Subjective and interactive duration estimation

Abstract

Scheduling of construction projects with an uncertainty content requires that the scheduler's subjective knowledge of various factors that might influence the duration of the activities comprising the project is incorporated. Depending on the participating factors and their significance, a different duration outcome is often observed for each activity. To include this uncertainty in the schedule, a statistical distribution is frequently used. This paper presents a system based on the premise that part of the information available, when duration distribution is being estimated, exists in a subjective form. We present an automated system that requires the modeler to specify the activity's minimum and maximum times and a set of linguistic descriptors of the external factors that are suspect of influencing the duration. The lower and upper end point estimates are often available from familiarity with the technology used, physical and logical constraints, or a combination of these situations. The subjective information collected by the modeler is modeled as fuzzy parameters and is quantified using fuzzy set theory. The result of the fuzzy set analysis is a sample of activity durations from the underlying distribution, which is then used to characterize the first two moments of that distribution. Since earlier research has shown that the beta distribution provides an adequate representation for construction durations, the end points specified by the user and the two moments resulting from the fuzzy set analysis are used to fit a beta distribution. The system then allows the user to visually assess the quality of the fit and modify the shape of the beta density using the visual interactive beta estimation system. The paper also presents a practical construction scheduling application to demonstrate the use of the developed system. Key words: construction management, scheduling, fuzzy sets, subjective duration estimation, beta distribution, linguistic variables.