An extension of a greedy heuristic for the knapsack problem

The paper considers some of the properties of an extension of the ‘one-at-a-time’ greedy heuristic for the knapsack problem to ‘two-at-a-time’. Although the worst case result is the same for both heuristics, on a prior basis, on some occasions, for some instance, the ‘two-at-a-time’ heuristic can be better. The paper considers also optimality conditions and ‘good’ sequencing of the activities for the heuristic.