Quantitative Techniques: Theory and Problems

MATHEMATICAL MODEL FOR TRANSPORTATION PROBLEM

Problem 5.1 [Cost Matrix or Minimisation Problem]

Build the mathematical model for the following transportation problem:

W_j → Warehouse, F_i → Factory and cell entries are unit/costs.

Solution

Step 1 → Introducing dummy warehouse with zero cost per unit as the total demand is not equal to total supply in order to make the problem balanced one.

Let x_ij represent the quantity transported from F_i to W_j

Formulation of the mathematical model for the transportation problems.

Minimise Z =

1x11