Linear and Integer Programming

Integer Programming (IP) is a modelling tool that has been widely applied in the last decades to obtain solutions for complex real problems, as those that arise in cutting and packing, location, routing and many other areas.

[1]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[2]  José M. Valério de Carvalho.  A Note on Branch-and-Price Algorithms for the One-Dimensional Cutting Stock Problems , 2002, Comput. Optim. Appl..

[3]  W. R. Pulleyblank,et al.  Polyhedral Combinatorics , 1989, ISMP.

[4]  J. M. Valério de Carvalho,et al.  On the extremality of maximal dual feasible functions , 2012, Oper. Res. Lett..

[5]  El-Ghazali Talbi,et al.  New lower bounds for bin packing problems with conflicts , 2010, Eur. J. Oper. Res..

[6]  George S. Lueker,et al.  Bin packing with items uniformly distributed over intervals [a,b] , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[7]  Sanjeeb Dash,et al.  Valid inequalities based on simple mixed-integer sets , 2006, Math. Program..

[8]  Cláudio Alves,et al.  Constructing general dual-feasible functions , 2015, Oper. Res. Lett..

[9]  Jacques Carlier,et al.  Computing redundant resources for the resource constrained project scheduling problem , 2007, Eur. J. Oper. Res..

[10]  Volker Kaibel,et al.  Integer Programming and Combinatorial Optimization, 11th International IPCO Conference, Berlin, Germany, June 8-10, 2005, Proceedings , 2005, IPCO.

[11]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[12]  François Vanderbeck,et al.  Exact Algorithm for Minimising the Number of Setups in the One-Dimensional Cutting Stock Problem , 2000, Oper. Res..

[13]  Ralph E. Gomory,et al.  An algorithm for integer solutions to linear programs , 1958 .

[14]  Sándor P. Fekete,et al.  New classes of fast lower bounds for bin packing problems , 2001, Math. Program..

[15]  Cláudio Alves,et al.  A survey of dual-feasible and superadditive functions , 2010, Ann. Oper. Res..

[16]  Cláudio Alves,et al.  On the Properties of General Dual-Feasible Functions , 2014, ICCSA.

[17]  Andrea Lodi,et al.  Strengthening Chvátal-Gomory cuts and Gomory fractional cuts , 2002, Oper. Res. Lett..

[18]  Robert E. Tarjan,et al.  Algorithmic Aspects of Vertex Elimination on Graphs , 1976, SIAM J. Comput..

[19]  Jacques Carlier,et al.  New reduction procedures and lower bounds for the two-dimensional bin packing problem with fixed orientation , 2007, Comput. Oper. Res..

[20]  Antoine Jouglet,et al.  A new lower bound for the non-oriented two-dimensional bin-packing problem , 2007, Oper. Res. Lett..

[21]  Hanif D. Sherali,et al.  Linear Programming and Network Flows , 1977 .

[22]  Alberto Caprara,et al.  Bidimensional Packing by Bilinear Programming , 2005, IPCO.

[23]  Cláudio Alves,et al.  Computing Valid Inequalities for General Integer Programs using an Extension of Maximal Dual Feasible Functions to Negative Arguments , 2012, ICORES.

[24]  Paul D. Seymour,et al.  Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.

[25]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[26]  Pamela H. Vance,et al.  Branch-and-Price Algorithms for the One-Dimensional Cutting Stock Problem , 1998, Comput. Optim. Appl..

[27]  Frits C. R. Spieksma,et al.  A branch-and-bound algorithm for the two-dimensional vector packing problem , 1994, Comput. Oper. Res..

[28]  José M. Valério de Carvalho,et al.  Exact solution of bin-packing problems using column generation and branch-and-bound , 1999, Ann. Oper. Res..

[29]  Cláudio Alves,et al.  Theoretical investigations on maximal dual feasible functions , 2010, Oper. Res. Lett..

[30]  Allan Borodin,et al.  On the Number of Additions to Compute Specific Polynomials , 1976, SIAM J. Comput..

[31]  Cláudio Alves,et al.  Cutting and packing : problems, models and exact algorithms , 2005 .

[32]  Cláudio Alves,et al.  Multidimensional dual-feasible functions and fast lower bounds for the vector packing problem , 2014, Eur. J. Oper. Res..

[33]  Claude-Alain Burdet,et al.  A Subadditive Approach to Solve Linear Integer Programs , 1977 .

[34]  David S. Johnson,et al.  Near-optimal bin packing algorithms , 1973 .

[35]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[36]  Vasek Chvátal,et al.  Edmonds polytopes and a hierarchy of combinatorial problems , 1973, Discret. Math..

[37]  Marco A. Boschetti,et al.  The two-dimensional finite bin packing problem. Part I: New lower bounds for the oriented case , 2003, 4OR.

[38]  François Clautiaux.  New collaborative approaches for bin-packing problems , 2010 .

[39]  Sándor P. Fekete,et al.  A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems , 2004, Math. Methods Oper. Res..