Optimization of a linear function over the set of stochastic efficient solutions

In this paper we study the problem of optimization over an integer efficient set of a Multiple Objective Integer Linear Stochastic Programming problem. Once the problem is converted into a deterministic one by adapting the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$2$$</EquationSource> </InlineEquation>-levels recourse approach, a new pivoting technique is applied to generate an optimal efficient solution without having to enumerate all of them. This method combines both techniques, the L-shaped method and the combined method developed in Chaabane and Pirlot (J Ind Manag Optim 6:811–823, <CitationRef CitationID="CR5">2010</CitationRef>). A detailed didactic example is given to illustrate different steps of our algorithm. Copyright Springer-Verlag Berlin Heidelberg 2014