork from employees in different firms, and physically collocating team members, while effective, is often expensive and impractical (Poltrock & Engelbec k, 1999 ). Polt-rock and Engelbeck (1999) have argued that even when physical collocation can be accomplis hed, it is often a hollow accomplish- ment because most employees participa te in more than one team – which makes physical collocation either impossibl e or extremely unproductiv e. Finally, advances in information and communicati on technology have allowed organizations to facilitate virtual team member coordinatio n in a cost effective manner. Among the technology solutions that aid virtual team member coordination are Negotiation Assistant , ThinkLets, and Inspire negotiation support systems to name a few (Chari & Agrawal, 2007; Vivacqua, Marques,Ferreira, & De Souza, 2011 ).

Virtual teams pose unique challenges to managemen t. On the one hand, virtual teams enable organizational, individual and task flexibility; improve resource utilization and reduce cost; and ex- pand organizati onal knowled ge generation by bringing together diverse range of knowledge, skills and competencies (McLean,2007). On the other hand, virtual teams pose challenges due to differences in culture and personalities (Klitmoller & Lauring, in press), lack of trust between team members, language barriers,temporal constraints, individual goals, institutiona l constrain ts (le-gal and political), and choice of technolo gy (e-mail, instant mes- saging, cell phones, intranet among others) (Aart et al., 2004;Bélanger & Watson-Manhei m, 2006; Fan, 2011 ). One of the ways to deal with the challenges posed by virtual teams is to develop an effective virtual team coordination strategy. An effective virtual team coordination strategy will involve supervision, standardi zation of work, standardizati on of output, standardization of skills and mutual adjustment (Aart et al., 2004 ). All of these coordinatio nactivities will require inter-team member communi cations that satisfy individual team member personal preferences and optimize the use of organizational resources (Sen & Durfee, 1998 ).

Research on communicati on in virtual teams indicate that good communi cation between team members lead to successful operation of a team (Anderson, McEwan, Bal, & Carletta, 2007 ) and poor communi cation leads to poor performance (Thompson & Couvert,2003). There are, however , challenges to good communication between virtual team members. Among these challenges are: obtaining timely communication feedback (Jarvenpaa & Leidner, 1999 ),building trust between team members (Fan, 2011 ), building a common sense of purpose between team members (Blackbur n, Furst, &Rosen, 2003 ) and team members’ access to rich communication

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1788 P.C. Pendharkar / Computers in Human Behavior 29 (2013) 1787–1798

media (Kayworth & Leidner, 2000 ). A few researchers indicated that the use of technology makes virtual team more productive in that technolo gy leads to shorter and more problem-cente red interactions than face-to-face workplace interactions (O’Conaillet al., 1993 ). While technology is generally beneficial, there are some shortcomings as well. Among the shortcomings are that the use of technology requires clarifications on individual contributions to the meetings (Doherty-Sn eddon et al., 1997 ) and smooth transition between speakers in virtual teams is not always possible. The use of technology can also allow a virtual team to recruit additional members (Lipnack & Stamps, 1997 ), which leads to increased communicati on requiremen ts. These increased communication requiremen ts need special handling to ensure improved productivity and performance of virtual team (Anderson et al.,2007). Improved communi cation tends to bind virtual teams,which leads to low dissolution rates; and long-term teams are generally more productive than short-term teams (Ortiz de Guinea,Webster, & Staples, 2012 ).

Certain team coordina tion activities, such as scheduling a meeting can be cognitively demanding for team members. Humans are known for their limited informat ion processing capabilities, biases,and use of sub-optimal heuristics that lead to inefficient results (Chari & Agrawal, 2007 ). To improve group meeting scheduling,researchers have often used automated intelligent software agents (Bui, Venkatesh, & Kieronska, 1999; Sen & Durfee, 1998 ). Sen and Durfee (1998) presented a protocol of distributed meeting scheduling where a central host coordinates with the team members to ar- range a team meeting time. The protocol uses a simple bidding contract net procedure to schedule meetings. Since Sen and Durfee (1998) approach had very limited learning capabiliti es, the cost of inter-agent communicati on was very high (Bui et al., 1999 ). Buiet al. (1999) presented a Bayesian classifier based framework for learning human-agent team meeting preferences to minimize communicati on cost. Bui et al. (1999) procedure, while useful,has a limitation in that conditional probability tables (CPT) are often sparse. These sparse CPTs make it difficult to use Bayesian network approach for electronic meeting scheduling.

In this paper, we follow the lead of Bui et al. (1999) study and use a genetic algorithm based procedure to fill sparse CPTs in an unbiased way. After obtaining complete CPT, we generate the virtual team coordina tion schedule based on estimated team availability. The rest of the paper is organized as follows. In next section, we describe some related work. In Section 3, we describe the virtual team meeting scheduling (VTMS) problem and propose a genetic algorithm (GA) procedure for filling sparse CPTs for the VTMS problem. In Section 4, we solve a simple VTMS problem using the GA procedure. In Section 5, we describe a developmen tof a compreh ensive simulation model for our experiments . In Sec- tion 6, we describe our simulation experiment design and results of our experiments . Finally, in Section 7, we conclude the paper with a summary.

2. Related work

Virtual team meeting facilitation has been recognized as a beneficial factor for the outcome of virtual team meetings (Vreede,Davidson, & Briggs, 2003 ). Virtual team facilitation requires scheduling a meeting, putting together a meeting agenda and managing virtual team meeting dynamics (Vivacqua et al., 2011 ). In our paper, we consider only one dimension of facilitation which is scheduling a virtual team meeting – also known as distributed meeting scheduling (DMS) in literature.

Behavioral and information systems researchers have demon- strated that people have rhythmic temporal patterns that are repeatable and predictable (Ballard & Waller, 2008; Briggs, Vreede,

Nunamak er, & David, 2001; Swigger, Hoyt, Serce, Lopez, & Alpa- slan, 2012 ). Swigger et al. (2012) summarized how time affects an individual’s availability for a virtual team meeting. Among these dimensio ns of time are: spatial-tem poral time-zone feature, person’s preference towards morning ness/eveningn ess, habitual punctuali ty/lateness, and work-related cycles. Achieving a consis- tent rhythm to improve group dynamics has been shown to be necessary and challenging in various domains including emergency response teams (Landgren, 2006 ) and global software developmen tteams (Swigger et al., 2012 ). Gupta, Crk, and Bondade (2011) arguethat effective time managemen t provides a strategic advantage for virtual teams and electronic tools such as calendars, diaries or to- do lists (Zibetti, Chevalier , & Eyraud, 2012 ) can facilitate time managemen t.

