A precedence-constraint-posting procedure to generate schedules maximizing quality with anytime property

Inspired by the popularity of anytime algorithms in solving complex real world problems, we define a class of scheduling problems. In addition to the normal resource constrained project scheduling assumptions, each activity in a project has a quality profile with an anytime property, which means that it can be stopped at any time and the quality of the output is proportional to its duration. Instead of finishing all activities as fast as possible, the goal of scheduling is to maximize the sum of qualities given a hard project due date. We formulate this quality maximization problem as a constraint-based optimization problem, analyze its complexity and present a precedence constraint posting procedure for generating a schedule with a good quality sum. Different constraint posting heuristics are evaluated based on the solution they can produce, CPU time and the number of posted constraints.