Sequential Cut Refinement Method in Multistage Stochastic Integer Programming: Application to a Unit Commitment Problem

2 Benders' method usually divides the collection of decision variables of a two-stage mathematical problem into two sets: a first set that comprises the collection of variables that represent first-stage decisions and a second set that includes the collection of variables that represent recourse actions or second-stage decisions. Usually, integer variables appear in the first set whereas the second set is formed by continuous variables with the purpose of having a convex recourse function. Convexity is then exploited in the construction of algorithms to obtain an optimal solution. In this paper we present an extension of Benders' method to deal with multistage problems with integer variables in any stage. This extension is based on the idea of sequentially refining the linear cuts that are used to represent an approximation of the recourse function in the master problem. Computationally cheaper cuts are obtained first and more expensive ones are calculated only if the desired tolerance is not reached. The paper includes an application of the proposed method to a stochastic weekly power generation unit commitment model.