The Mathematics of the Degree of Operating Leverage in Respect of Non-Linear Profit Functions

2011 ◽  
Author(s):  
Sandip Sinha
Keyword(s):  
Non Linear ◽  
Profit Functions ◽  
Operating Leverage

Optimum linear indices for non-linear profit functions

1993 ◽  
Vol 56 (1) ◽  
pp. 43-50 ◽  
Author(s):  
H. Pasternak ◽  
J. I. Weller
Keyword(s):  
Selection Index ◽  
Selection Intensity ◽  
Production Traits ◽  
Milk Production Traits ◽  
Optimum Selection ◽  
Non Linear ◽  
Linear Index ◽  
Standard Linear ◽  
Profit Functions ◽  
Selection Intensities

AbstractAn iterative method is presented, based on the method of Moav and Hill (1966) to derive the optimum linear selection index for any number of traits with linear or non-linear profit functions. For non-linear profit functions the index weights will be functions of the trait means prior to selection and the selection intensity. Using the equations developed, the optimum selection index for three dairy cattle milk production traits was computed. Convergence was obtained after three to four iterations, and was robust to the starting values used for iteration. The ratio of expected genetic gains were only marginally different for selection intensities of 1 and 4 standard deviation units. Differences were greater for the index coefficients. All alternative indices tested gave lower gains in profit than the optimum index. For linear profit functions this index reduces to the standard linear index, and for two uncorrelated traits this index reduces to the index of Moav and Hill (1966).

Optimum linear selection indexes for multiple generation objectives with non-linear profit functions

1995 ◽  
Vol 61 (1) ◽  
pp. 165-175 ◽  
Author(s):  
J. C. M. Dekkers ◽  
P. V. Birke ◽  
J. P. Gibson
Keyword(s):  
Optimal Control ◽  
Net Present Value ◽  
Selection Index ◽  
Index Theory ◽  
Planning Horizon ◽  
Simultaneous Optimization ◽  
Linear Selection ◽  
Non Linear ◽  
Profit Functions ◽  
Selection Indexes

AbstractA method to obtain linear selection indexes that maximize objectives that involve average profit in one or more generations within a planning horizon based on non-linear profit functions, was derived through application of optimal control theory. The method involves simultaneous optimization of indexes for each generation in the planning horizon. Optimum linear indexes were found to be conform indexes derived from selection index theory, with economic values equal to a weighted sum of partial derivatives of the profit function at the trait means which result in each generation of the planning horizon. Numerical procedures to derive optimum indexes are presented. Methods and properties of alternative strategies for selection witli non-linear profit functions are illustrated for selection on egg weight and rate of lay in poultry. In the example, the additional benefit of selection indexes that maximize cumulative net present value of profit over a planning horizon of10 years was small relative to use of traditional selection procedures. Optimal indexes were also derived with a derivative-free non-linear programming optimizer, with identical results. The latter method also allows incorporation of additional constraints.Possible extensions of the optimal control methodology to address other problems related to optimization of selection over multiple generations are discussed.

Linear selection indices for non-linear profit functions

1988 ◽  
Vol 75 (4) ◽  
pp. 553-560 ◽  
Author(s):  
Y. Itoh ◽  
Y. Yamada
Keyword(s):  
Selection Indices ◽  
Linear Selection ◽  
Non Linear ◽  
Profit Functions

Selection indices for non-linear profit functions

1983 ◽  
Vol 64 (4) ◽  
pp. 339-344 ◽  
Author(s):  
M. E. Goddard
Keyword(s):  
Selection Indices ◽  
Non Linear ◽  
Profit Functions

B. The Non-Linear Calculations for Pulsating Stars

1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy
Keyword(s):  
Major Part ◽  
Afternoon Session ◽  
Discussion Session ◽  
Pulsating Stars ◽  
Fourth Symposium ◽  
Non Linear ◽  
Considerable Discussion ◽  
Informal Approach ◽  
Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

A decomposition method in non-linear programmm

Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér
Keyword(s):  
Decomposition Method ◽  
Non Linear

The licensing and accreditation debate: Linear thinking in a non-linear world?

1979 ◽  
Author(s):  
George W. Howe ◽  
James H. Dalton ◽  
Maurice J. Elias
Keyword(s):  
Non Linear
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