[For the entire collection see Zbl 0658.00020.]
A brief analysis of the behavior of linear integer programming is given in the introduction. It includes some ideas on complexity theory and a discussion of two-stage stochastic integer programming (SIP). The links between parametric linear programming and the stochastic version of it is illustrated by means of an example.
Section 2 presents the distribution problem in SIP. A machine investment problem is used as an example for introducing a probabilistic version of NP-hard optimization problems. A heuristic is proposed for solving them. Its behavior is evaluated and bounds for the makespan of m machines is derived. They are functions of the expected value of the processing times and the total workload. A lemma states limit properties.
Asymptotic results for other combinatorial problems are studied. Three classes of problems are defined (number problems, Euclidean problems and graph problems). Theoretical examples are developed for determining the behavior of the proposed approaches for tackling these problems. The uniform distribution case serves for deriving particular results.
The paper is closed with the discussion of multistage programs. A generalization of the two-stage machine investment problem is used for establishing how to derive a characterization of the asymptotic properties of the calculated optimal value. Dynamic programming routines are usable for solving these problems.