This paper examines a new greedy heuristic for the integer knapsack problem. The proposed heuristic selects items in non-increasing order of their maximum possible contribution to the solution value given the available knapsack capacity at each step. The lower bound on the performance ratio for this "total-value" greedy heuristic is shown to dominate the corresponding lower bound for the density-ordered greedy heuristic.
Kohli, Rajeev, and Ramesh Krishnamurti. "A Total-Value Greedy Heuristic for the Integer Knapsack Problem." Operations Research Letters 12, no. 2 (August 1992): 65-71.
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