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A Model for Collaborative Scheduling Based on Competencies short paper Tomasz Kajdanowicz [email protected] www.kajdanowicz.com Wrocław, Poland

CDVE 2011 - A Model for Collaborative Scheduling Based onCompetencies

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Page 1: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

A Model for Collaborative Scheduling Based on

Competencies short paper

Tomasz [email protected]

www.kajdanowicz.comWrocław, Poland

Page 2: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

Presentation outline

1. Introduction to the problem2. A Model for Collaborative Scheduling

Based on Competencies3. Conclusions

Page 3: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

Introduction to the problem

Program

Project

Task

Competency

Employee Employee Employee

Competency

Competency

Task

Project

Programs’ accomplishment• appropriate human

resources• appropriate competencies

Page 4: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

Introduction to the problemQ

uest

ions • Can the portfolio of projects be

collaboratively accomplished with assumed competencies of the given personnel resources?

• What is the best subset of projects to be realized with given human resources and competencies constraints?

• How should the tasks be optimally accomplished in the collaborative projects?

• Which criteria of optimality are important?• minimal time to acomplish the

portfolio of projects• minimal work cost• maximal competency of human

resources

Pro

ble

m

pro

file

• Extended version of Knapsack problem (NP-hard)

• feasibility assessment of a project portfolio must assume the analysis of time constraints and temporality of competence in each individual task in each of projects

• staff competencies change over time• solution of the problem must be

posed to optimize the quantitative criterion such as return on investment, the duration of the project portfolio, the level of staff competence, etc.

Page 5: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

Introduction to 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

Page 6: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

Introduction to the problem

OBS RAM/RAEW WBS

Optimize CompetenciesSchedule

Page 7: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

A Model for Collaborative Scheduling Based on Competencies

• 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}

• m emploees: j=1,..,m• For each employee a set of competencies:

r=1,…,R

Page 8: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

A Model for Collaborative Scheduling Based on Competencies

• competence expertise zjrt : each rth competence possessed by jth employee at a given time period t quantitatively indicated by a real number

• zjrt changes over time• time required by an employee to

complete the task: dkr (in a situation when the

employee has the highest possible competency expertise)

Page 9: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

A Model for Collaborative Scheduling Based on Competencies

• employee time capacity to work: ajt [0,1]

• time limits (due technical and organisational constraints) to task k and competence r: bkr

• Final decision variable: xkjrt [0,1]– the time the employee j works in task k in

competence r in period t

Page 10: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

A Model for Collaborative Scheduling Based on Competencies

• process of competence expertise growth and decay

• if an employee j worked during x time in competence r his competence expertise grows by ×x and is a constant related to competence r

• knowledge depreciation in competence r is reflected by forgetting factor

Page 11: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

A Model for Collaborative Scheduling Based on Competencies

• Objective Function

• benefits in competence expertise obtained by whole staff in the planning horizon T

Page 12: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

A Model for Collaborative Scheduling Based on Competencies

• constraints– in one period t an employee j can not

work above his capacity

– the required overall work time dkr for each competence r in each task k must be allocated with proper amount of work time provided by employees

Page 13: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

A Model for Collaborative Scheduling Based on Competencies

• constraints– effective work time in task k and in competence r must be

limited to bkr

– all tasks are performed in planned time (between start and due time)

Page 14: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

6. Conclusions

• is static and the decision about whole schedule is taken at time t=0

• requires full list of all competencies in order to accomplish tasks

• assumes constant number of employees in time T

Cons

• reflects the nature of problem well making it an optimization problem

• rhe solution consists of work time matrices x for all emploee

• can be aproximated and reduced to linear programming problem

• Can be solved using metaheuristics (eg. genetic algorithms, ant-colony optimization, etc.)

Pros

Page 15: CDVE 2011  - A Model for Collaborative Scheduling Based onCompetencies

Thank you for attention!

Tomasz [email protected]

www.kajdanowicz.comWrocław, Poland