Allocation of resources according to a fractional objective |
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Authors: | KM Mjelde |
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Institution: | SHAPE Technical Centre, The Hague, The Netherlands |
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Abstract: | The problem considered is that of the allocation of resources to activities according to a fractional measure given by the ratio of “return” to “cost”. The return is the sum of returns from the activities, each activity being described by a concave return function. There is a positive fixed cost and a variable cost that depend linearly on the allocations. Properties related to the uniqueness of optimal solutions and the number of non-zero allocations are derived. A method is given by which any set of feasible allocations can be used to derive an upper bound of the optimal value of the objective function: optimal and almost-optimal allocations can be recognized. Allocations can be generated by a fast incremental method that is described. The method utilizes data in sequential order and can be used to solve large problems. |
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