Study on longer and shorter boundary duration vectors with arbitrary duration and cost values

We use the project network in AOA form (arrows denote the activities and nodes denote the status of the project) to represent a large-scale project. The activity duration and the activity cost are both random variables which take arbitrary integer values with the arbitrary probability distribution. Under the project time (the deadline to complete the project) constraint and the budget constraint, this paper studies how to schedule all activity durations of the project. Two algorithms are proposed to generate all upper and lower boundary vectors for the project, respectively. All feasible activity durations of the project are among such upper and lower boundary vectors.