Planning and Scheduling

In this chapter, we use the generic term planning to encompass both planning and scheduling problems, and the terms planner or planning system to refer to software for planning or scheduling. Planning is concerned with reasoning about the consequences of acting in order to choose from among a set of possible courses of action. In the simplest case, a planner might enumerate a set of possible courses of action, consider their consequences in turn, and choose one particular course of action that satis es a given set of requirements. Algorithmically, a planning problem has as input a set of possible courses of actions, a predictive model for the underlying dynamics, and a performance measure for evaluating courses of action. The output or solution to a planning problem is one or more courses of action that satisfy the speci ed requirements for performance. Most planning problems are combinatorial in the sense that the number of possible courses of actions or the time required to evaluate a given course of action is exponential in the description of the problem. Just because there is an exponential number of possible courses of action does not imply that a planner has to enumerate them all in order to nd a solution. However, many planning problems can be shown to be NP-hard, and, for these problems, all known exact algorithms take exponential time in the worst case. The computational complexity of planning problems often leads practitioners to consider approximations, computation time versus solution quality tradeo s, and heuristic methods.