In telecommunication and transportation systems, the uncapacitated multiple allocation hub location problem (UMAHLP) arises when we must flow commodities or information between several origin–destination pairs. Instead of establishing a direct node to node connection from an origin to its destination, the flows are concentrated with others at facilities called hubs. These flows are transported ...

Direct current (DC) electricity distribution systems have been proposed as an alternative to traditional, alternating current (AC) distribution systems for commercial buildings. Partial replacement of AC distribution with DC distribution can improve service to DC loads and overall building energy efficiency. This article develops (i) a mixed-integer, nonlinear, nonconvex mathematical programmin...

Robust optimization extends stochastic programming models by incorporating measures of variability into the objective function. This paper explores robust optimization in the context of two-stage planning systems. First, we propose the use of a generalized Benders decomposition algorithm for solving robust models. Next, we argue that using an arbitrary measure for variability can lead to sub-op...

Multistage stochastic linear programming has many practical applications for problems whose current decisions have to be made under future uncertainty. There are a variety of methods for solving the deterministic equivalent forms of these dynamic problems, including the simplex and interior point methods and nested Benders decomposition { which decomposes the original problem into a set of smal...

This document shows how to model two-stage stochastic linear programming problems in a GAMS environment. We will demonstrate using a small example, how GAMS can be used to formulate and solve this model as a large LP or using specialized stochastic solvers such as OSL-SE and DECIS. Finally a tailored implementation of the Benders Decomposition algorithm written in GAMS is used to solve the model.

Handling uncertainty in natural inflow is an important part of a hydroelectric scheduling model. In a stochastic programming formulation, natural inflow may be modeled as a random vector with known distribution, but the size of the resulting mathematical program can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such probl...

Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. In this paper a generalized Benders decomposition algorithm ...

This paper describes an exact algorithm capable of solving large-scale instances of an important hub location problem called the Uncapacitated Hub Location Problem with Multiple Assignments. The algorithm applies Benders decomposition to a strong path-based formulation of the problem. The standard decomposition algorithm is enhanced through the inclusion of several features such as the use of a...

The traffic assignment problem is one of the most important problems for analyzing and optimizing the transportation network to find optimal flows. This study presented a new formulation based on a generalized Benders' decomposition approach to solve its important part, i.e. user equilibrium problems, in deterministic and stochastic cases. The new approach decomposed the problem into a master p...

This paper considers the primary and secondary path generation problem in traffic engineering. We first present a standard MILP model. Since its size and integrality gap are very large, we then apply a Benders decomposition to isolate the failure case capacity constraints, related linearisation variables and linearisation constraints. The disaggregated Benders cuts are generated, which is actua...