Schedulin g a virtual team meeting is difficult because it requires mash up of several dimensions of time that increases cognitive load. Cognitive load refers to quantity of information that is memorized and the number of processes that are involved in per- forming a task at hand (Paas & van Merrienb oer, 1994 ). Sweller(1988) identified three types of cognitive load: intrinsic, extraneous, and germane. Intrinsic cognitive load is related to informat ion to be processed (e.g., mash up for different dimensions of time for all team members). Extraneous cognitive load is related to shield- ing from non-relev ant informat ion to complete the task at hand. Fi- nally, germane cognitive load is related to selecting, recording and structuring relevant information .

Zibetti et al. (2012) showed that information technology (IT)plays a vital role in managing cognitive load student homework scheduling. IT can simplify data recording and structuring features and lower extraneous cognitive load. Intelligent learning and data mash up can be easily incorporated using IT to lower intrinsic cognitive load. In addition to better cognitive load management, IT based virtual team meeting scheduling may increase team member motivatio n and coordina tion (Zibetti et al., 2012 ).

DMS is recognized as a very complex NP-hard problem (Barbati,Bruno, & Genovese, 2012; BenHassine & Ho, 2007 ) for which optimal solutions cannot be obtained. Sen and Durfee (1998) arguedthe reasons that complicate DMS. Among the reasons were: communicati on delays, concurrent scheduling of multiple meetings,partial control of informat ion and schedule, dynamic nature of scheduling due to changing schedule and cancellations , and information overload leading to bottlenecks. Sen and Durfee (1998)proposed a multistage negotiation protocol (MNP) for DMS. In the MNP each person acted as either a host or invitee. The host acted as an agent who would contact other agents (invitees) to determine a schedule for a meeting. The MNP consisted of three different strategies: announcement , bidding and commitmen t.The announcement strategies consisted of two options best andgood meeting times as per the subjective judgment of the host.In bidding strategy, both host and invitees would bid on times suggested by the host or suggest alternatives . Commitmen t strategie sinvolved tentative commitmen ts by host and invitees to tenta- tively block off their calendars so that other meetings cannot be schedule d during suggested times under considerati on for a meeting. Using simulations , Sen and Durfee (1998) measured the performance of their protocol based on two metrics of performanc e(success in scheduling a meeting) and efficiency (measured by low communi cation cost). Sen and Durfee (1998) made additional assumpti ons of non-cooperati ve agents and independen t schedules of agents that generally follow uniform distribution . The results of their experiments for scheduling two-person meetings indicated that the communicati on cost increases with increase in the length of meeting. Additionally, they found that announcement strategie s involving a host suggestin g good meeting times con- verge faster resulting in low communi cation cost. For commitmen tstrategy, Sen and Durfee (1998) found that an agent will exercise

P.C. Pendharkar / Computers in Human Behavior 29 (2013) 1787–1798 1789

non-commi tted strategy more often than committed strategy to increase his/her availability for other meetings should a meeting that an agent is committed to gets canceled.

BenHassine and Ho (2007) argue that complications of DMS not only rest with finding an optimal schedule but also with securing an appropriate location for a meeting. With frequent scheduling and cancellation of meetings, communication delays and location availability; dynamic bottlenecks are introduced in DMS making the problem difficult to resolve. BenHassine and Ho (2007) viewedthe DMS as a constrain t satisfaction problem (CSP) that included member’s preferenc es and system constraints. The results of their experiments indicated that incorporating agents’ preferences low- ers communicati on cost and ensures privacy of individua l agents.

Berger et al. (2009) study the DMS problem from a different perspective. In their study, they consider their agents as travelling agents that have to travel from one location to another just for meetings. At each location, an agent must reach the location in time, attend a meeting for entire duration and reach the next meeting location in time. They make simple assumptions where each agent belongs to a group and one agent attending a meeting from a group at one location was satisfacto ry. Using graph theory and computational geometry, Berger, Klein, Nussbau m, Sack, and Yi (2009) propose a heuristic algorithm to maximize attendance in meetings at different locations.

Niederer and Schatten (2009) mention that recent advances in mobile technolo gies add another dimension that complicates the DMS. They argue that people on the move have to make ‘‘free- busy’’ calculations anywhere at any time. They suggest a MeetMe scheduling concept where a central coordinator software agent learns users’ preferences, calculates the best fitting time slots and distributes calculatio n results.

A number of studies in literature have suggested incorporati on of agents’ preferences to minimize communicati on cost for the DMS (Shakshuki, Koo, & Benoit, 2007 ). Lee et al. (2010) suggestthe use of type-2 fuzzy personal ontology to facilitate DMS. Rigiand Khoshalhan (2010) suggest the use of analytical hierarchy process to elicit agents’ preferenc es to facilitate DMS. Sulaiman, Lai,Selamat, and Muda (2009) use a neural network to learn and pre- dict agents’ availabili ty preferences to lower communication cost for DMS. Chun, Wai, and Wong (2003) argued that an automated system incorporati ng human factors such as politics, personal preferences and power structure is extremely useful for DMS. Chunet al. (2003) suggests a DMS automated system that incorporates preference rules and show that such a system leads to lower conflicts.

The summary of literature indicates that DMS is an extremely difficult task. However, human behavior can be predictabl e to an extent and technolo gy can be used to reduce cognitive load and communicati on costs for DMS. In our research, we use an intelligent agent to learn the predictable patterns of human behavior while reducing cognitive load by improving data recording and data mashing via the use of IT.

3. A virtual team meeting scheduling problem and the genetic algorithm procedure

We describe the VTMS problem using previous studies (Buiet al., 1999; Sen & Durfee, 1998 ) as a guideline, improve its defini-tion and simplify the notation as necessary. We assume that each team member works five days a week and 8 h a day. These fivedays are given by set D = {1, 2, 3, 4, 5}. Additionally, we assume that meeting durations are 1 h long, which gives eight meeting slots each day. These meeting slots are represented as set S = {1, 2, 3, 4, 5, 6, 7, 8}. Thus, there are forty possible meeting times per week and each of these meeting schedules can be repre-

sented by a ordered pair (d, s) e D � S, where variables d and s rep-resent a particular day in set D and meeting time slot s in set Srespectively . We design an intelligent agent to learn a team member’s preference function from historical observations . Based on historical observations , a team member’s preferenc e function, F,can be represented as follows.

FðD� SÞ ! fA;U; ?g:

The preference function, for each team-member , maps the members availability over forty (d, s) ordered pairs. If the member is available to meet during a particular (d, s) then that particular ordered pair is assigned a value of A. If a person is unavailable to meet during a particular (d, s) then the ordered pair is assigned avalue of U, all the remaining ordered pairs that are neither assigned a value of A or U are assigned a value of ‘‘?’’ which represents un-known value for these ordered pairs.

