By D R & Wallenius, K T Shier
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Additional info for Applied Mathematical Modeling: A Multidisciplinary Approach
This phase begins with some (at least tentative) formal statement of the identiﬁed problem. I assume that the modeling © 1999 by Chapman & Hall/CRC team either has members with expertise in the arena or at least has ready access to appropriate specialists. The signiﬁcant variables including inputs and outputs need to be identiﬁed and precisely deﬁned. In many situations, the initial choice of variables may turn out to require some augmentation or pruning or both. For example, if an agricultural state has one snake farm, its special inputs and outputs are unlikely to be useful in a statewide model of farm operation.
Labor (in hours) 4. capital investment (in dollars) We used three outputs O1, O2, and O3, each measured in bushels and consisting of one or more types of grain. The types of grain are distinguished by the amounts of water required for growth. , with very low rainfall), land with enough rainfall for sorghum and corn, and irrigated land. At this stage for each farm j we must split the ﬁrst input (land) x1j into three parts x1j (1), x1j (2), and x1j (3), according to the number of acres used in the respective land types: (1) dry land, (2) moderately moist land, and (3) irrigated land.
Hn (u, v)}. 19) as the eﬃciency of DMUj relative to the multipliers u, v. Clearly, 0 < ej (u, v) ≤ 1 = ek (u, v). 21) Next, deﬁne u, v which we call the DEA radial eﬃciency of DMUj . If ej = 1 we say that DMUj is DEA radial eﬃcient. As the qualiﬁer “radial” suggests, there may be other stronger types of eﬃciency and we will consider this below. The formulation of ej (u, v) and of ej is a typical mathematical construct. That these quantities always exist and that they are uniquely deﬁned require proofs which are omitted since they are readily available in Charnes, Cooper, and Thrall .