Production Operations

Download Extension of Data Envelopment Analysis with Preference by Tarja Joro, Pekka J. Korhonen PDF

By Tarja Joro, Pekka J. Korhonen

This publication offers an creation to incorporating choice info in facts Envelopment research (DEA) with a different emphasis in price potency research. as well as theoretical concerns, quite a few illustrative examples are incorporated. accordingly, the booklet can be utilized as a instructing textual content in addition. just a modest mathematical history is required to appreciate the most ideas. the one must haves are a) familiarity with linear algebra, specially matrix calculus; b) wisdom of the simplex procedure; and c) familiarity with using computing device software.

The e-book is geared up as follows. bankruptcy 1 presents motivation and introduces the elemental recommendations. bankruptcy 2 presents the elemental principles and versions of information Envelopment research. The effective frontier and construction danger set techniques play a massive function in all concerns. that is why those thoughts are thought of extra heavily in bankruptcy three. because the methods brought during this learn are encouraged through a number of aim Linear Programming, the fundamental recommendations of this box are reviewed in bankruptcy four. bankruptcy five additionally compares and contrasts info Envelopment research and a number of target Linear Programming, supplying a few cornerstones for ways offered later within the e-book. bankruptcy 6 discusses the conventional techniques take into consideration choice info in DEA. In bankruptcy 7, worth potency is brought, and bankruptcy eight discusses functional points. a few extensions are offered in bankruptcy nine, and in bankruptcy 10 worth potency is prolonged to hide the case whilst a construction danger set isn't convex. 3 applied purposes are reviewed in bankruptcy eleven.

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Additional info for Extension of Data Envelopment Analysis with Preference Information: Value Efficiency

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Their model was the so-called additive model. Other models considering simultaneous input minimization and output maximization exist; see, for example, Warwick DEA-User Manual (Thanassoulis 1992; Thanassoulis and Dyson 1992; Zhu 1996; Briec 1997; Joro et al. 1998). , Chambers et al. 1996, 1998; Fa¨re and Grosskopf 1997; Chung et al. 1997). In the following, we present the combined unified model. The modification of the basic models for the unified models is straightforward. 12b). Thus η describes how much an inefficient unit has to improve (increase outputs and decrease inputs) proportionally its inputs and outputs, simultaneously, for becoming efficient.

Because we have the term ε(s+ + sÀ), ε > 0, in the objective function, the solution is point B. 5, which indicates that point g is superefficient. 36 3 Production Possibility Set and Efficiency Fig. 4 Efficiency and Dimensionality In DEA, there is often necessary to reduce the number of variables in the analysis. That’s why it is important to know how efficiency may change in variable reduction. We illustrate with a simple example that all changes are possible for units, which are originally efficient and inefficient, but weakly efficient.

U0, ∃ j 2 {1, 2, . , s + m} such that u1j – u0j ¼ 0; otherwise u0 is strongly inefficient. Because u0 is inefficient, then ∃ i 2 {1, 2, . , s + m} such that u1i – u0i > 0. Choose w0j ¼ 1, if u1j – u0j ¼ 0, j 2 {1, 2, . , s + m} and w0j ¼ 0 otherwise ) η* ¼ 0. On the other hand, choose w1i ¼ 1, if u1i – u0i > 0, i 2 {1, 2, . , s + m} and w1j ¼ 0 otherwise ) η* > 0. b u0 is inefficient, but weakly efficient ( ∃ w0 ! 0, w0 6¼ 0 such that η* ¼ 0 ^ ∃ w1 ! 0, w1 6¼ 0 such that η* > 0. Assume ∃ w0 ! 0, w0 6¼ 0 such that η* ¼ 0 ) u0 is not strongly inefficient (see 2.

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