Table 2 Mathematical formulation of the...

Table 2

Mathematical formulation of the linear optimization problem

Decision variable	Let $x_{i j}$ be the flow of milk from dairy farm i to dairy j
Objective function	Minimize: $\sum_{i = 1}^{n} \sum_{j = 1}^{n} c_{i j} * x_{i j}$ , where c_ij represents the transportation cost from dairy farm i to j
Supply constraint	The total milk supplied by each dairy farm should not exceed its capacity: $\sum_{j = 1}^{n} x_{i j} \leq {s u p p l y}_{i}$ , for all i
Demand constraint	The total milk demanded by each dairy should be met: $\sum_{i = 1}^{n} x_{i j} = {d e m a n d}_{j}$ , for all j

Source(s): Table created by the authors