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A. Bertossi's Algoritmi e Strutture di Dati PDF

By A. Bertossi

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5) where d{0, D) and d{0, P) mean "distance from zero to D" and "distance from zero to P," respectively. 7. Improvement The above ratio is referred to as a "radial measure" and can be interpreted as the ratio of two distance measures. 4 for D and from the intersection of 2/2 = | y i and 2/2 = 20 — 3yi for P. 5) then gives This interpretation as a ratio of distances aligns the results with our preceding discussion of such ratios. Because the ratio is formed relative to the Euclidean distance from the origin over the production possibility set, we will always obtain a measure between zero and unity.

2 show what is needed to bring each DMU onto the efficient frontier. 2. 5000 0,6250 B B B B B B B B to A's input will bring A onto the efficient frontier by reducing its input 50% while leaving its output at its present value. 6667 x 3 = 2 will position C on the frontier. And so on. 6n Efficient Frontier 40) CO y m H «x-^ 5- 3 - X *o '^ 00 2- •c •G V 1 0- C , ,— 2 1 1 1 1 3 4 5 6 1— 1 1 Employee Figure 2 . 1 . 3 shows 6 DMUs with 2 inputs and 1 output where the output value is unitized to 1 for each DMU.

Let an optimal solution of {LPo) be (i>' = I/*, ^ — /x*) and the optimal objective value ^*. The solution (v = V*^u — /i*) is also optimal for {FPQ), since the above transformation is reversible under the assumptions above. {FPo) and {LPo) therefore have the same optimal objective value 6*. , they are independent of the units of measurement used in the sense that multiplication of each input by a constant 6i > 0, i = l , . . , m , and each output by a constant Pr > 0, r = 1 , . . , s, does not change the obtained solution.

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Algoritmi e Strutture di Dati by A. Bertossi

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