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Presentation at CDVE 2011
Citation preview
A Model for Collaborative Scheduling Based on
Competencies short paper
Tomasz [email protected]
www.kajdanowicz.comWrocław, Poland
Presentation outline
1. Introduction to the problem2. A Model for Collaborative Scheduling
Based on Competencies3. Conclusions
Introduction to the problem
Program
Project
Task
Competency
Employee Employee Employee
Competency
Competency
Task
Project
Programs’ accomplishment• appropriate human
resources• appropriate competencies
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.
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
Introduction to the problem
OBS RAM/RAEW WBS
Optimize CompetenciesSchedule
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
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)
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
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
A Model for Collaborative Scheduling Based on Competencies
• Objective Function
• benefits in competence expertise obtained by whole staff in the planning horizon T
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
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)
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