We assume that a team member’s preference function contains two components. The first component is the seasonal component,which accounts for rhythmic temporal patterns of an individual team member (Swigger et al., 2012 ). The second component is the random component which is unpredictab le. The random component includes unpredictab le activities such as family emergen- cies, sickness and/or accidents. Additionally , we make an assumpti on of common sense . The common sense assumption allows us to eliminate possibilities of scheduling meetings on aday where common sense would dictate that most team members will not be available (Thanksgiving, Christmas break etc.). The common sense assumption also allows us to avoid including an additional dimensio n of week-of-the-y ear where, regardles s of seasonal component, certain weeks of a year will have higher team member unavailability than other weeks.

The objective of any intelligent agent designed for learning ateam member preference is to learn the team member’s seasonal component. This seasonal component can only be learnt over time when enough data are available. Unfortunate ly, dynamic and vola- tile nature of teams makes it difficult to obtain such data over ex- tended periods of time. Thus, in most cases, it is more pragmatic to obtain information over a few weeks and develop an intelligent agent. For a decision maker, given some historical information on his/her past meeting attendance, the probability of his/her availability for a particular (d, s) using Bayesian posterior probabili ty rule can be represented as follows:

Pðf jðd; sÞÞ ¼ Pððd;sÞjf Þ�Pðf ÞPðd;sÞ , where f = {A, U} represents actual histori-

cal values for the decision maker for the particular (d, s). A reader may note that we do not compute probability values for f = ? because these values represent unknown and are not useful for decision-mak ing purposes. The posterior probability rule can be simplified as follows (Bui et al., 1999 ):

Pðf jðd; sÞÞ ¼ Pððd;sÞjf Þ�Pðf Þa , where a is a normalization constant .

The value of P(f = A) represent historical meeting attendance percentage for a team member, and the value of P(f = U) =1 � P(f = A).

For initial historical data acquisition, we assume that a secretary (facilitator) announces a meeting and gathers available time and unavailable times from each of team members. Once all team members respond, the secretary selects a time slot that is available for all team members, if no such time slot is available then the secretary selects the next best slot where maximum number of team members are available . Over a period of time, data about which time slots were available and unavailable for a team member and his /her attendan ce percentage for meetings are recorded. At the very least the secretary has to send two communicati ons (meeting announcement and meeting time confirmation), read several emails, and manually select the best available time. The cognitive load of secretary’s work increases exponenti ally with increase in the number of team members and, as each team mem-

Fig. 2. Individual team member frequency and probability matrices.


ber’s schedule is known to the secretary, a team member’s privacy may be compromise d. Some cognitive load reduction is possible by using online tools such as Doodle (http://www.do odle.com ) where a secretary emails a meeting URL and members respond to their availability online and get an email confirmation on the meeting time from the secretary. However, technology alone plays a limited role and it is well known that tools such as Doodle do not allow calendar management or privacy for multiple meetings involving multiple agents. Better calendar managemen t tools such as Tungle (http://www.tungle.me ) are becoming available that provide inter- faces to mobile devices. However, these tools are of limited help due to dynamic nature of DMS making inclusion of member preferences very important.

To illustrate an example of how a team member preference function can be learnt, we assume that D = {1, 2, 3, 4, 5} and S = {1, 2, 3, 4} for ease of exposition and effective paper space utilization. Addition ally, we assume the actual preference function matrix for a team member that will be learnt via observati ons is shown in Fig. 1.

A team member preference matrix is unknown to the other team members and the secretary. This matrix is estimated through historical observations. Assume that historical observati ons of 78 prior (d, s) meeting confirmations/exemptions about a team member are available . For our problem, we randomly generate this data using a procedure that randomly selects a (d, s) pair, say (1, 1) and then select a random number between zero and one, say 0.6; since the random number is less than availability probability of 0.7 at (1, 1) location of availability matrix in Fig. 1, we add an entry of one in the frequency table assuming that the team member is available for meeting for the (d, s) pair of (1, 1). We repeat this process 78 times to obtain the available and unavailable frequency matrices shown on the left side of Fig. 2. The rows in the matrix represent five days and columns represent four time slots.

The frequency matrices are normalized by their row sums to compute the probabili ty that a team member is available or unavailable for a particular time slot on a given day. The blank cells in the matrices represent unknown s (‘‘?’’). For time slots containing non-blank values, future availability and unavailability of ateam member can be computed using Bayesian posterior probability rule described before. For example, assuming a team member observed prior probability of attendance is 80% then the posterior availability and unavailability probabilitie s for a team member with probability matrices shown in Fig. 2 and day time ordered pair of (1, 1) are given as follows.

Pðf ¼ Ajð1;1ÞÞ ¼ 0:364�0:8a and Pðf ¼ Ujð1;1ÞÞ ¼ 0:125�0:2

a . Using avalue of a = 0.3162, we have the probability that (1, 1) will be available for team member as 92% and unavailable as 8%. We com- bine the available and unavailabl e probabili ties into a single performance metric called availability index (AI). This AI is computed using following formula.

AIððd; sÞÞ ¼ Pðf ¼ Ajðd; sÞÞ1þ Pðf ¼ Ujðd; sÞÞ :

Fig. 1. The actual team member preference matrix.

The AI has a range between zero and 1. For our example, the AI for the team member is approximat ely 0.853.

Assumin g that the historical team member frequency matrices are available and there are no cells with blank values , a secretary can proactively compute availabili ty matrix scores for all team members, add them up to compute team availability index, rank the different team availability index matrix scores for (d, s) ordered pairs in descending order and pick a few top few slots as a team’s best availability meeting times. Team members can respond to their availability and suggest other time slots if they are unavailable to meet during the few top slots identified by the secretary.A secretary can update the frequency tables for the team members accordin gly.

Unfortunate ly, the key assumption of no cells with blank values is less likely to be satisfied in the real-world situation. Blank values are more likely to occur as we increase the number of time slots for a day. Given privacy concerns, it is difficult to ask team members to give informat ion on their availabili ty for all the (d, s) pairs. Re- cently, Pendharkar (2008) identified a GA procedure to handle the problem of missing probability values. The procedure uses amaximum entropy based non-linear programming formulation to estimate probabilities for blank cells.

Using Pendhark ar’s (2008) GA procedure, each of the (d, s) ordered pair can be assigned into one of two sets—B and F—whereall the cells representing (d, s) pairs containing blanks are assigned to set B, otherwise they are assigned to set F. The GA procedure seeks to identify values pds to be assigned to each cell in the probability table by solving the following non-linear programming (NLP) problem.

Maximize n ¼ �Xpds2B

ðpds lnðpdsÞÞ �Xpds2F

pds lnpds

ods

� �" #:

Subjec t to:

Xm

s¼1

pds ¼ 1;

pij P 0

The variables ods are the actual observed cell values in the non- blank cells of the probability tables and unknown variables pds areunbiased probability estimates for a cell (d, s). The variable m is the number of available time slots in a day.

