Constrained Cutting Rate-Tool Life Characteristic Curve, Part 1: Theory and General Case

1998 ◽  
Vol 120 (1) ◽  
pp. 156-159 ◽  
Author(s):  
C. L. Hough ◽  
Y. Chang
Keyword(s):  
Tool Life ◽  
Characteristic Curve ◽  
Sufficient Conditions ◽  
Global Optimum ◽  
Optimal Parameters ◽  
Constraint Equations ◽  
Machining Economics ◽  
Life Model ◽  
Cutting Rate ◽  
Necessary And Sufficient

The concept of a cutting rate-tool life (R-T) characteristic curve is extended to the general machining economics problem (MEP) with a quadratic-logarithmic tool life and constraint equations. The R-T characteristic curve presents the general loci of optima, which is useful in selecting optimal parameters for multiple machining conditions. The necessary and sufficient conditions for the global optimum of the unconstrained MEP are presented. These conditions are equivalently applied to the concept of the constrained R-T characteristic curve. In terms of quadratic geometric programming the objective function and constraints of the general MEP are called as quadratic posylognomials (QPL). The QPL problems are classified as convex and nonconvex and the convexity is determined by the second order terms of the tool life model. Nonlinear programming and an exhaustive method are demonstrated to determine the R-T characteristic curve for three cases of posynomial, convex QPL, and non-convex QPL problems.

Constrained Cutting Rate-Tool Life Characteristic Curve, Part 2: Convex Programs

1998 ◽  
Vol 120 (1) ◽  
pp. 160-165 ◽  
Author(s):  
C. L. Hough ◽  
Y. Chang
Keyword(s):  
Sensitivity Analysis ◽  
Tool Life ◽  
Simplex Method ◽  
End Milling ◽  
Characteristic Curve ◽  
Convex Programs ◽  
Machining Economics ◽  
Cutting Rate ◽  
Primal Dual ◽  
Simplex Tableau

Based on the concept in Part 1, Theory and General Case, algorithms to determine the constrained R-T characteristic curve are established for convex constrained machining economics problems. The first algorithm is for posynomial problems with the linear-logarithmic tool life equation. The R-T curve may be determined by applying the simplex method to the log-dual problems. Sensitivity analysis of the optimal simplex tableau enables obtaining the loci of optima easily. The second algorithm is for the quadratic posylognomial problems with quadratic-logarithmic tool life equation using the property of primal-dual feasibility. End milling examples constructed in Part 1 illustrate the algorithm comparing to the exhaustive method.

Cutting Rate-Tool Life Characteristic Functions for Material Removal Processes—Part 1: Theory

1976 ◽  
Vol 98 (2) ◽  
pp. 481-486 ◽  
Author(s):  
M. Y. Friedman ◽  
V. A. Tipnis
Keyword(s):  
Tool Life ◽  
Material Removal ◽  
Characteristic Curve ◽  
Geometric Interpretation ◽  
Characteristic Functions ◽  
Economic Optimization ◽  
Profit Rate ◽  
Comprehensive Development ◽  
Cutting Rate ◽  
Removal Processes

The existence of cutting rate-tool life (R-T) characteristic functions for material removal operations is introduced in this paper. This new concept enables a comprehensive development of a theory for economic optimization encompassing commonly used criteria of cost, production rate, and profit rate in machining when more than one cutting variable is involved. The theory provides conditions for the existence of economic optima, all of which must lie on the R-T characteristic curve for a given operation. The analysis of the theory is carried out for one and two independent cutting variables. For these two cases, it is proven that the locus of the tangent points of constant cutting rate and constant tool life curves describes the R-T characteristic curve, and also that the tool life is maximum along a given constant cutting rate curve at the point of tangency and vice versa. This geometric interpretation provides useful application of the concept as shown in Part 2.

