Multi-stage Stochastic Linear Programming: Scenarios Versus Events

To solve the multi-stage linear programming problem, one may use a deterministic or a stochastic approach. The drawbacks of the two techniques are well known: the deterministic approach is unrealistic under uncertainty and the stochastic approach suffers from scenario explosion. We introduce a new scheme, whose objective is to overcome both drawbacks. The focus of this new scheme is on events instead of scenarios and for this reason we call it Multi-stage Event Linear Programming (ELP). As we show in the theoretical results and in the preliminary computational experiments, the ELP approach represents a promising compromise between the stochastic and the deterministic approach, regarding capacity to deal with uncertainty and computational tractability.