Full ready presentation on Transportation Problem

This is an complete presentation on Transportation Problem in Operations Research

1. Transportation Problem Presented By: Auntor Khastagir Pujan Roll: 1738 Semester: 4 th Presented To: Mrs Chandra Das Assistant Professor and Head Business Administration, USTC WELCOME

2. Contents Introduction Types of Transportation Problem Objectives of the Transportation Problem Application of Transportation Problem Methods Used in Transportation Problem Conclusion

3. What is Transportation Problem

4. Types of Transportation Problem Balanced Transportation Problem Unbalanced Transportation Problem Minimization Problem Maximization Problem Transshipment Problem Multi-Commodity Transportation Problem Time-Dependent Transportation Problem Stochastic Transportation Problem Capacitated Transportation Problem Assignment Problem Vehicle Routing Problem (VRP)

5. Balanced Transportation Problem : Definition : The total supply equals the total demand. Example : A company needs to transport goods from its warehouses to retail outlets, with the total quantity of goods in the warehouses matching the total quantity needed by the outlets. Unbalanced Transportation Problem : Definition : The total supply does not equal the total demand. Example : A situation where there is excess supply or excess demand, requiring adjustments like adding dummy sources (for excess demand) or dummy destinations (for excess supply) to balance the problem.

6. Minimization Problem : Definition : The objective is to minimize the total transportation cost. Example : Finding the least expensive way to ship products from factories to various distribution centers. Maximization Problem : Definition : The objective is to maximize a certain benefit, such as profit or efficiency. Example : Allocating shipments to maximize profit margins, taking into account varying costs and selling prices at different locations.

7. Transshipment Problem : Definition : Involves intermediate points (transshipment points) where goods can be temporarily stored before reaching their final destinations. Example : Products shipped from factories to warehouses (transshipment points) and then to retail stores. Multi-Commodity Transportation Problem : Definition : Deals with transporting multiple types of commodities simultaneously. Example : A logistics company transporting food, electronics, and clothing from various suppliers to various markets, considering the distinct requirements for each commodity.

8. Time-Dependent Transportation Problem : Definition : The transportation costs or times vary depending on the time of day or other temporal factors. Example : Scheduling deliveries to avoid peak traffic hours to minimize transportation time and costs. Stochastic Transportation Problem : Definition : Incorporates uncertainty in parameters like supply, demand, or transportation costs. Example : Planning shipments when future supply or demand levels are uncertain and might fluctuate.

9. Capacitated Transportation Problem: Definition : Includes constraints on the maximum amount that can be shipped along each route. Example : Delivery trucks with specific load capacities or limited storage capacity at the destinations. Assignment Problem: Definition : A special case where the objective is to assign resources to tasks on a one-to-one basis at minimal cost or maximum profit. Example : Assigning a fleet of trucks to various delivery routes where each truck is assigned to exactly one route.

10. Vehicle Routing Problem (VRP): Definition : Focuses on the optimal routes for a fleet of vehicles delivering to multiple locations. Example : Determining the best routes for delivery trucks to minimize travel time or distance while meeting customer delivery windows.

11. Objectives of Transportation Problem Determination of a transportation plan of a single commodity from a number of sources to a number of destinations, such that total cost of transportation is minimized.

12. Application of Transportation Problem It is used to compute transportation routes in such a way as to minimize transportation cost for finding out locations of warehouses. It is used to find out locations of transportation corporations depots where insignificant total cost difference may not matter. Minimize shipping costs from factories to warehouses(or from warehouses to retail outlets). Determine lowest cost location for new factory, warehouse, office, or other oulet facility. Find minimum cost production schedule that satisfies firms demand and production limitations.

13. Methods Used in Transportation Problem North-West Corner Method: A basic approach for finding an initial feasible solution in transportation problems by starting at the top-left corner of the transportation tableau and allocating shipments until reaching the bottom-right corner.

14. Methods Used in Transportation Problem Vogel's Approximation Method: A technique used in solving transportation problems that considers both the difference between the two lowest costs in each row and column, allowing for a more efficient initial allocation.

15. Methods Used in Transportation Problem Stepping Stone Method: An iterative optimization technique applied to transportation problems, involving moving units of goods from one cell to another in a way that improves the total cost of transportation.

16. Methods Used in Transportation Problem Modified Distribution Method: An improved version of the stepping stone method that efficiently identifies the optimal solution for transportation problems by systematically evaluating all possible routes and reallocating goods until an optimal solution is reached.

17. Conclusion The transportation problem is a pivotal topic within operations research, addressing the optimal distribution of goods from multiple sources to multiple destinations. It encompasses various types, including balanced and unbalanced transportation problems, each with distinct characteristics and challenges. The primary objective is to minimize the total transportation cost while meeting supply and demand constraints effectively. Applications of the transportation problem span across industries such as logistics, manufacturing, and supply chain management, highlighting its practical relevance and significance. Methods like the Northwest Corner Rule, Least Cost Method, and Vogel's Approximation Method provide systematic approaches to finding initial feasible solutions, while optimization techniques like the Modified Distribution Method (MODI) further refine these solutions for cost minimization. In essence, understanding and solving transportation problems is crucial for efficient resource allocation and cost management, offering significant benefits to businesses and economies by optimizing their logistical operations.