In the next section, we use the GA procedure to identify the missing condition al values for the example in Fig. 1. For the details

http://www.doodle.com

http://www.tungle.me


of the GA procedure, we direct the reader to Pendharkar (2008)study. Summary of major GA operation s is provided in Appendix A.

Fig. 4. Evolution of best member and average population fitness for unavailable probability matrix NLP.

4. An application of the GA procedure and its solution for asimple vtms problem

In this section, we solve the missing probabili ties problem described in previous section by highlight ing all the steps. We apply Pendharkar ’s (2008) GA procedure to solve the NLP and compute missing probabili ties for the example illustrated in Fig. 2. Method- ologically, we do not make any changes to Pendharkar’s (2008) GAprocedure except that we apply it to the VTMS problem in a suit- able way. The contribution of our research is proposing the VTMS problem, which lends itself towards application of the GA procedure. The primary benefit of our VTMS problem and the GA procedure is that the extensive need for collecting historical data is no longer necessary and intelligent DMS agents can be designed despite partial availability of data. Since we have two different matrices that contain missing probabilities, we independen tly apply the GA procedure twice, once for each of the two matrices. For our GA experiments , after initial experimentati on, we used a mutation rate of 0.05, a crossover rate of 0.5 and the total learning generations of 600. Figs. 3 and 4 illustrate the results of our GA experiments for the two matrices. The figures indicate that the GA population fitness converged before 600 learning generations.

We use the best population member genes to identify the complete probability values (pds) for unavailabl e and available probability matrices. Then as illustrated in previous section, we computed the posterior probabili ty matrices and availability index matrix. All these matrices are illustrate d in Fig. 5. Using the availability index matrix, it is easy to identify that, based on historical data, the top-three best available meeting day-time ordered pairs for a team member would be (5, 1), (1, 1), and (2, 3). These pairs are shown in Fig. 4 as shaded matrix cells of availability index matrix.

Since, from Fig. 1, we know the actual team member preferences that were used to generate initial frequency matrices in Fig. 2, we can compare the performance of GA solution to the actual team member preferences . After normalizing rows in Fig. 1,we can compute the actual team member AI values as shown in Fig. 6.

We statistical ly compare the GA estimated AI matrix from Fig. 5and actual AI matrix from Fig. 6 and find no significant differenc ein means (t-value = 0.437, df = 19). The root-mea n-square (rms) error between AI matrices was 0.23. Thus, despite 35–40% missing values in the original frequency matrices, the GA procedure does a good job in estimating team member AI matrix. The top three

Fig. 3. Evolution of best member and average population fitness for available probability matrix NLP.

identified availability index pairs from Fig. 5 appear to be good meeting times for the team member as evidenced from the actual team member’s AI matrix in Fig. 6.When a virtual team contains n > 1 members, the (d, s) ordered pairs can be represented as (di, -si) ordered pairs for each team member i = {1, . . . , n}. Once AI matrices for each team member are computed, a separate team availabili ty index (TAI) matrix can be computed by adding individual team member availability index cell values as: at

ds ¼Pn

i¼1aids ,

where atds represents the cell values in the team availabili ty matrix

for a particular (d, s) ordered pair. Similarly, aids represents team

member i’s availabili ty matrix value for a particular (d, s) pair. To identify top three best meeting times for a virtual team meeting,all the entries in the team availabili ty matrix can be sorted in descending order and the top three ai

ds and their respective ordered pairs would represent best three choices.

5. A genetic learning based simulation model

We built a genetic learning based simulation model for our experime nts. We used the object-oriented C++ programmin g language for our model developmen t. The three major class imple- mentations for our simulation system were: the Member class,the Team class and the Genetic Algorithm class. In addition to these classes, we develope d several other utility classes necessary for performi ng simulatio n. These utility classes included a linked list data structure class, random number generation classes, and statistical test functionality classes.

The member class containe d primitive data attributes for storing the cardinali ties for sets D and S, which are the number of days and time slots for meeting time matrices; the number of missing values in available probability matrix (APM) and unavailable probability matrix (UPM); and prior probabilitie s for a team member availabili ty and unavailabi lity. In addition to the primitive variables, we used several reference variables and dynamic memory allocation data structures. Among the reference variables and dynamic memory allocations were: a pointer to genetic algorithm object, ten arrays to store actual and estimated values of team member APM, UPM, available posterior probability matrix (APPM),unavailabl e posterior probabili ty matrix (UPPM), and AI. Addition- ally, we used one dynamical memory allocation matrix to store the values for alpha matrices. The primary methods for the member class included a Randomize method that used an input seed to randomly generate a team member’s actual APM and UPM; a Normal-ize method, which normalized the rows of a matrix so that sum of all the entries in a row is equal to one; a Start method, which used the actual APM and UPM to probabili stically generate available and unavailabl e frequency matrices as shown in Fig. 2 and then used

Fig. 5. Solution matrices for a team member example.

Fig. 6. The team member probability and AI matrices.


the frequency matrices to generate estimated APM and UPMs as shown in Fig. 2; a GAEnt method, which called the GA object and

solved the maximum entropy non-linear constrained program to complete the missing values in the estimated APM and UPM; and

1 Accessed 30.01.13.


a APMAI method, which computed alpha values and actual and estimated values for a team member’s actual AI and estimated AI. The constructor of the Member class used three input values:team member ID, the number of days and the number of time slots in the team meeting schedule. Based on these input values, dynamic memory allocations for the eleven different arrays described above were made. The destructor released the memory for dynamic memory allocations and deleted the GA object. In addition to the methods described above, we included several getter methods that would return the values of primitive and reference variables for access in the simulation program or for providing an output to an external file.

The team class contained several primitive variables to store the values for the number of days, the number of periods per day, the number of team members, simulation seed number and variables for storing the values of root-mean- square errors between actual team matrices and GA estimated team matrices. In addition to the primitive variables, several dynamic memory and reference variable data structures were used to store values of team availability matrix, team unavailability matrix, a pointer to a linked list containing the list of team members in the team, team AI matrix and estimated team AI matrix. Among the four primary methods in the team class were the Normalize and the Aggregate methods ,which were used to normalize the rows of group availability and unavailability matrices; and aggregate team matrices to compute group AI, group availability, and unavailability matrices. A Simula-tion method was used to perform simulation. This method searched through each team member in the list of team members and called the previously described Start method for each team member. After calling the Start method for each team member,the Normalize method for each team member was called. Next,for each team member in the linked list, the GAEnt method was called to compute the missing values in each of team member’s estimated APMs and UPMs. Finally, ComputeErrors method was used to compute errors between the actual and estimated matrices. The constructor for the team class contained four input variables. These four variables were: the number of team members,the number of days (i.e., number of rows in the APM and the UPM), the number of meeting time periods (i.e., number of columns in the APM and the UPM), and the simulation seed number.The input variables were used to dynamically assign memory to the arrays for storing various matrix values. The destructor freed dynamically assigned memories for arrays and reference variables.We used several other methods for accessing the values of root- mean-squar e errors and printing these values in external files.

