Martin W. P. Savelsbergh

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We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch and bound tree We present classes of models for which this approach decomposes the problem provides tighter LP(More)
In the rst part of the paper we present a framework for describing basic tech niques to improve the representation of a mixed integer programming problem We elaborate on identi cation of infeasibility and redundancy improvement of bounds and coe cients and xing of binary variables In the second part of the paper we discuss recent extensions to these basic(More)
The branch and bound procedure for solving mixed integer programming MIP problems using linear programming relaxations has been used with great success for decades Over the years a variety of researchers have studied ways of making the basic algorithm more e ective Breakthroughs in the elds of computer hardware computer software and mathematics have led to(More)
The generalized assignment problem examines the maximum pro t assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents A new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a(More)
We investigate the implementation of edge-exchange improvement methods for the vehicle routing problem with time windows with minimization of route duration as the objective. The presence of time windows as well as the chosen objective cause verification of the feasibility and profitability of a single edge-exchange to require an amount of computing time(More)
We investigate strong inequalities for mixed 0-1 integer programs derived from flow cover inequalities. Flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be(More)
We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchand-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP(More)