This paper addresses the problem of finding cutting planes for multi-stage stochastic integer programs.We give a general method for generating cutting planes for multi-stage stochastic integer programs basedon combining inequalities that are valid for the individual scenarios. We apply the method to generatecuts for a stochastic version of a dynamic knapsack problem and to stochasti...

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N , these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any c...

We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and Lagrangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. Numerical experience is presented for some two-stage test problems.

Stochastic integer programming is more complicated than stochastic linear programming, as will be explained for the case of the two-stage stochastic programming model. A survey of the results accomplished in this recent field of research is given.

This article considers two versions of the stochastic bin packing problem with chance constraints. In the first version, we formulate the problem as a two-stage stochastic integer program that considers item-tobin allocation decisions in the context of chance constraints on total item size within the bins. Next, we describe a distributionally robust formulation of the problem that assumes the i...

In order to implement the cellular manufacturing system in practice, some essential factors should be taken into account. In this paper, a new mathematical model for cellular manufacturing system considering different production factors including alternative process routings and machine reliability with stochastic arrival and service times in a dynamic environment is proposed. Also because of t...

In this paper, we focus on multiobjective integer programming problems with random variable coefficients in objective functions and/or constraints. For such multiobjective problems, after reformulation of them on the basis of an expectation optimization model and a variance minimization model for the chance constrained programming, incorporating fuzzy goals of the decision maker for the objecti...

Ships play the major role in bulk transportation and they need their special energy system. This paper proposes a stochastic programing method for optimal sizing of a hybrid ship power system with energy storage system (ESS), photovoltaic power (PV) and diesel generator. To account for uncertainties, in this study a two-stage stochastic mixed-integer non-linear programing is used to model the o...

This paper addresses the class of nonlinear mixed integer stochastic programming problems. In particular, we consider two-stage problems with nonlinearities both in the objective function and constraints, pure integer first stage and mixed integer second stage variables. We exploit the specific problem structure to develop a global optimization algorithm. The basic idea is to decompose the orig...