An Explanation and Comparison of the Zero-One Integer Programming Algorithms of Bush, Balas, and Healy as Used on a Particular Resource Allocation Problem.
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Problem manipulation has been defined as the restatement of a mathematical programming problem in an alternative, but essentially equivalent form, more amenable to solution than the original. Richard L. Bush was interested in a particular type of problem manipulation which resulted in an equivalent knapsack problem form for a mathematical programming problem. Stanley Zionts modification of Balas method of implicit enumeration minimizes zero-one integer programming problems with less than or equal to constraints. The Healy algorithm is applicable where variables must be either or one, and the variables are divided into integer sets such that the variables in each set sum to unity. The author presents a detailed explanation and comparison of these algorithms as used on a particular resource allocation problem. Modified author abstract
- Operations Research