Logistics, defined

Let us consider a product which is sold entirely on the basis of personal recommendation. The rate of sale will depend on the number of people who have already bought the product. Thus initially sales will increase exponentially. Eventually the market will be saturated, and only replacement purchases will be made. If the frequency cui ve may be assumed to be symmetrical about a single maximum value, the cumulative distribution cui ve is known as the logistics cui ve and is defined by Eq. (9-91) ... 

Example 10 Logistics Curve We shall derive the logistics curve representing the ciimiilarive-freqiiency distrihiitions of the normal distrihiition curve defined by Eqs. (9-72) and (9-73). In this case, y varies between a cumulative probability of zero and unity as z varies from — to -l-oo. Since the upper bound is unity, c = 1. From Table 9-10 the area under the right-hand side of the curve between = 0 and z = z may be read. Since the frequency curve is symmetrical about the mean, this is also the area between = 0 and z=z. Hence, the area under the frequency curve, which represents the cumulative probability, is 0.50000 at = 0 and the 80 percentile, for which the area is 0.80000, corresponds to the value = 0.842. We substitute these values into Eqs. (9-92) through (9-94) to give... 

A simple two-dimensional analogue of the logistic equation, introduced by Henon in 1976 [henou76], is defined by... 

Sigmoid, the characteristic S-shaped curves defined by functions such as the Langmuir isotherm and logistic function (when plotted on a logarithmic abscissal scale). 

Specific predictive factors for outcome after surgical intervention have not been well defined in the literature. In one prospective, multicenter observational study of 95 patients, the state of consciousness was the only predictive factor retained in a logistic regression analysis." In this study, there was a 2.8-fold increased risk for poor outcome for each increase on a three-step scale (awake/drowsy, somnolent/ stuporous, and comatose), and good outcomes (modified Rankin Scale score <2) were achieved in 86%, 76%, and 47% of patients within each group, respectively. 

It is worth noting the distinction between the Hill equation and the logistic equation, which was first formulated in the 19th century as a means of describing the time-course of population increase. It is defined by the expression ... 

A quant is a meaningful logistic disposition unit, which can be cost tracked in the value chain. If, for example, a batch problem exists, a quant corresponds exactly to the batch size. If continuous production exists, a quant corresponds to a meaningful small rounding unit and in the case of a filling process to the respective bundling units. Quants can be individually defined. 

Because of the large number of aspects that must be covered by the model, it is important to have it well structured for further maintenance of the decision support system. A simplified representation is shown in Figure 5.8. The modeling was done such that the sections defining the general logistics were clearly separated from those closely related to the process. Also, the parts that refer to input/output to the user interfaces were strictly kept apart from the model itself to allow a smoother development. 

Mentzer JT, DeWitt W, Keebler JS, Soonhong M, Nix NW, Smith CD, Zacharia ZG (2001) Defining Supply Chain Management. Journal of Business Logistics 22 (2) 1-25... 

Fig. 15. Relationship between the alfentanil plasma concentrations and the probability of needing naloxone to restore adequate spontaneous ventilation. The diagram at the upper part shows the alfentanil plasma concentrations of the patients who required naloxone (upward deflection) or did not require naloxone (downward deflection). The plasma concentration-effect curve for this clinical endpoint (lower part) was defined from the quantal data shown in the upper diagram using logistic regression. Bars indicate SE of C5o%. (From Ausems ME, Hug CC, Stanski DR, Burm AGE. Plasma concentrations of alfentanil required to supplement nitrous oxide anaesthesia for general surgery. Anaesthesiology 1986 65 362-73, reproduced by permission.)...

Multiple regression as presented so far is for continuous outcome variables y. For binary, categorical and ordinal outcomes the corresponding technique is called logistic regression. Suppose that in our earlier example we defined success to be disease-free for five years then we might be interested identifying those variables/factors at baseline that were predictive of the probability of success. 

For a scientific discipline such a modular systems development - which is the mathematical basis of farther building of logistics and architecture of distributed networks design and engineering - it is a very important to define the components for a relevant mathematical model. It is well known that the most convenient way to manipulate and compose components is the usage of components with following characteristics of the component [1-3] ... 

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