Integer Programs and Valid Inequalities for Planning Problems

2000 ◽  
pp. 239-251 ◽  
Author(s):  
Alexander Bockmayr ◽  
Yannis Dimopoulos
Keyword(s):  
Valid Inequalities ◽  
Integer Programs ◽  
Planning Problems

Valid Inequalities for Structured Integer Programs

2014 ◽  
pp. 281-319 ◽  
Author(s):  
Michele Conforti ◽  
Gérard Cornuéjols ◽  
Giacomo Zambelli
Keyword(s):  
Valid Inequalities ◽  
Integer Programs

scholarly journals Extended Model Formulation of the Proportional Lot-Sizing and Scheduling Problem with Lost Demand Costs

2011 ◽  
Vol 5 (1) ◽  
pp. 49-56
Author(s):  
Waldemar Kaczmarczyk
Keyword(s):  
Lot Sizing ◽  
Valid Inequalities ◽  
Mixed Integer ◽  
Extended Model ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Model Formulation ◽  
Mip Models ◽  
Planning Problems ◽  
Lot Sizing And Scheduling

We consider mixed-integer linear programming (MIP) models of production planning problems known as the small bucket lot-sizing and scheduling problems. We present an application of a class of valid inequalities to the case with lost demand (stock-out) costs. Presented results of numerical experiments made for the the Proportional Lot-sizing and Scheduling Problem (PLSP) confirm benefits of such extended model formulation.

scholarly journals Consistency Cuts for Dantzig-Wolfe Reformulations

2022 ◽  
Author(s):  
Jens Vinther Clausen ◽  
Richard Lusby ◽  
Stefan Ropke
Keyword(s):  
Valid Inequalities ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Linear Programming Relaxation ◽  
Linear Programs ◽  
Integer Programs ◽  
New Family ◽  
Integer Linear Programs ◽  
Integer Solutions ◽  
Online Library

A New Family of Valid-Inequalities for Dantzig-Wolfe Reformulation of Mixed Integer Linear Programs In “Consistency Cuts for Dantzig-Wolfe Reformulation,” Jens Vinther Clausen, Richard Lusby, and Stefan Ropke present a new family of valid inequalities to be applied to Dantzig-Wolfe reformulations with binary linking variables. They show that, for Dantzig-Wolfe reformulations of mixed integer linear programs that satisfy certain properties, it is enough to solve the linear programming relaxation of the Dantzig-Wolfe reformulation with all consistency cuts to obtain integer solutions. An example of this is the temporal knapsack problem; the effectiveness of the cuts is tested on a set of 200 instances of this problem, and the results are state-of-the-art solution times. For problems that do not satisfy these conditions, the cuts can still be used in a branch-and-cut-and-price framework. In order to show this, the cuts are applied to a set of generic mixed linear integer programs from the online library MIPLIB. These tests show the applicability of the cuts in general.

A characterization of minimal valid inequalities for mixed integer programs

1982 ◽  
Vol 1 (2) ◽  
pp. 63-66 ◽  
Author(s):  
Achim Bachem ◽  
Ellis L. Johnson ◽  
Rainer Schrader
Keyword(s):  
Valid Inequalities ◽  
Mixed Integer ◽  
Integer Programs ◽  
Mixed Integer Programs
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