Notation

Description

n

Periodic intervals

C

Cost

$P^{\prime }$

Price

$u_p^{\left(c^{\prime }\right)}$

Production capacity per unit of product p

$u_{pm}^{\left(m\right)}$

Unit p product demand for m components

${C^{\prime }}_t$

The available production capacity of an assembly plant in the t period

$C_{tms}^{\left(o\right)}$

The ordering cost of components ordered by the assembly plant at time t from supplier s of m components

$C_{tp}^{\left(p\right)}$

The unit cost for the assembly plant to produce product p during time t

$Q_{\tau lrp}^{\left(p\right)}$

The forecast demand for p product by r grade customers in l area during the marketing session

${P^{\prime }}_{tlrp}^{\left(p\right)}$

The unit price of product p supplied by the assembly plant to r grade customers in region l during time period t

${P^{\prime }}_{tms}^{\left(m\right)}$

The assembly plant purchases the unit price of components from s supplier of m components in time period t

$U_{tms}^{\left(m\right)}$

The maximum supply of s supplier of m component in time period t

$I_m^{\left(m\right)}$

Initial inventory of assembly plant m components

$C_m^{\left(h\right)}$

An assembly plant stores the unit cost of m components for a period of time

$C_p^{\left(h\right)}$

An assembly plant stores the unit cost of p products for a period of time

$C_{lp}^{\left(d\right)}$

Unit cost of transportation of product p from the assembly plant to area l

Superscript:

m

Represent component

p

Represent product

o

Represent order cost

c’

Represent production capacity

h

Represent inventory cost

d

Represent transportation cost

Sets:

S

A set of suppliers, $s\in \left\{1,2,3,\cdots ,S_0\right\}=S$

M

Component types, $m\in \left\{1,2,3,\cdots ,M_0\right\}=M$

P

Product type, $p\in \left\{1,2,3,\cdots ,P_0\right\}=P$

T

Period set, $T=\left\{1,2,3,\cdots ,T_0\right\}$ , $t\in T$ , $\tau \in T$

R

Customer rating, $r\in \left\{1,2,3,\cdots ,R_0\right\}=R$

L

A set of region, $l\in \left\{1,2,3,\cdots ,L_0\right\}=L$

Decision variables:

$B_{tm}^{\left(m\right)}$

Initial inventory of assembly plant m components in time period t

$E_{tm}^{\left(m\right)}$

The assembly plant’s ending inventory of components m at time t

$B_{tp}^{\left(p\right)}$

Initial inventory of p product in time period t

$E_{tp}^{\left(p\right)}$

The assembly plant’s ending inventory of product p in time period t

$Q_{tms}^{\left(m\right)}$

The number of components the assembly plant purchases from s supplier of m components in time period t

$Q_{tp}^{\left(p\right)}$

The number of p products produced by the assembly plant in time period t