Parametric integer linear programming: a synthesis of branch and bound with cutting planes
A branch and bound algorithm is designed to solve the general integer linear programing problem with parametric right-hand sides. The right-hand sides have the form b + THETA d, where b and d are conformable vectors, d consists of nonegative constants, and THETA varies from zero to one. The method consists of first determining all possible right-hand side ineger constants and appending this set of integer constants to the initial tableau to form an expanded problem with a finite number of family members. The implicit enumeration method gives a lower bound on the integer solutions. The branch and bound method is used with fathoming tests that allow one family member possibly to fathom other family members. A cutting plane option applies a finite number of cuts to each node before branching. In addition, the cutting plane method is invoked whenever some members are feasible at a node and others are infeasible. The branching and cutting process is repeated until the entire family of problems has been solved. 3 tables.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (USA); Missouri Univ., Rolla (USA). Dept. of Computer Science
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 6997550
- Report Number(s):
- SAND-80-2223C; CONF-801126-1
- Resource Relation:
- Conference: ORSA/TIMS joint national meeting, Colorado Springs, CO, USA, 9 Nov 1980
- Country of Publication:
- United States
- Language:
- English
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