Models for facility location & Capacity allocation Capacitated plant location model with single sourcing

In some cases, companies want to design supply chain networks in which a market is supplied from only one factory, referred to as a single source. Companies may impose this constraint because it lowers the complexity of coordinating the network and requires less flexibility from each facility.

Min $D_j{c}_{ij}{x}_{ij},+f_i{y}_i,$ Total cost

${\displaystyle \underset{?}{\overset{?}{}}}{x}_{ij}=1,$ Market $j,j=1,..,6$ Market constraints

${\displaystyle \underset{j}{\overset{i}{}}}{x}_{ij}{K}_i{y}_i$ Factory $i,i=1,$dots,$5$ Factory constraints

$x_{ij}=1$ if Market $j$ is supplied from Factory i and $x_{ij}=0$ otherwise

$y_i=0$ if Factory $i$ is to be shut down and $y_i=1$ otherwise.

$D_1{x}_{11}+D_2{x}_{12}+D_3{x}_{13}+D_4{x}_{14}+D_5{x}_{15}+D_{66}{x}_{16}$