A minmax regret approach to the critical path method with task interval times

The execution of a given project, with a number of interrelated tasks due to precedence constraints, represents a challenge when one must to control the available resources and the compromised due dates. In this paper, we analyse this problem under uncertain individual task completing times, specifically, we will assume that a given range, for the admissible values of each individual completing time, is available. Taking into account that the precedence relations between tasks must be preserved, each realization of the admissible execution times for the set of tasks will define a new scenario determining the ending time for the project and the subset of critical tasks. The minmax regret criterion will be used in order to obtain a robust approximation to the critical set of tasks determining the overall execution time for the project.