Plant Demand

Capacity

Price
1 400 500 100
2 300 600 140
3 420 200 120
4 380 300 150

The demand for a perishable item over the next four months is 400, 300, 420, and 380 tons, respectively. The supply capacities for the same months are 500, 600, 200, and 300 tons. The purchase price per ton varies from month to month and is estimated at $100, $140, $120, and $150, respectively. Because the item is perishable, a current month’s supply must be consumed within 3 months (starting with current month). The storage cost per ton per month is $3. The nature of the item does not allow back-ordering. Solve the problem as a transportation model, and determine the optimum delivery schedule for the item over the next 4 months.
(a) Formulate the problem as a transportation model.
(b) Find the initial basic feasible solution to the above transportation problem by using North West Corner Rule, Least Cost Rule and Vogel’s Approximation Method.