The GA class contained primitive variables to store GA parameters. These GA parameters were crossove r, mutation, the number of learning generations, the number of variables, the average fit-ness of population, the best fitness member of population and population size. The primary methods in the GA class were: Initializemethod which randomly initialized the population using uniform distribution , Fitness method which computed the fitness of the population (i.e., entropy objective function value of the non-linear program), Mutate method which mutated the genes of a population member based on the mutation rate, and Crossover method which used tournament selection to select two parents for reproduction to create offsprings. More information on the GA operation s is provided in the Appendix A. Several other methods and variables were used to integrate the GA within the overall simulatio n framewor k.These methods facilitated the flow of data between the GA and other classes described above.

A separate driver file was created to run the simulation. This driver file initialize d the simulation paramete rs of simulatio n seed,the number of days, the number of periods, the number of team members in a team and simulation size. After initializing these parameters, constructor of Team class was called the Simulation

method and then the Aggregate and Normaliz e methods. In the end, other methods were used from the team class to print out the errors in an external file which was used in data analysis.

6. Simulation experiments and results

We conduct several simulation experiments to investigate the impact of increasing team size on the accuracy of estimated TAI matrix with respect to actual TAI matrix. First, we identify the mathematical complexity of having all team members attend ameeting. Assuming that there are n > 1 members in a team, the number of possible team meetings is given by following relation:

Xn

k¼2

nk

� �:

Using the relation, there is one unique possibility of two team member meeting. This possibility increases to 4 different possible team meetings with 3 members (1 with all three members and 3two different team member meetings with one absentee), which in turn increases to 15 different possibilities with a team with only four members. Thus, complexity of conflict in schedules for team members increases exponentially. Assuming totally random team member schedules, the probability of having all members in a team attend a meeting at a particular time period decrease s exponentially and is given by following relation.

Pn

n

� �� ¼ 1Pn

k¼2

n

k

� � :

Using the aforementi oned mathematical expositio n, we expect that the estimate d TAI matrix may have higher error rates when compare d with the actual TAI matrix as team size increases. Thus,we test the proposed procedure for relatively smaller team sizes of 2, 4, 6, and 8. For our simulation experiments, we assume two scenerios: (1) five working days in a week and eight meeting slots per day (i.e., d = 5 and s = 8) and (2) five working days in a week and four meeting slots per day (i.e., d = 5 and s = 4). This creates 40 (d, s) or 20 (d, s) pairs in our probabili ty matrices. Further, we assume that the prior historical data on 200 (d, s) pairs are available for each team member. This data is similar to the data shown in Fig. 2 and is generated using simulated team member preference matrices similar to those shown in Fig. 1. Assuming that a team member spends 30–40% of his/her job time on meetings 1, data on 200 (d, s) pairs or 200 h is equal to monitoring a team members’meeting schedule for approximatel y 17–13 weeks or approximat ely three to four months.

Once this prior historical data are available, as shown in Fig. 2, it can be used to create initial team member frequency matrices.Once team member frequency matrices are available, we compute the estimated team member AI matrix using the methodol ogy described in Section 2. For each team size and (d, s) pair, we ran 30 different simulatio ns with 30 different initial simulation seed numbers . Since the performanc e of a GA is sensitive to its parameters, we used two pairs of parameters for our experime nts as well.These two pair of parameters were represented by crossover rate (v) and mutation rate (l). Specifically for the first set of experiments, we used high values with v = 0.5 and l = 0.15. For the second set of experiments , we used low values with v = 0.3 and l = 0.05. We breakdown the results of our experiments into two sub-section s based on two different (d, s) pairs.

Fig. 7. Graphical display of simulation experiment results (v = 0.5 and l = 0.15).



6.1. Experiment 1: Five days and eight meeting slots per day

Tables 1 and 2 illustrate descriptive statistics for the number of missing values in team member availability and unavailability frequency matrices for different team sizes. For a team member availability frequency matrix there were approximat ely 8 missing (d, s)pairs on average per simulation. The average minimum and maximum per simulation are also listed. Each simulation consisted of simulating 200 different meetings. For unavailability frequency matrices the average number of missing values for a team member varied between approximat ely 3 to approximat ely 7 when GA parameters were assigned high values. For low values of GA parameters, the average number of zeros for unavailability frequency matrices were slightly lower and varied between approxi- mately 2–3.

We illustrate the root-mea n-squared (RMS) error results between estimated TAI and actual TAI matrices for our simulation experiments in Figs. 7 and 8. As expected, the RMS error increases with the increase in team size. To statistically test the differenc e of means of RMS error for different team sizes, we performed student t-tests. The t-test for difference in means assumes equal sample sizes with each sample having equal variance (Hinkle, Wiersma,& Jurs, 1988 ). Even when variances are unequal, t-test is known to be very robust (Hinkle et al., 1988 ). In most of our paired com- parisons, sample sizes were always equal and variances were fairly similar so t-test appeared to be an appropriate choice. Since we expect that higher team size will lead to higher RMS error, we performed one tail t-tests. The results of our t-tests are reported in Table 3. All the differences in means were significant at 0.01 statistical level of significance. The RMS averages for GA parameters with low values (v = 0.3 and l = 0.05) were lower than the RMS averages for GA parameters with high values (v = 0.5 and l = 0.15).

6.2. Experiment 2: Five days and four meeting slots per day

For our second set of experime nts, we reduced the number of meeting slots available per day by 50% to four. Table 4 and 5 illus-

Table 1Descriptive statist ics on number of missing (d, s) pairs in a team member availability Mat

Team size

Mean (standard deviation) for 30 simulations runs

Average minimum psimulation

GA Parameters v = 0.5 and l = 0.15 2 7.01 (4.64) 04 7.50 (7.03) 0.25 6 8.38 (7.94) 0.33 8 7.89 (8.27) 0.25

GA Parameters v = 0.3 and l = 0.05 2 6.18 (8.24) 04 7.47 (10.78) 06 7.92 (10.59) 0.33 8 7.91 (10.91) 0.25

Table 2Descriptive statist ics on number of missing (d, s) pairs in a team member unavailability m

Team size


Average minimum psimulation

GA Parameters v = 0.5 and l = 0.15 2 6.30 (3.54) 04 5.28 (3.81) 06 4.25 (3.57) 08 3.35 (3.41) 0

GA Parameters v = 0.3 and l = 0.05 2 3.10 (3.60) 04 2.17 (3.04) 06 2.05 (2.74) 08 2.03 (2.85) 0

trates descriptive statistics for the number of missing values in team member availability and unavailability frequency matrices for different team sizes. Unlike our first set of experiments,descriptive statistics across different GA set of parameters were

rix.

er Average maximum per simulation

Median for 30 simulation runs

23.5 7.5 25.75 7.25 24.00 8.33 24.63 7.25

28 0.5 31.25 0.25 29.67 0.33 32.87 0.25

atrix.

er Average maximum per simulation


11 79.75 6.5 9.33 4.83 8.75 3.125

10 0.5 8.75 08 07.87 0

Table 3t-Test results of difference in means.

