This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely related convexification ...

This paper presents an exact algorithm for the Lock Scheduling Problem (LSP) based on a Combinatorial Benders decomposition. LSP consists of three strongly interconnected sub problems: scheduling the lockages, assigning ships to chambers, and positioning the ships inside the chambers. These three sub problems are interpreted resp. as a scheduling, an assignment, and a packing problem. By combin...

We propose the concept of partial Benders decomposition, based on the idea of retaining a subset of scenario subproblems in the master formulation and develop a theory to support it that illustrates how it may be applied to any stochastic integer program with continuous recourse. Such programs are used to model many practical applications such as the one considered in this paper, network design...

An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. When applied to problems with a nite number of scenarios, the algorithm is shown to converge globally and to run in polynomial-time.

We propose a novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems that have to consider a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of transmission and generation in which policy constraints are designed to incenti...

Network design problems arise in many different application areas such as air freight, highway traffic and communications systems. This thesis concerns the development, analysis and testing of new techniques for solving network design problems. We study the application of Benders decomposition to solve mixed integer programming formulations of the network design problem. A new methodology for a...

Large scale dispatching problems are technically characterized as classical NP-hard problems which means that they cannot be solved optimally with existing methods in a polynomial time. Benders decomposition is recommended for solving large scale Mixed Integer Programming (MIP). In this paper we use the Bender Decomposition technique for reformulating the Ready Mixed Concrete Dispatching Proble...

Nowadays, researches pay more attention to environmental concerns consisted of various communities. This study proposes a multi-echelon, multi-period closed-loop supply chain (CLSC). A comprehensive model considers the selection of selection of technology and environmental effects. The supply chain is under a build-to-order (BTO) environment. So, there is not a final product inventory. Also, th...