A fuzzy time-dependent project scheduling problem

• A Fuzzy Time-dependent Project Scheduling Problem (FTPSP) is introduced and formulated.
• The formula used to estimate the completion time in this problem is developed.
• A collection of FTPSP models are proposed.
• The proposed FTPSP models are handled through fuzzy simulation and genetic optimization.

In this study, we introduce a Fuzzy Time-dependent Project Scheduling Problem (FTPSP), in which activity duration times are represented in the form of fuzzy sets. The duration times are considered to be time-dependent as well. Under these circumstances, the resulting FTPSP becomes far more complex when compared with the existing project scheduling problems. The complexity stems from the fact of computing the completion time of the entire project, a core issue when dealing with project scheduling problems. We first elaborate on the difficulties with the computing of the completion time. Subsequently, we develop a computational formula for estimating the overall completion time of FTPSP. Next, we formulate the FTPSP and propose three fuzzy programming models to address various requirements arising within this framework. The proposed models are handled through techniques that combine mechanisms of fuzzy simulation and genetic optimization. In this setting, fuzzy simulation is exploited to estimate the value of uncertain functions that do not exist in conventional certain project scheduling problems. Numerical experiments are included to illustrate the effectiveness of the algorithm.