Team size = 2 mean (SD) Team size = 4 mean (SD) Team size = 6 mean (SD) Team size = 8 mean (SD) |t|-Value P(T 6 t)

GA Parameters v = 0.5 and l = 0.15 0.46 (0.09) 0.61 (0.13) 8.56 0.000 *

0.46 (0.09) 0.74 (0.17) 9.81 0.000 *

0.46 (0.09) 0.83 (0.2) 11.18 0.000 *

0.61 (0.13) 0.74 (0.17) 5.79 0.000 *

0.61 (0.13) 0.83 (0.2) 7.51 0.000 *

0.74 (0.17) 0.83 (0.2) 4.21 0.000 *

GA Parameters v = 0.3 and l = 0.05 0.379 (0.089) 0.490 (0.132) 5.86 0.000 *

0.379 (0.089) 0.574 (0.1887) 6.63 0.000 *

0.379 (0.089) 0.675 (0.246) 6.91 0.000 *

0.490 (0.132) 0.574 (0.1887) 3.78 0.000 *

0.490 (0.132) 0.675 (0.246) 4.9 0.000 *

0.574 (0.1887) 0.675 (0.246) 2.85 0.004 *

* Significant at 99% level of significance.

Table 4Descriptive statistics on number of missing (d, s) pairs in a team member availability Matrix.

Team size


Average minimum per simulation

Average maximum per simulation


GA Parameters v = 0.5 and l = 0.15 2 1.7 (3.33) 0 12 04 3.8 (4.97) 0 12.25 06 3.98 (4.91) 0 14.83 08 5.05 (5.74) 0 17.63 5.75

GA Parameters v = 0.3 and l = 0.05 2 1.68 (3.33) 0 12 04 3.8 (4.97) 0 12.25 06 3.97 (4.91) 0 14.83 08 5.07 (5.75) 0 17.62 6

Table 5Descriptive statistics on number of missing (d, s) pairs in a team member unavailability Matrix.

Team size


Average minimum per simulation

Average maximum per simulation





similar. This may be due to the fact that Experiment 2 represents lower level of complexi ty due to reduced number of meeting slots.

We illustrate the root-mean- squared (RMS) error results between estimated TAI and actual TAI matrices for our second set of simulation experiments in Figs. 9 and 10 . Like our first set of experiments , the RMS error increased with the increase in team size. To statistically test the differenc e of means of RMS error for different team sizes, we performed student t-tests. Since we expect that higher team size will lead to higher RMS error, we performed one tail t-tests. The results of our t-tests are reported in Table 6. All the differenc es in means were significant at 0.01 statistical level of significance. The RMS averages for GA paramete rs with low values (v = 0.3 and l = 0.05) and GA parameters with high values (v = 0.5 and l = 0.15) were similar due to lower problem complexity.

The results of our experiments indicate that the proposed intelligent agent procedure can be successfully applied for virtual team member coordina tion for team of sizes varying between 2 and 8

team members. It is possible to implement data acquisition and processin g procedure online, where a software agent can con- stantly updates the team availability index matrix values with the top 25% of high value (dt, st) ordered pair shaded in green color,next 25% in yellow and bottom 50% in red. Each team member can select which of green and yellow cell day-time slots are available to him/her and select a few red color cells as well. Once all the team members enter the data, a software agent can confirm the meeting schedule where all team members are available . If no such meeting time can be found then the software agent will identify the next best meeting time, where most of the team members are available.Once the meeting is scheduled and held, the team leader can enter the attendance information in the system to update the meeting attendan ce prior probability, availability and unavailability matrices for each of team members.

Using the software a total of two communicati ons take place for scheduling a meeting. The first communicati on asks the virtual




team members to go to the intranet and rank their choices, and second communi cation confirms the meeting time and date. It is possible to automate the second communicati on, where the meeting confirmation can be confirmed by the intelligent agent. When second communicati on is automate d, only one human initiated communicati on will take place.

7. Summary and conclusion s

We proposed an intelligent agent approach to learn virtual team member meeting preferences , facilitate virtual team member meeting coordina tion, and reduce inter-agent communi cation for scheduling a virtual team meeting. Our intelligent agent requires

Table 6t-Test results of difference in means.

Team size = 2 mean (SD) Team size = 4 mean (SD) Team size = 6 m

GA Parameters v = 0.5 and l = 0.15 0.364 (0.084) 0.499 (0.113)0.364 (0.084) 0.648 (0.141)0.364 (0.084)

0.499 (0.113) 0.648 (0.141)0.499 (0.113)

0.648 (0.141)

GA Parameters v = 0.3 and l = 0.05 0.360 (0.086) 0.506 (0.105)0.360 (0.086) 0.638 (0.149)0.360 (0.086)

0.506 (0.105) 0.638 (0.149)0.506 (0.105)

0.638 (0.149)

* Significant at 99% level of significance.

a maximum of two communications to schedule a meeting. The intelligent agent considers team members’ historical attendance and availability to suggest possible meeting times so that cognitive load is lowered. In addition to the reduced information and cognitive load, the intelligent agent approach addresses the issues of confidentiality and/or privacy by eliminating the need for a human to know an individua l team member schedule . It is possible to design an intelligent agent that shows the meeting times in a team member’s local time zones, which will eliminate the time conver- sion complexi ties that may arise if a human is used to coordinate virtual team meeting.

We found that the reliability of schedule s generated by an intelligent agent will generally reduce with increasing team size. The reduction in reliability is due to two factors: the complexity of problem domain and the computational complexity. While coordination between large teams will always be complex, computational complexity can be reduced by gathering team member’s prior historical availability data for a longer time. Gathering prior meeting data for a team member over a long period of time may reduce missing values in team availability and unavailability frequency matrices, which in turn may lower computational complexity. For larger teams, the appropriate ness of gathering team member’s prior availability data must be evaluated in the context of organizati onal economic constraints.

