$1.$ Formulate the problem for identifying plants and warehouse location

simultaneously with quantity shipped between various plants to minimize the total

costs for the network model given in Fig$\mathrm{.}1.[12$ Marks$]$

Notations for the network model are given below:

m is the number markets or demand points

n is the number of potential factory location

l is the number of suppliers

t is the number of potential warehouse locations

$1$

Suppliers Plants Warehouses Market

s

Fig$\mathrm{.}1$ Stages in Supply Network

Dj Annual demand from customer j

Ki is the potential capacity of factory at site i

Sh is the supply capacity at supplier h

We is the warehouse capacity at site e

Fi is the Fixed cost of locating a plant at site i

Fe is the fixed cost of locating a warehouse at site e

Chi is the cost of shipping one unit from supply source h to factory i

Cie is the cost of producing and shipping one unit from factory i to warehouse e

Cej is the cost of shipping one unit from warehouse e to customer j

xej is the quantity shipped from warehouse e to market j

xie is the quantity shipped from factory at site i to warehouse e

xhi is the quantity shipped from supplier h to factory at site i

Assume the binary variable required for the model.