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Estimation of Activities Duration by Continuous Phase Type Distribution and Project Scheduling with Uncertain Activity Durations

Sheikhian Kazeroni, Mohammad | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55942 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Varmazyar, Mohsen
  7. Abstract:
  8. We examined the Phase-Type distribution to calculate project activity duration and solve the resource constraint project scheduling problem with non-deterministic activity duration through meta-heuristic techniques. The activity usually doesn't have a fixed duration. The problem is caused by numerous factors that exist when carrying out a project, such as a lack of resources, late delivery of resources, and mistakes made by people. The literature review revealed that the scheduling problem had been thoroughly researched. The more accurate and realistic the activity duration estimates, the better the project planning and cost control. For this purpose, in this research, the duration of the activities is considered non-deterministic, and the Phase-Type distribution is used to estimate the activity duration due to its features, such as proper fitting on skewed data. The research has two main phases. In the initial phase of this research, the quality and superiority of the Phase-Type distribution in estimating the duration of activities in scheduling problems have been investigated. In total, 930 activities with different skewness were investigated and their duration was estimated by Phase-Type, Normal, Lognormal, PERT, and Permachandra methods. The obtained results show that the Phase-Type distribution function not only has an estimate with a lower error in all cases but also has a significant difference with other methods when the data has high skew. In the second phase of the research, we solved RCPSP. In this phase, three problems with 100 activities with different skewness were examined, and the activity duration is an estimate obtained through the Phase-Type distribution. The problem was solved via meta-heuristic methods such as Genetic Algorithm, Particle Swarm Optimization, Tabu Search and Simulated Annealing. The obtained results show that particle swarm optimization has the best performance among other algorithms. And finally, in the third phase of this research, the scheduling problem was solved in the case where the duration of all activities is uncertain. The solution of the problem has been done in two modes with resource constraint and without resource constraint, which finally defines the whole problem as a Phase-Type distribution function and a comparison has been made with two normal and lognormal distribution functions
  9. Keywords:
  10. Scheduling ; Meta Heuristic Algorithm ; Expectation Maximazation Algorithm ; Phase-Type Distribution ; Genetic Algorithm ; Particles Swarm Optimization (PSO)

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