Equation Descriptions
Description of Equation 1
Uppercase P equals lowercase a plus the product of lowercase b and uppercase Q. Uppercase P, therefore, equals the sum of two expressions: uppercase P subscript zero minus the quotient of uppercase P subscript zero over uppercase N, and uppercase Q times the quotient of uppercase P subscript zero over the product of uppercase N and uppercase Q subscript zero.
Description of Equation 2
Uppercase C equals lowercase a prime minus the product of lowercase b prime and uppercase V M.
Description of Equation 3
Lowercase a prime equals the quotient of two expressions: uppercase C subscript zero plus the quotient of uppercase C subscript zero over uppercase N, and 1 plus uppercase D V M. Lowercase b prime equals the quotient of two expressions: uppercase C subscript zero divided by uppercase N times uppercase V M subscript zero, and the square of 1 plus uppercase D V M.
Description of Equation 4
Uppercase B E N subscript Net equals uppercase S PLUS subscript 1 minus uppercase S PLUS subscript zero.
Description of Equation 5
Uppercase S PLUS subscript zero equals the product of uppercase V M subscript zero and the expression uppercase C subscript zero plus the quotient of uppercase C subscript zero over uppercase N, minus zero point five times the square of uppercase V M subscript zero times the quotient of uppercase C subscript zero over the product of uppercase N and uppercase V M subscript zero, minus the product of uppercase C subscript zero and uppercase V M subscript zero.
Description of Equation 6
Uppercase S PLUS subscript 1 equals the product of the expression uppercase C subscript zero plus the quotient of uppercase C subscript zero over uppercase N and the expression uppercase V M subscript 1 divided by 1 plus uppercase D V M, minus the expression zero point five times the square of uppercase V M subscript 1 times the product of the quotient of uppercase C subscript zero over uppercase N times uppercase V M subscript zero and the square of 1 plus uppercase D V M, minus the product of uppercase C subscript zero, 1 minus uppercase D C, and uppercase V M subscript 1.
Description of Equation 7
Uppercase C S subscript 1 equals the product of uppercase C subscript zero, 1 minus uppercase D C, and 1 plus uppercase D V M.
Description of Equation 8
Uppercase Y equals the output of the function lowercase f with input uppercase S subscript uppercase I, uppercase I subscript lowercase j, uppercase B subscript lowercase k, and uppercase I T subscript lowercase l.
Description of Equation 9
Uppercase W T P equals the product of uppercase T S, alpha subscript Log, and the output of the function uppercase F with input uppercase T, eta subscript uppercase T, sigma subscript uppercase T, and eta subscript the variable sigma subscript uppercase T.
Description of Equation 10
Uppercase W T P equals the product of uppercase T S, alpha subscript Log, and the expression the product of eta subscript uppercase T and the quotient of delta uppercase T over uppercase T plus the product of eta subscript sigma and the quotient of delta sigma over sigma.
Description of Equation 11
Productivity equals the quotient of Output over Input.
Description of Equation 12
Delta uppercase P equals the quotient of uppercase O over uppercase I subscript 2 minus the quotient of uppercase O over uppercase I subscript 1. Delta uppercase P therefore equals uppercase O times the quotient of uppercase I subscript 1 minus uppercase I subscript 2 over the product of uppercase I subscript 1 and uppercase I subscript 2. Delta uppercase P is therefore approximately equal to uppercase O times the quotient of delta uppercase C subscript Log over the product of uppercase I subscript 1 and uppercase I subscript 2, which is exactly equal to uppercase P subscript 1 times the quotient of delta uppercase C subscript Log over uppercase I subscript 2.
Description of Equation 13
Delta uppercase P prime equals the quotient of uppercase O subscript 2 over uppercase I subscript 2 minus the quotient of uppercase O subscript 1 over uppercase I subscript 1. Delta uppercase P prime therefore equals the quotient of the expression uppercase O subscript 2 times uppercase I subscript 1 minus uppercase O subscript 1 times uppercase I subscript 2 over the product of uppercase I subscript 1 and uppercase I subscript 2.
Description of Equation 14
Eta superscript uppercase V M subscript uppercase C equals the quotient of delta uppercase V M divided by uppercase V M over delta uppercase C divided by uppercase C. Eta superscript uppercase V M subscript uppercase C therefore equals the quotient of two expressions: the quotient of delta lowercase V M divided by uppercase V M over delta uppercase T divided by uppercase T, and the quotient of delta uppercase C divided by uppercase C over delta uppercase T divided by uppercase T. Eta superscript uppercase V M subscript uppercase C therefore equals eta superscript uppercase V M subscript uppercase T divided by eta superscript uppercase C subscript uppercase T.
Description of Equation 15
Uppercase B lowercase e lowercase n subscript Net equals delta uppercase C S. Uppercase B lowercase e lowercase n subscript Net therefore equals uppercase C S subscript 1 minus uppercase C S subscript zero. Uppercase B lowercase e lowercase n subscript Net therefore equals the difference of two expressions: the integral from zero to lowercase q subscript 1 of the function lowercase p lowercase q lowercase d lowercase q minus the product of lowercase p subscript 1 and lowercase q subscript 1, and the integral from zero to lowercase q subscript zero of lowercase p lowercase q lowercase d lowercase q minus the product of lowercase p subscript zero and lowercase q subscript zero. Uppercase B lowercase e lowercase n subscript Net therefore equals the integral from lowercase q subscript zero to lowercase q subscript 1 of lowercase p lowercase q lowercase d lowercase q minus the product of lowercase p subscript 1 and delta lowercase q plus the product of lowercase q subscript zero and delta lowercase p.