Prior research in virtual team design shows that sharing computing facilities reduces communication needs between team members located at one site (Anderson et al., 2007 ). Hybrid structures such as face-to-face meetings for members located at one site and virtual team meetings of sub-teams located at geographically separated sites may allow better control on communi cation requiremen ts for larger teams. Under such conditions, multi-agent team scheduling architecture may be appropriate to manage computational complexity.

Appendi x A. GA crossover and mutation operators

Since we are designing a GA procedure to solve a constrain ed optimizati on problem, we design special genetic operators to constrain the search in a feasible solution area as identified by the constraint. The initial population is randomly generated by selecting random numbers equal to the number of variables in a positive real interval (0, 1). In order to satisfy the constrain t, the variables are then normalized using their total sum. Each of the normalized random variables represents a gene in a population member.

While initial population satisfies the constraint of the non-linear programmin g problem, the GA operators of crossover and mutation may result in violation of the constraint. Thus, we design

ean (SD) Team size = 8 mean (SD) |t|-Value P(T 6 t)

6.13 0.000 *

11.96 0.000 *

0.711 (0.169) 11.38 0.000 *

5.86 0.000 *

0.711 (0.169) 7.04 0.000 *

0.711 (0.169) 2.57 0.008 *

6.85 0.000 *

11.01 0.000 *

0.729 (0.166) 12.45 0.000 *

5.50 0.000 *

0.729 (0.166) 7.03 0.000 *

0.729 (0.166) 3.35 0.001 *


special crossover and mutation operators so that the constraint of the non-linear programmin g problem is satisfied all the time. We describe these special crossove r and mutation approaches below.

Crossover operator

A special crossover operator was designed to satisfy the constraint. For example, if variable si,j represents a probability number in ith row and jth column of a probability table then for a hypo- thetical 12 row and 3 column probability table, a population member P1 with 36 genes can be represented as follows:

P1 ¼ hs1;1; s1;2; s1;3; s2;1; . . . ; s12;2; s12;3i:

Assume another parent P2 with 36 genes represented as follows.

P2 ¼ h!s1;1;!s1;2;

!s1;3;!s2;1; . . . ; !s12;2;

!s12;3i:

Assuming a random crossove r point after the third gene, we can create two children C1 and C2 as follows.

C1 ¼ s1;1; s1;2; s1;3; 1�X3

j¼1s1;j

� � !s2;1P12i¼2

P3j¼1

!si;j

; . . . ;

*

1�X3

j¼1

s1;j

!!s12;2P12

i¼2

P3j¼1

!si;j

; 1�X3

j¼1

s1;j

!!s12;3P12

i¼2

P3j¼1

!si;j

+;

and

C2 ¼ !s1;1;!s1;2;

!s1;3; 1�X3

j¼1

!s1;j

!s2;1X12

i¼2

X3

j¼1

si;j

; . . . ;

*

1�X3

j¼1

!s1;j

!s12;2P12

i¼2

P3j¼1si;j

; 1�X3

j¼1

!s1;j

!s12;3P12

i¼2

P3j¼1si;j

+:

The above crossover operators retain the genes of the parents up to the crossover point. The genes after the crossover point are product of one minus cumulati ve distribution of genes before the crossover point, and genes of the other parent normalized by the other parent’s cumulative distribut ion of genes after the crossover point.

We illustrate the crossove r concept using a simple example of two parents with 5 genes. Assume P1 ¼ h0:2;0:2;0:2;0:2;0:2i;P2 ¼ h0:1;0:15;0:2;0:25;0:3i and crossover point after the third gene as before. We get two children C1 and C2 as follows.

C1 ¼ 0:2;0:2;0:2; ð1� 0:6Þ 0:25 0:25þ 0:3

; ð1� 0:6Þ 0:30:25þ 0:3

� �¼ h0:2;0:2;0:2;0:182; 0:218i; and

C2 ¼ 0:1;0:15;0:2; ð1� 0:45Þ 0:20:2þ 0:2

; ð1� 0:45Þ 0:20:2þ 0:2

� �¼ h0:1;0:15;0:2;0:275; 0:275i:

It is easy to verify that the children produced by our crossover operator will always satisfy the constrain t of the non-linea r program. We avoid a formal mathematical proof as it is trivial.

8.2. Mutation operator

The non-linea r programm ing problem constraint eliminates the possibility of single gene mutation unless the gene is replaced by an exact replica of itself. The next best possibilit y is to consider two gene mutation. In our mutation approach , we consider a swap mechanism with two possibilities applied with equal probability.In the first possibility, we randomly pick two genes and swap their values. In the second possibility, we randomly pick two genes and

replace the value of one gene with sum of original values of both genes and the other gene with a value of zero. In our five gene simple example, we mutate C1 using first possibility and C2 using the second possibilit y. We assume that genes 2 and 5 will be swapped in each case. The result of C1 and C2 after mutation is as follows.

C1 ¼ h0:2;0:218;0:2;0:182;0:2i; and

C2 ¼ h0:1;0:425;0:2;0:275;0i:

Our mutation operator causes minimal disruption to majority of genes of the children and introduces a zero value into the genes. It is important to note that we shy away from introducing a value of 1 in the genes of population members to ensure that pi,j e [0, 1)constrain t is satisfied throughout the GA run.

The GA uses ‘‘survival of the fittest’’ approach to guide the population towards higher fitness. Since the objective of our LS non-linea r programming problem is to maximiz e the value of n,the fitness of the population member was represented as n. The selection operator used for our GA is the ranking selection operator (Goldberg & Deb, 1991 ). The time complexi ty of the ranking selection operator for a population size of # is O(# log #) (Goldberg &Deb, 1991 ).

References

Aart, C. J., Wielinga, B., & Schreiber, G. (2004). Organizational building blocks for design of distributed intelligent system. International Journal of Human Computer Studies, 61 , 567–599.

Anderson, A. H., McEwan, R., Bal, J., & Carletta, J. (2007). Virtual team meetings: An analysis of communication and context. Computers in Human Behavior, 23 ,2558–2580.

Ballard, D., & Waller, M. (2008). All in the timing considering time at multiple stages of group research. Small Group Research, 39 , 328–335.

Barbati, M., Bruno, G., & Genovese, A. (2012). Applications of agent-based models for optimizatioin problems: A literature review. Expert Systems with Applications,39, 6020–6028.

Bélanger, F., & Watson-Manheim, M. B. (2006). Virtual teams and multiple media:Structuring media use to attain strategic goals. Group Decision and Negotiation,15, 299–321.

Benhassine, A., & Ho, T. B. (2007). An agent-based approach to solve dynamic meeting scheduling problems with preferences. Engineering Applications of Artificial Intelligence, 20 , 857–873.

Berger, F., Klein, R., Nussbaum, D., Sack, J.-R., & Yi, J. (2009). A meeting scheduling problem respecting time and space. Geoinformatica, 13 , 453–481.

