Stochastic Constraint Programming: A Scenario-Based Approach

TL;DR

This paper introduces scenario-based stochastic constraint programming, a method for modeling and solving decision problems under uncertainty by translating stochastic models into conventional constraint programs, leveraging existing solvers.

Contribution

It presents a formal semantics for stochastic constraint programs and a compilation technique into standard constraint programs, enabling practical decision-making under uncertainty.

Findings

Framework implemented in stochastic OPL language

Applied to portfolio, agricultural, and inventory problems

Demonstrates versatility and effectiveness of the approach

Abstract

To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic variables, which follow a discrete probability distribution. We provide a semantics for stochastic constraint programs based on scenario trees. Using this semantics, we can compile stochastic constraint programs down into conventional (non-stochastic) constraint programs. This allows us to exploit the full power of existing constraint solvers. We have implemented this framework for decision making under uncertainty in stochastic OPL, a language which is based on the OPL constraint modelling language [Hentenryck et al., 1999]. To illustrate the potential of this framework, we model a wide range of problems in areas as diverse as portfolio diversification, agricultural planning and production/inventory management.