Open Access
An Algorithm for Solving Integer Interval Linear Programming Problems: A New Method for Mixed Integer Programming.
Abraham Charnes,Frieda Granot +1 more
- 01 Mar 1973
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TL;DR: In this paper, a branch and bound method is used to solve integer linear programming problems, where the problem is transformed into an equivalent integer interval linear programming problem, and then a branch-and-bound method is applied to solve the equivalent problem.
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Abstract: : The paper presents a new algorithm for solving integer linear programming problems. First the problem is transformed into an equivalent integer interval linear programming problem; and then a branch and bound method is applied to solve the equivalent problem. At each stage an interval linear programming problem of the most trivial type is to be solved. Gains in solution efficiency over other integer programming methods are anticipated. The method is equally valid for mixed integer problems. (Author)
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Citations
Enumerative Methods in Integer Programming
TL;DR: In this article, enumerative methods in integer programming are discussed and a proper utilization of the logical inequalities is the best way for replacing a host of feasibility tests, which are proposed for enumeration.
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Technical Note-On Intersection Cuts in Interval Integer Linear Programming
TL;DR: The idea is to apply the cutting-plane algorithm directly on the interval problem without transforming the problem into an equivalent standard integer problem, which would significantly increase the effective size of the problem.
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