Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
On an optimization problem with nested constraints
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Lower and upper bounds for the allocation problem and other nonlinear optimization problems
Mathematics of Operations Research
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The paper deals with the problem of maximizing a separable concave function over integer points of a polymatroid, known to be the integer case of the resource allocation problem. The Bottom Up algorithm for the case when the polymatroid is specified by an explicit list of constraints was presented by H. Groenevelt (European Journal of Operational Research 54 (1991) 227-236). We give a new proof of optimality of the Bottom Up algorithm. It is considerably shorter and simpler than the original proof. Our prood is based on the analysis of the greedy algorithm for this problem and properties of greedy solutions.