Critical Path for Projects with Activity Durations Modelled as Z-Fuzzy Numbers
Marchwicka Ewa and Kuchta Dorota
The objective of the research is to test the method of critical path calculation with fuzzy activity durations in different possible scenarios and to suggest method’s improvements. The method uses Z-fuzzy numbers and incorporates historical records to assess credibility. An experiment with sequential activities was constructed. Normal distribution was used to reflect the behavior of human estimators. The scenarios were generated using computer simulations. The error in the critical path length was calculated. Two basic adjustments of the method have been identified (adjusted formula, unified conversion rule). The results show that there is a gain when using the adjusted method, which is observed for pessimists or optimists or for the volatile case, but only if it contains a predominance of optimistic (or pessimistic) estimations. The adjusted method can be used within the teams that experience a bias in their estimations, e.g. because of the customer that has strict time expectations.
Keywords: Critical path, activity durations, Z-fuzzy numbers, project management, credibility assessment, optimism bias