Why is Scheduling Difficult? A CSP Perspective

Interest in Constraint Satisfaction Problems (CSP) continues to grow, fueled by both their uniform problem representation, i.e., constraint graph, and conceptually clear problem solver, i.e., heuristically guided variable and value ordering. With the advent of interval constraints, e.g, temporal and spatial, and their associated consistency techniques, and the availability of Constraint Language Programming (CLP) it has become possible to explore complex problems such as planning and scheduling. This paper explores how a sequence of successively more complex scheduling problems can be modeled as a CSP, and the relevance of existing CSP problem solving heuristics. A number of problems arise with the CSP paradigm in modeling and solving scheduling problems: 1) Scheduling is an optimization problem in a very large combinatorial space. Therefore a good solution must be found as quickly as possible. 2) The existence of alternative process plans introduces disjunctive constraints in the constraint graph. 3) In most scheduling problems there exists a plethora of constraints. It is often the case that the problem is infeasible, requiring that one or more constraints be relaxed in order to find a solution. 4) Scheduling, and resource allocation problems in general, have constraint graphs in which many variables are tightly coupled (by capacity constraints) restricting the assignment of the same value to a single variable.