Description of Equation 16
Uppercase B lowercase e lowercase n subscript Net equals delta uppercase C S. Uppercase B lowercase e lowercase n subscript Net therefore equals the product of two expressions: the quotient of lowercase a over the product of lowercase q subscript zero and lowercase q subscript 1, all raised to the power of the quotient of 1 over lowercase b, and the sum of 2 times lowercase q subscript zero to the power of the sum of 1 and the quotient of 1 over lowercase b times the expression lowercase b minus 1, plus the product of lowercase q subscript 1 and lowercase q subscript zero to the power of the quotient of 1 over lowercase b, minus the expression lowercase q subscript 1 to the power of the quotient of 1 over lowercase b times lowercase q subscript zero times the expression 2 times lowercase b minus 1, all divided by the expression lowercase b minus 1.
Description of Equation 17
Uppercase B lowercase e lowercase n subscript Net equals the product of lowercase a and uppercase V M subscript 2 minus uppercase V M subscript zero, minus the product of the quotient of lowercase b over 2 and uppercase V M subscript 2 squared minus uppercase V M subscript zero squared, minus the product of uppercase C subscript 1 and delta uppercase V M, plus the product of uppercase V M subscript zero and delta uppercase C. In this equation, lowercase a equals uppercase C subscript zero plus the quotient of uppercase C subscript zero over eta superscript uppercase V M subscript uppercase C, and lowercase b equals the product of the quotient of uppercase C subscript zero over eta superscript uppercase V M subscript uppercase C and uppercase V M subscript zero.
Description of Equation 18
Delta lowercase p equals delta uppercase C. Delta lowercase p therefore equals the product of uppercase C subscript zero, eta superscript uppercase C subscript uppercase T, and the quotient of delta uppercase T over uppercase T.
Description of Equation 19
Lowercase p subscript 1 equals lowercase p subscript zero minus the product of delta uppercase C and eta.
Description of Equation 20
Delta lowercase q equals delta uppercase V M. Delta lowercase q therefore equals the product of uppercase V M subscript zero, eta superscript uppercase V M subscript uppercase T, and the quotient of delta uppercase T over uppercase T.
Description of Equation 21
Uppercase B lowercase e lowercase n subscript Net equals delta uppercase C S plus delta uppercase C S prime.
Description of Equation 22
Uppercase B lowercase e lowercase n subscript Net equals delta uppercase C S plus delta uppercase C S prime. Uppercase B lowercase e lowercase n subscript Net therefore equals the product of three expressions: the quotient of 2 times lowercase b minus 1 over lowercase b, the quotient of lowercase a over the product of lowercase q subscript zero and lowercase q subscript 1, raised to the power of 1 divided by lowercase b, and the quotient of the expression the product of 2, lowercase q subscript zero to the power of the sum of 1 and the quotient of 1 over lowercase b, and lowercase b minus 1 plus the product of lowercase q subscript 1 times lowercase q subscript zero to the power of the quotient of 1 over lowercase b minus lowercase q subscript 1 to the power of the quotient of 1 over lowercase b times lowercase q subscript zero times the expression the product of 2 and lowercase b minus 1, over lowercase b minus 1.
Description of Equation 23
Uppercase T C equals the product of uppercase N and the output of the function uppercase C with input uppercase N and uppercase K, plus the output of the function lowercase f with input uppercase K.
Description of Equation 24
Delta uppercase T C divided by delta uppercase N equals the output of the function uppercase C with input uppercase N and uppercase K plus the quotient of the product of uppercase N and delta uppercase C over delta uppercase N.
Description of Equation 25
Uppercase C equals lowercase t times the sum of lowercase c subscript lowercase h lowercase r times uppercase D and mu times uppercase D, plus the quotient of the product of lowercase a and uppercase D over uppercase Q, plus the quotient of the product of lowercase w and uppercase Q over 2, plus the expression the sum of uppercase Q, lowercase t times uppercase D, and lowercase k prime times sigma times uppercase D, all raised to the power of one-half, times lowercase w times lowercase k, plus the output of the function Backorder Cost with input lowercase t and sigma.
Description of Equation 26
Uppercase C superscript uppercase T subscript zero equals uppercase C superscript uppercase T P T subscript zero, plus uppercase C superscript uppercase I N V subscript zero, plus uppercase C superscript uppercase P R O C subscript zero.
Description of Equation 27
Uppercase C subscript zero equals uppercase C superscript uppercase T subscript zero divided by uppercase V M subscript zero. Uppercase C subscript zero therefore equals the quotient of uppercase C superscript uppercase T P T subscript zero over uppercase V M subscript zero plus the quotient of uppercase C superscript uppercase OTHER subscript zero over uppercase V M subscript zero.
Description of Equation 28
Uppercase D C equals the quotient of uppercase C subscript zero minus uppercase C subscript 1 over uppercase C subscript zero. Uppercase D C therefore equals the sum of two expressions: the quotient of uppercase C superscript uppercase T P T subscript zero minus uppercase C superscript uppercase T P T subscript 1 over uppercase C subscript zero, and the quotient of uppercase C superscript uppercase OTHER subscript zero divided by uppercase V subscript zero minus uppercase C superscript uppercase OTHER subscript 1 divided by uppercase V subscript 1 over uppercase C subscript zero. Uppercase D C therefore also equals the sum of two expressions: the quotient of uppercase C superscript uppercase T P T subscript zero minus uppercase C superscript uppercase T P T subscript 1 over uppercase C subscript zero, and the quotient of the product of uppercase C superscript uppercase OTHER subscript zero and uppercase V subscript 1 divided by uppercase V subscript zero, minus uppercase C superscript uppercase OTHER subscript 1, over the product of uppercase C subscript zero and uppercase V subscript 1.