Methods to Learn

In practice, most scheduling problems are an abstraction of the real problem being solved. For example, when you plan your day, you schedule the activities which are critical; that is you schedule the activities which are essential to the success of your day. So you may plan what time to leave the house to get to work, when to have meetings, how you share your vehicle with your spouse and so on. On the other hand, you probably do not consider the activities that are easy to arrange like brushing your teeth, going to the shops, making photocopies and other such tasks that can usually be accomplished whenever you have the time available. Often, if a schedule goes wrong, it is because a missed or underestimated activity had a significant impact on the schedule. We typically learn which activities are critical by experience and create an abstract scheduling problem including only these critical activities. Instead of scheduling the non-critical activities we estimate their effects in the abstract scheduling problem. Most industrial scheduling problems are also an abstraction of the real problem. It is common to only schedule activities on bottleneck resources and let the other activities fall into place once these are scheduled. Deciding which resources are bottlenecks is currently done by experienced human experts who determine what needs to be considered to create an accurate and high quality schedule. Unfortunately this process is both time consuming and error prone. We want to automate the process of creating a good quality abstract scheduling model. In this paper we describe an abstraction method for scheduling problems. Abstraction reduces the complexity of optimizing the entire problem by solving it in stages. We create an abstract model of a scheduling problem using a subset of the activities and approximate the remaining activities. We then search for a good solution to the abstract model, and extend this solution to a full solution to the entire problem. While the approach reduces complexity there is a risk that the abstract solution will not produce a good full solution. This paper is organized as follows. First we describe the abstraction process in Section 2. In Section 3 we introduce methods which select abstract models with the objective of determining a good abstract model whose solutions can