Determining Minimum Transportation Cost with Linear Programming

What data do we have regarding the suppliers and customer zones?

How can we formulate this as a transportation problem and solve it using linear programming to find the minimum transportation cost?

What are the constraints for each supplier and customer zone?

Suppliers and Customer Zones Data:

There are three suppliers: Supplier 1 can supply 300 products, Supplier 2 can supply 340 products, and Supplier 3 can supply 340 products.

Customer 1 needs 100 products, Customer 2 needs 150 products, Customer 3 needs 220 products, and Customer 4 needs 350 products.

Formulating the Problem:

To determine the minimum transportation cost, we can use linear programming with decision variables Xij.

The objective is to minimize the total transportation cost based on the given costs for shipping products from suppliers to customer zones.

Constraints:

• Supply constraints for each supplier: Xij <= Supplier Capacity
• Demand constraints for each customer zone: Xij >= Customer Demand
• Non-negativity constraint: Xij >= 0

Explanation:

In this scenario, we have three suppliers with specific product capacities and four customer zones with varying demand levels. By formulating the problem as a transportation issue with linear programming, we can optimize the transportation cost to meet the full demand at each customer zone.

The objective is to minimize the total transportation cost, taking into account the costs specified in the table for shipping products from suppliers to customer zones. By setting up the constraints for supply, demand, and non-negativity, we ensure that the solution aligns with the available resources and requirements.

Through linear programming techniques, we can efficiently calculate the optimal quantity of products to transport from each supplier to every customer zone, considering the capacity limitations and demand needs. By solving this problem using the provided constraints and costs, we can determine the minimum transportation cost to meet the full demand at each customer zone.