Towards Stochastic Constraint Programming: A Study of Online Multi-choice Knapsack with Deadlines

Constraint Programming (CP) is a very general programming paradigm that proved its efficiency on solving complex industrial problems. Most real-life problems are stochastic in nature, which is usually taken into account through different compromises, such as applying a deterministic algorithm to the average values of the input, or performing multiple runs of simulation. Our goal in this paper is to analyze different techniques taken either from practical CP applications or from stochastic optimization approaches. We propose a benchmark issued from our industrial experience, which may be described as an On-Line Multi-Choice Knapsack with Deadlines. This benchmark is used to test a framework with four different dynamic strategies that utilize a different combination of the stochastic and combinatorial aspects of the problem. To evaluate the expected future state of the reservations at the time horizon, we either use simulation, average values, systematic study of the most probable scenarios, or yield management techniques.