  Optimization problems with random data have a wide range of applications. A
typical feature of many such problems is that some variables have to be
optimized before certain random coefficients have been realized and for other
variables it is sufficient to decide on them afterwards. This leads to a
multiple stage decision process. To optimize the variables in the first of two
subsequent stages the stochastic problem is transformed into a deterministic
program, called the (deterministic equivalent of the) recourse problem. In case
of stochastic linear programs with finitely distributed random data this
non-stochastic substitute is just a linear program. In the same way a multiple
objective linear program is obtained if the original problem has multiple
objective functions. In the first of the two stages, a decision maker usually
would chose a feasible point out of the set of all Pareto-optimal points. This
choice however has consequences to later stage decisions. We claim that the
decision process in the earlier of the two stages is not fully transparent if a
classical multi-objective decision process is applied: in addition to the
original objectives of the problem a decision maker may have a preference for
largest possible flexibility in later stage decisions. This additional
objective is taken into account if the recourse problem in case of multiple
objectives is taken to be a polyhedral convex set optimization problem instead
of a multi-objective linear program only. We also discuss several surrogate
problems to the recourse problem such as the wait-and-see problem and the
expected valued problem for the multi-objective case. The new approach based on
set optimization is illustrated by an example, the multi-objective newsvendor
problem.
