Stochastic Constraint Programming: A Scenario-Based Approach

Many decision problems contain uncertainty. Data about events in the past may not be known exactly due to errors in measuring or difficulties in sampling, whilst data about events in the future may simply not be known with certainty. For example, when scheduling power stations, we need to cope with uncertainty in future energy demands. As a second example, nurse rostering in an accident and emergency department requires us to anticipate variability in workload. As a final example, when constructing a balanced bond portfolio, we must deal with uncertainty in the future price of bonds. To deal with such situations, [27] proposed an extension of constraint programming, called stochastic constraint programming, in which we distinguish between decision variables, which we are free to set, and stochastic (or observed) variables, which follow some probability distribution. A semantics for stochastic constraint programs based on policies was proposed and backtracking and forward checking algorithms to solve such stochastic constraint programs were presented.