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L. Chai et al.
A =
⎡
⎢
⎢
⎢
⎣
a 11 a 12 · · · a 1n
a 21 a 22 · · · a 2n
· · ·
a n1
· · ·
a n2
· · · · · ·
· · · a nn
⎤
⎥
⎥
⎥
⎦
The row vector of the direct consumption coefficient matrix A indicates that the ith (i = 1,2, … ,n) product is the direct input amount of each product in the production
unit. The column vector of matrix A is expressed as the direct consumption of the
j-th (j = 1,2, … n) product to the various products in the row.
(2) Total consumption factor
The complete consumption coefficient refers to the quantity of products of the i-th
department that needs to be completely consumed when each unit of the final product
is produced by the department. The direct consumption coefficient reflects the direct
relationship between various products. It indicates that a certain product directly
consumes various products (including itself) in the production process of a unit
product, and it refers to the total product. However, in addition to direct links between
products, there are also indirect links, and consumption caused by indirect links is
called indirect consumption. The sum of direct connection and indirect connection
is called complete connection; the sum of system direct consumption and all indirect
consumption is called complete consumption. Generally recorded as
Full contact = Direct contact + All indirect contact
Complete consumption = Direct consumption + All indirect consumption
Complete consumption f actor = Direct consumption f actor + I ndirect consumption f actor
The complete consumption coefficient is expressed as b ij and its meaning is the
complete consumption of the i-th product by the physical product produced by the
j-th product. Its relationship with the direct consumption coefficient is expressed as
b i j = a i j +
n
k=1
b ik a k j (i, j = 1, 2, . . . , n)
where
n
k=1 b ik a k j represents the sum of all indirect consumption of a unit of the
j-th product to the i-th product.
Using matrix operations, b ij can be calculated, and B is expressed as
B =
⎡
⎢
⎢
⎢
⎣
b 11 b 12 · · · b 1n
b 21 b 22 · · · b 2n
· · ·
b n1
· · ·
b n2
· · · · · ·
· · · b nn
⎤
⎥
⎥
⎥
⎦
L. Chai et al.
A =
⎡
⎢
⎢
⎢
⎣
a 11 a 12 · · · a 1n
a 21 a 22 · · · a 2n
· · ·
a n1
· · ·
a n2
· · · · · ·
· · · a nn
⎤
⎥
⎥
⎥
⎦
The row vector of the direct consumption coefficient matrix A indicates that the ith (i = 1,2, … ,n) product is the direct input amount of each product in the production
unit. The column vector of matrix A is expressed as the direct consumption of the
j-th (j = 1,2, … n) product to the various products in the row.
(2) Total consumption factor
The complete consumption coefficient refers to the quantity of products of the i-th
department that needs to be completely consumed when each unit of the final product
is produced by the department. The direct consumption coefficient reflects the direct
relationship between various products. It indicates that a certain product directly
consumes various products (including itself) in the production process of a unit
product, and it refers to the total product. However, in addition to direct links between
products, there are also indirect links, and consumption caused by indirect links is
called indirect consumption. The sum of direct connection and indirect connection
is called complete connection; the sum of system direct consumption and all indirect
consumption is called complete consumption. Generally recorded as
Full contact = Direct contact + All indirect contact
Complete consumption = Direct consumption + All indirect consumption
Complete consumption f actor = Direct consumption f actor + I ndirect consumption f actor
The complete consumption coefficient is expressed as b ij and its meaning is the
complete consumption of the i-th product by the physical product produced by the
j-th product. Its relationship with the direct consumption coefficient is expressed as
b i j = a i j +
n
k=1
b ik a k j (i, j = 1, 2, . . . , n)
where
n
k=1 b ik a k j represents the sum of all indirect consumption of a unit of the
j-th product to the i-th product.
Using matrix operations, b ij can be calculated, and B is expressed as
B =
⎡
⎢
⎢
⎢
⎣
b 11 b 12 · · · b 1n
b 21 b 22 · · · b 2n
· · ·
b n1
· · ·
b n2
· · · · · ·
· · · b nn
⎤
⎥
⎥
⎥
⎦