AbstractThe problem considered is that of the allocation and replenishment of several resources in integer quantities in such a way as to maximize the sum of the returns from activities with concave return functions. All the resources are of the same physical type and each resource has an effectiveness of 0 or 1 against each activity, depending on the geographical locations of the resources and the activities or on other constraints. Solutions with objective values arbitrarily close to the optimal value are generated by the application of resourcewise optimization to an associated problem in continuous variables, and the rounding of a continuous solution to an integer solution according to given rules. The application of other continuous methods is indicated. Some properties of optimal integer solutions are derived.