This paper presents a multistage stochastic linear programming problem solved by a stochastic nested Benders decomposition algorithm. The algorithm allows the node aggregation and division of the scenario tree into connected subtrees forming arbitrary subproblems that will be solved as the algorithm proceeds. Different aggregation strategies have been tested and numerical results of the applica...

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen’s inequa...

We study a class of two-stage stochastic integer programs with general integer variables in both stages and finitely many realizations of the uncertain parameters. Based on Benders’ method, we propose a decomposition algorithm that utilizes Gomory cuts in both stages. The Gomory cuts for the second-stage scenario subproblems are parameterized by the first-stage decision variables, i.e., they ar...

Given a connected and undirected graph G, the degree preserving spanning tree problem (DPSTP) asks for a spanning tree of G with the maximum number of vertices with the same degree in the tree and in G. These are called full degree vertices. We introduce integer programming formulations, valid inequalities and four exact solution approaches based on different formulations. Two branch-and-bound ...

Abstract We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). call this algorithm nested Benders (NC-NBD). NC-NBD is based on solving dynamically improved linear outer approximations of the MINLP, obtained by piecewise relaxations functions. Those MILPs are solved global optimality using an enhancement decomposi...

in this paper, a new model is proposed for the integrated logistics network designing problem. in many research papers in this area, it is assumed that there is only one option for the capacity of each facility in the network. however, this is not a realistic assumption because generally there may be many possible options for the capacity of the facility that is being established. usually the c...

We study a class of two-stage stochastic integer programs with general integer vari4 ables in both stages and finitely many realizations of the uncertain parameters. Based on Benders’ 5 method, we propose a decomposition algorithm that utilizes Gomory cuts in both stages. The Go6 mory cuts for the second-stage scenario subproblems are parameterized by the first-stage decision 7 variables, i.e.,...

In this thesis, we review and synthesize a number of algorithmic approaches for optimizing the job-shop scheduling problem (JSSP). The complexity of the JSSP leads to large and difficult combinatorial optimization models. In Chapter 1, we review first an analytical method based on Mixed Integer Programming (MIP). Second, we review an assumption-based heuristic method. In Chapter 2, the JSSP is ...

Benders decomposition has been widely used for solving network design problems. In this paper, we use a branch-and-cut algorithm to improve the separation procedure of Gabrel et al. and Knippel et al. for capacitated network design. We detail experiments on bi-layer networks, comparing with Knippel’s previous results.

The problem addressed in this paper is related to an aerospace company seeking to change its outsourcing strategies in order to meet the expected demand increase and customer satisfaction requirements regarding delivery dates and amounts. A bilinear goal programming model is developed to achieve the company’s objectives. A modified Benders decomposition method is successfully applied to handle ...