Valid Inequalities for Problems with Additive Variable Upper Bounds 1 2

نویسندگان

  • George L. Nemhauser
  • Martin W. P. Savelsbergh
چکیده

We study the facial structure of a polyhedron associated with the single node relaxation of network ow problems with additive variable upper bounds. This type of structure arises for example in network design/expansion problems, in production planning problems with setup times. We rst derive two classes of valid inequalities for this polyhedron and give the conditions under which they are facet-deening. Then we generalize our results through sequence independent lifting of valid inequalities for lower-dimensional projections. Our computational experience with large network expansion problems indicates that these inequalities are very eeective in improving the quality of the linear programming relaxations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Valid Inequalities for Problems with Additive Variable Upper Bounds

We study the facial structure of a polyhedron associated with the single node re laxation of network ow problems with additive variable upper bounds This type of structure arises for example in network design expansion problems in production planning problems with setup times We rst derive two classes of valid inequalities for this polyhedron and give the conditions under which they are facet d...

متن کامل

Valid inequalities for problems with additive variable upper

We study the facial structure of a polyhedron associated with the single node relaxation of network flow problems with additive variable upper bounds. This type of structure arises, for example, in production planning problems with setup times and in network certain expansion problems. We derive several classes of valid inequalities for this polyhedron and give conditions under which they are f...

متن کامل

Network design arc set with variable upper bounds

In this paper we study the network design arc set with variable upper bounds. This set appears as a common substructure of many network design problems and is a relaxation of several fundamental mixed-integer sets studied earlier independently. In particular, the splittable flow arc set, the unsplittable flow arc set, the single node fixed-charge flow set, and the binary knapsack set are facial...

متن کامل

The 0-1 Knapsack problem with a single continuous variable

Constraints arising in practice often contain many 0-1 variables and one or a small number of continuous variables. Existing knapsack separation routines cannot be used on such constraints. Here we study such constraint sets, and derive valid inequalities that can be used as cuts for such sets, as well for more general mixed 0-1 constraints. Specifically we investigate the polyhedral structure ...

متن کامل

Cutting planes from conditional bounds : a new approach to set covering

A conditional lower bound on the minimand of an integer program is a number which would be a valid lower bound if the constraint set were amended by certain inequalities, also called conditional. If such a conditional lower bound exceeds some known upper bound, then every solution better than the one corresponding to the upper bound violates at least one of the conditional inequalities. This yi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999