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Transportation models and its variants. Chapter 5 Dr. Ayham Jaaron. What is Transportation model?.
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Transportation models and its variants Chapter 5 Dr. AyhamJaaron
What is Transportation model? • The transportation problem is one of the subclasses of linear programming problem where the objective is to transport various quantities of a single homogeneous product that are initially stored at various origins, to different destinations in such a way that the total transportation cost is minimum.
Purpose of Transportation models • Transportation models or problems are primarily concerned with the optimal (best possible) way in which a product produced at different factories or plants (called supply origins) can be transported to a number of warehouses (called demand destinations). The objective in a transportation problem is to fully satisfy the destination requirements within the operating production capacity constraints at the minimum possible cost.
Medical Supply Transportation Problem • A Medical Supply company produces catheters in packs at three production facilities. • The company ships the packs from the production facilities to four warehouses. • The packs are distributed directly to hospitals from the warehouses. • The table on the next slide shows the costs per pack to ship to the four warehouses.
Source: Adapted from Lapin, 1994 Medical Supply TO WAREHOUSE FROM PLANT Seattle New York Phoenix Miami Atlanta $19 $ 7 $ 3 $21 Roswell15 21 18 6 Dallas 11 14 15 22 Capacity Atlanta 100 Roswell 300 Dallas 200 Demand Seattle 150 New York 100 Phoenix 200 Miami 150
A 100 R 300 D 200 Source: Adapted from Lapin, 1994 Northwest Corner Method S N P M Capacity To From 19 7 3 21 15 21 18 6 11 14 15 22 Demand 150 100 200 150 600 Begin with a blank shipment schedule. Note the shipping costs in the upper right hand corner of each cell.
Problem • For the transportation model provided below, calculate the optimal amount that should be ordered from each source, and what is the total cost of these amounts using the least-cost method?
Problem (2)...VAM The Saussy Lumber Company ships pine flooring to three building supply houses from its mills in Pineville, Oak Ridge, and Mapletown. Determine the best transportation schedule for the data given in the accompanying table. Use the Vogel Approximation method.
Comparing the starting solution obtained from Transportation methods • Problem Set 5.3A (page211):
Non-Traditional Transportation Models • The application of the transportation model is not limited to transporting commodities between geographical sources and destinations. • Other applications are: • Production inventory control • Equipment maintenance. • And many other applications....
