$S_i$ : Variable production cost of Toyota corolla vehicle

$M_i$ : In factory variable costs $($Labor & Energy$)$

$H_i$ : Raw material cost

$L_i$: Cost of transporting raw materials to the Factory

$S_1=830+330+375=1535$

$S_2=790+450+645=1885$

$S_3=1045+480+750=2275$

$S_i=M_i+H_i+L_i$

Problem: The wiring harnesses of the Toyota corolla vehicle, which can be produced in Turkey $($P$1),$ the United Kingdom $($P$2)$ and Japan $($P$3),$ will be produced from distributionn centers in Belgium $($D$2)$ and the Czech Republic $($D$1)$ to markets in Europe $($Ci$)$ to meet customer demands. and will be distributed. A model will be established to calculate the amount of vehicles that each factory should produce, provided that it meets customer demands and minimizes the total cost.

Markets where the vehicle will be offered,

$C_1=$ Turkey $,C_2=$ Russia $,C_3=$ Czech Republic $,C_4=$ Italy $,C_5=$ France $,C_6=$ Spain $,C_7=$ Germany $,C_8=$ England $,C_9=$ Poland $,C_{10}=$ South Africa

The problem will be solved with a transportation model that aims to minimize the cost. Parameters to be used in solving the problem;

$a_i$ : Production capacities of factories $($pieces$/$year$)$

$b_i$: Market demands $($units$/$year$)$

$P_i$: Production centers

$D_i$: Distribution Centers

$C_i$: Customer Markets

$c_{ij}$: Transport cost between $$ and $Dj(\frac{}{?}$ vehicle$)$

$d_{ij}$ : Amount of vehicles to be shipped from Pi to $Dj($pieces$/$year$)$

$m_{ij}$ : Transport costs between $Di$ and $Cj(\frac{}{?}$ vehicle$)$

$x_{ij}$: Amount of vehicles to be shipped from Di to $Cj($pieces$/$year$)$

$S_i$: Production cost of V$1$ vehicle $(\frac{}{?}$ vehicle$)$

The solution function is as follows.MinZ$={\displaystyle \underset{i=1}{\overset{3}{}}}{\displaystyle \underset{j=1}{\overset{2}{}}}(S_i+c_{ij})d_{ij}+{\displaystyle \underset{i=1}{\overset{2}{}}}{\displaystyle \underset{j=1}{\overset{10}{}}}(m_{ij}{x}_{ij})$

Production centers capacity constraints:

$a_1$:$30\mathrm{.}000$ unit$\frac{s}{y}$ear $,F_1$ Production Capacity Constraint

$a_2$:$50\mathrm{.}000$ unit$\frac{s}{y}$ear $,F_2$ Production Capacity Constraint

$a_3$:$90\mathrm{.}000$ unit$\frac{s}{y}$ear $,F_3$ Production Capacity Constraint

${\displaystyle \underset{j=1}{\overset{2}{}}}{d}_{ij}{a}_i,(i=1,2,3),{\displaystyle \underset{j=1}{\overset{10}{}}}{x}_{ij}={\displaystyle \underset{i=1}{\overset{3}{}}}{d}_{\text{i}\text{k}\text{i}},(i=1,2)$

Distribution Center restrictions:

${\displaystyle \underset{i=1}{\overset{3}{}}}{d}_{i1}80\mathrm{.}000$ units $\frac{?}{\text{y}\text{e}\text{a}\text{r}},{\displaystyle \underset{i=1}{\overset{3}{}}}{d}_{i2}40\mathrm{.}000$ uni$\frac{t}{y}$ear Demand Limits:

$x_{11}+x_{12}=b_1(17\mathrm{.}000$ units$/$year$),$ Turkish market demand amount

$x_{11}+x_{12}=b_1(3\mathrm{.}500$ units$/$year$),$ Russian market demand

$x_{11}+x_{12}=b_1(2\mathrm{.}500$ units$/$year$),$ Czech market demand quantity

$x_{11}+x_{12}=b_1(8\mathrm{.}900$ units$/$year$),$ Italian market demand

$x_{11}+x_{12}=b_1(9\mathrm{.}200$ units$/$year$),$ French market demand

$x_{11}+x_{12}=b_1(16\mathrm{.}400$ units$/$year$),$ Spanish market demand

$x_{11}+x_{12}=b_1(10\mathrm{.}500$ units$/$year$),$ German market demand

$x_{11}+x_{12}=b_1(5\mathrm{.}000$ units$/$year$),$ UK market demand

$x_{11}+x_{12}=b_1(1\mathrm{.}500$ units$/$year$),$ Polish market demand

$x_{11}+x_{12}=b_1(2\mathrm{.}100$ units$/$year$),$ South African market demand

$x_{ij}0,(i=1,2),(j=1,2,3,4,5,6,7,8,9,10)$