Dantzig-Wolfe decomposition and branch-and-price solving in G12

Introduction to Dantzig-Wolfe Decomposition and Branch-and-Price Solving using G12

Branch-and-Price Solving in G12

Combinatorial optimisation problems are easy to state but hard to solve, and they arise in a huge variety of applications. Branch-and-price is one of many powerful methods for solving them. This paper describes how Dantzig-Wolfe decomposition, column generation and branch-and-price are integrated into the hybrid optimisation platform G12 [13]. The G12 project is developing a software environmen...

Dantzig-Wolfe Decomposition for Solving Multistage Stochastic Capacity-Planning Problems

We describe a multistage, stochastic, mixed-integer programming model for planning capacity expansion of production facilities. A scenario tree represents uncertainty in the model; a general mixed-integer program defines the operational submodel at each scenario-tree node, and capacity-expansion decisions link the stages. We apply “variable splitting” to two model variants, and solve those vari...

Dantzig-wolfe Decomposition with Gams

This document illustrates the Dantzig-Wolfe decomposition algorithm using GAMS.

Mechanism Design via Dantzig-Wolfe Decomposition

In random allocation rules, typically first an optimal fractional point is calculated via solving a linear program. Lying in the feasible region of the linear program, the fractional point satisfies the underlying constraints. In effect, the point represents a fractional assignment of objects or more generally packages of objects to agents. In order to implement an expected assignment, one must...