The Properties of Bond Graph Junction Structure Matrices

1973 ◽  
Vol 95 (4) ◽  
pp. 362-367 ◽  
Author(s):  
J. R. Ort ◽  
H. R. Martens
Keyword(s):  
Sufficient Conditions ◽  
Bond Graph ◽  
Bond Graphs ◽  
Flow Equations ◽  
Correct Number ◽  
Constraint Equations ◽  
Necessary And Sufficient ◽  
Fundamental Theorems ◽  
Junction Structure ◽  
The Relationship

Some fundamental theorems concerning the relationship between the junction structure of bond graphs and the effort and flow equations, are presented. Necessary and sufficient conditions are stipulated to guarantee the correct number of constraint equations. The structure and rank of the coefficient matrices of the effort and flow equations are examined. An orthogonality relationship between effort and flow equations is established. The development yields the result that the number of effort and flow equations corresponding to a causal assignment are sufficient and their coefficient matrices are of maximum rank.

scholarly journals Metric Subregularity for Subsmooth Generalized Constraint Equations in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
He Qinghai ◽  
Yang Ji ◽  
Zhang Binbin
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Normal Cones ◽  
Metric Subregularity ◽  
Constraint Equations ◽  
Asplund Spaces ◽  
Necessary And Sufficient ◽  
Generalized Constraint

This paper is devoted to metric subregularity of a kind of generalized constraint equations. In particular, in terms of coderivatives and normal cones, we provide some necessary and sufficient conditions for subsmooth generalized constraint equations to be metrically subregular and strongly metrically subregular in general Banach spaces and Asplund spaces, respectively.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Budgeting in Socio-economic Development Strategies (Raising a Problem)

2008 ◽  
pp. 134-151
Author(s):  
A. Shastitko ◽  
M. Ovchinnikov
Keyword(s):  
Economic Policy ◽  
Economic Development ◽  
Social Change ◽  
Eastern Europe ◽  
Statistical Data ◽  
Sufficient Conditions ◽  
Transitional Period ◽  
Socio Economic Development ◽  
Necessary And Sufficient ◽  
Economic Development Strategies

The article proposes an approach to the analysis of social change and contributes to the clarification of concepts of economic policy. It deals in particular with the notion of "change of system". The author considers positive and normative aspects of the analysis of capitalist and socialist systems. The necessary and sufficient conditions for the system to be changed are introduced, their fulfillment is discussed drawing upon the historical and statistical data. The article describes both economic and political peculiarities of the transitional period in different countries, especially in Eastern Europe.

Inventory optimization considering the vehicle capacity and specifics of cash flows at rental storage sites

2020 ◽  
pp. 77-90
Author(s):  
V.D. Gerami ◽  
I.G. Shidlovskii
Keyword(s):  
Supply Chain ◽  
Inventory Management ◽  
Sufficient Conditions ◽  
Cash Flows ◽  
Management Systems ◽  
Cargo Capacity ◽  
Special Modification ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Vehicle Capacity

The article presents a special modification of the EOQ formula and its application to the accounting of the cargo capacity factor for the relevant procedures for optimizing deliveries when renting storage facilities. The specified development will allow managers to take into account the following process specifics in the format of a simulated supply chain when managing inventory. First of all, it will allow considering the most important factor of cargo capacity when optimizing stocks. Moreover, this formula will make it possible to find the optimal strategy for the supply of goods if, also, it is necessary to take into account the combined effect of several factors necessary for practice, which will undoubtedly affect decision-making procedures. Here we are talking about the need for additional consideration of the following essential attributes of the simulated cash flow of the supply chain: 1) time value of money; 2) deferral of payment of the cost of the order; 3) pre-agreed allowable delays in the receipt of revenue from goods sold. Developed analysis and optimization procedures have been implemented to models of this type that are interesting and important for a business. This — inventory management systems, the format of which is related to the special concept of efficient supply. We are talking about models where the presence of the specified delays for the outgoing cash flows allows you to pay for the order and the corresponding costs of the supply chain from the corresponding revenue on the re-order interval. Accordingly, the necessary and sufficient conditions are established based on which managers will be able to identify models of the specified type. The purpose of the article is to draw the attention of managers to real opportunities to improve the efficiency of inventory management systems by taking into account these factors for a simulated supply chain.

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