Model Formulation for the General Transportation Problem

Variables:

$$ xij: Quantity of goods transported from warehouse i to retail outlet j$.$ cij: Cost per unit of goods transported from i to j$.$

$$ si: Supply at warehouse i$.$

$$ dj: Demand at retail outlet j$.$ Objective:

Minimize total transportation cost:

Minimize Z $=$ X X cij xij, Supply constraints: Pj xij $<=$ si for all i$.$

$$ Demand constraints: Pi xij $>=$ dj for all j$.$

$$ Non$-$negativity: xij $>=0$ for all i$,$ j$.$ For ILP, additionally, xij must be integers. I am trying to code this in intelij using java