Presentation at CDVE 2011

1. A Model for Collaborative Scheduling Based onCompetencies shortpaper Tomasz Kajdanowicz tomasz.kajdanowicz@pwr.wroc.pl www.kajdanowicz.com Wrocław, Poland

2. Presentation outline Introduction to the problem A Model for Collaborative Scheduling Based onCompetencies Conclusions

3. Introductionto the problem

4. Introductionto the problem

5. Introductionto the problem Scheduling with constraints Interesting aspect in the operational research area with consideration of collaborative aspects of the problem ability to implement the modern computational intelligence methods Result: a schedule for tasks implementation that optimize assumed target function Requirements quantitative description of all competencies required to accomplish tasks in projects quantitative description of competencies of the staff

6. Introductionto the problem WBS OBS RAM/RAEW Competencies Schedule Optimize

7. A Model for Collaborative Scheduling Based onCompetencies T time periods czasu: t=1,…,T n projects: i=1,…,n K tasks: k=1,…K (K ≥ n) Each of task k: Earliest possible start time k{1,…,T} Latest possible due time k{1,…,T} memploees: j=1,..,m For each employee a set of competencies: r=1,…,R

8. A Model for Collaborative Scheduling Based onCompetencies competence expertisezjrt: each rth competence possessed by jth employee at a giventime period t quantitatively indicated by a real number zjrtchangesovertime time required by an employee to complete the task: dkr(in a situation when the employee has the highest possible competency expertise)

9. A Model for Collaborative Scheduling Based onCompetencies employee timecapacityto work: ajt [0,1] time limits (duetechnical and organisationalconstraints) to taskk and competencer:bkr Finaldecision variable: xkjrt [0,1] the time the employee j works in task k incompetence r in period t

10. A Model for Collaborative Scheduling Based onCompetencies process of competence expertise growth and decay 𝑧𝑗𝑟𝑡=𝑧𝑗𝑟1−𝛽𝑟𝑡−1+𝛼𝑟𝑘=1𝐾𝑠=1𝑡−1𝑥𝑘𝑗𝑟𝑠 if an employee j worked during x time in competence r his competence expertisegrows by 𝛼𝑟×xand 𝛼𝑟is a constant related to competence r knowledgedepreciation in competence r is reflected by forgetting factor 𝛽𝑟

11. A Model for Collaborative Scheduling Based onCompetencies Objective Function 𝑔(𝑥)=𝑟=1𝑅𝑗=1𝑚(𝑧𝑗𝑟𝑇+1−𝑧𝑗𝑟1) benefits in competence expertise obtainedby whole staff in the planning horizon T

12. A Model for Collaborative Scheduling Based onCompetencies constraints in one period t an employee j can not work above his capacity 𝑘=1𝐾𝑟=1𝑅𝑥𝑘𝑗𝑟𝑡≤𝑎𝑗𝑡 the required overall work time dkrfor each competence r in eachtask k must be allocated with proper amount of work time provided by employees 𝜌=1𝛿𝑘𝑗=1𝑚𝑥𝑘𝑗𝑟𝜌=𝑑𝑘𝑟

13. A Model for Collaborative Scheduling Based onCompetencies constraints effective work time in task k and in competence r must be limited to bkr 𝑗=1𝑚𝑥𝑘𝑗𝑟𝑡≤𝑏𝑘𝑟 all tasks are performed in planned time (between start and due time) 𝑡−𝜌𝑘𝑥𝑘𝑗𝑟𝑡≥0 oraz 𝛿𝑘−𝑡𝑥𝑘𝑗𝑟𝑡≥0

14. 6. Conclusions

15. Thank you for attention! Tomasz Kajdanowicz tomasz.kajdanowicz@pwr.wroc.pl www.kajdanowicz.com Wrocław, Poland