Optimal Project Completion Time, a Multi-Objective Model and Monte Carlo Simulation-Optimization Solution

In the literature of project scheduling it is very common to assume deterministic durations of project activities. Yet, activities with random durations are possible in many situations. In contrast, crashing activities of construction projects reduces their completion time, but this is achieved at additional charges compared to the normal execution charges. It is very common to penalize late completion of construction projects, yet, some sponsors are willing to reward early completion; for example, due to the opportunity cost involved, an oil company is willing to pay an incentive for fixing an oil pipeline proportional to earliness of project completion time. This paper presents a multi-objective project-scheduling model along with a Monte Carlo simulation optimization solution using a general-purpose simulation software. The model determines the optimal crashing levels of the projects' activities, whose durations are random, to minimize the expected project completion time and to maximize the expected profit of the project.