Blackburn, R. S., Furst, S. A., & Rosen, B. (2003). Building a winning virtual team. In C.Gibson & S. Cohen (Eds.), Virtual teams that work: Creating conditions for effective virtual teams (pp. 95–120). San Francisco, CA: Jossey Bass.

Briggs, R. O., Vreede, G. J., Nunamaker, J. F., David, T. H. (2001). Thinklets: Achieving predictable patterns of group interaction with group support systems. In Proceedings of 34th hawaii international conference on system sciences . January 3–6, 2001. 6 p.

Bui, H., Venkatesh, H. S., & Kieronska, D. (1999). Learning other agents’ preferences in multi-agent negotiation using the Bayesian classifier. International Journal of Cooperative Information Systems, 8, 275–293.

Chari, K., & Agrawal, M. (2007). Multi-issue automated negotiations using agents.INFORMS Journal on Computing, 19 , 588–595.

Chun, A., Wai, H., & Wong, R. Y. M. (2003). Optimizing agent-based meeting scheduling through preference estimation. Engineering Applications of ArtificialIntelligence, 16 , 727–743.

Doherty-Sneddon, G., Anderson, A. H., O’Malley, C., Langton, S., Garrod, S., & Bruce,V. (1997). Face-to-face interaction and video mediated communication: Acomparison of dialogue structure and co-operative task performance. GroupDynamics: Theory, Research and Practice, 7(4), 297–323.

Fan, Z-. P. (2011). Trust estimation in a virtual team: A decision support method.Expert Systems with Applications, 38 , 10240–10251.

Gluckler, J., & Schrott, G. (2007). Leadership and performance in virtual teams:Exploring brokerage in electronic communication. International Journal of e- Collaboration, 3(3), 31–52.

Goldberg, D. E., & Deb, K. (1991). A comparative analysis of selection schemes used in genetic algorithms. In G. Rawlins (Ed.), Foundations of Genetic Algorithms (pp. 47–56). San Mateo, CA: Morgan Kaufmann.

Gupta, A., Crk, I., & Bondade, R. (2011). Leveraging temporal and spatial separations with the 24-h knowledge factory paradigm. Information Systems Frontiers, 13 ,397–405.

Hinkle, D. E., Wiersma, W., & Jurs, S. G. (1988). Applied statistics for the behavioral sciences (2nd ed.). Boston: Houghton Mifflin Company.

Jarvenpaa, S. L., & Leidner, D. E. (1999). Is anybody out there? Antecedents of trust in global virtual teams. Journal of Management Science, 14 , 29–64.


Kayworth, T., & Leidner, D. (2000). The global virtual manager: A prescription for success. European Management Journal, 18 (2), 183–194.

Klitmoller, A., & Lauring, J. (in press). When global virtual teams share knowledge:Media richness, cultutal difference and language commonality. Journal of World Business, Available from http://www.sciencedirect.com/science/journal/aip/10909516.

Landgren, J. (2006). Making action visible in time-critical work. in Proceedings of the CHI (pp. 201–210).

Lee, C. -S., Wang, M. -H., Wu, M. -H., Hsu, C. -Y., Lin, Y. -C., & Yen, S. -J. (2010). A type- 2 fuzzy personal ontology for meeting scheduling system. In Proceedings of IEEE international conference on fuzzy systems (8 pp).

Lipnack, J., & Stamps, J. (1997). Virtual teams: Reaching across space, time and organizations with technology . New York: Wiley.

McLean, J. (2007). Managing global virtual teams. The British Journal of Administrative Management, Summer (pp. 16–16).

Niederer, M., & Schatten, A. (2009). Agent-based meeting scheduling support using mobile clients. In Proceedings of second international conference on the applications of digital information and web technologies (pp. 719–724).

O’Conaill, B., Whittaker, S., & Wilbur, S. (1993). Conversations over videoconferences: An evaluation of video mediated interaction. Human-Computer Interaction, 8, 382–428.

Ortiz de Guinea, A., Webster, J., & Staples, D. S. (2012). A meta-analysis of the consequences of virtualness on team functioning. Information and Management,49, 301–308.

Paas, F., & van Merrienboer, J. J. G. (1994). Instructional control of cognitive load in the training of complex cognitive tasks. Educational Psychology Review, 6, 51–71.

Pendharkar, P. C. (2008). Maximum entropy and least square error minimizing procedures for estimating missing conditional probabilities in Bayesian networks. Computational Statistics and Data Analysis, 52 (7), 3583–3602.

Poltrock, S. E., & Engelbeck, G. (1999). Requirements for a virtual collocation environment. Information and Software Technology, 41 , 331–339.

Rigi, M. A., & Khoshalhan, F. (2010). Adaptive modeling of user’s preferences in multi-agent meeting scheduling problem using analytical hierarchy process. In Proceedings of international conference on intelligent computer communication and processing (pp. 67–72).

Sen, S., & Durfee, E. H. (1998). A formal study of distributed meeting scheduling.Group Decision and Negotiation, 7, 265–289.

Shakshuki, E., Koo, H. -H., & Benoit, D. (2007). Negotiation strategies for agent-based meeting scheduling system. In Proceedings of international conference on information technology (pp. 637–642).

Sulaiman, M. N., Lai, T. E., Selamat, M. H., & Muda, Z. (2009). Improving agent-based meeting scheduling through preference learning. Journal of Theoretical and Applied Information Technology, 6(3), 155–164.

Sweller, J. (1988). Cognitive load during problem solving: Effects on learning.Cognitive Science, 12 , 257–285.

Swigger, K., Hoyt, M., Serce, F. C., Lopez, V., & Alpaslan, F. N. (2012). The temporal communication behaviors of global software development student teams.Computers in Human Behavior, 28 (2), 384–392. http://dx.doi.org/10.1016/j.chb.2011.10.008.

Thompson, L., & Couvert, M. (2003). Teamwork online: The effects of computer conferencing on perceived confusion, satisfaction and post discussion accuracy.Group Dynamics, 7, 135–151.

Vivacqua, A. S., Marques, L. C., Ferreira, M. S., & De Souza, J. M. (2011).Computational indicators to assist meeting facilitation. Group Decision and Negotiation, 20 , 667–684.

Vreede, G. J., Davidson, R. M., & Briggs, R. O. (2003). How a silver bullet may lose its shine. Communications of the ACM, 46 , 96–101.

Zibetti, E., Chevalier, A., & Eyraud, R. (2012). What type of information displayed on digital scheduling software facilitates reflective planning tasks for students? Contributions to the design of a school task management tool. Computers in Human Behavior, 28 (2), 591–607. http://dx.doi.org/10.1016/j.chb.2011.11.005.

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http://www.sciencedirect.com/science/journal/aip/10909516




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Genetic learning of virtual team member preferences