1. CHAPTER V Transportation Models Instructor : Lect.Volkan ÇETİNKAYA

2.  The Transportation Model is a special class of linear programs that deals with shipping a commodity from sources (factories) to destinations (warehouses).  The objective is to determine the shipping schedule that minimizes total shipping cost while satisfying supply and demand limits.

4. POLAND S. AFRICA BRAZIL AUSTRALIA İSKENDERUN ANTALYA GÖKOVA TEKİRDAĞ TRABZON 12 10 11 15 20 15 17 20 22 28 15 22 23 25 27 25 27 30 32 35 SOURCES Coal Mine SUPPLY DESTINATIONS Thermal Power Plants DEMAND 8 6 5 2 5 4 3 5 4 21 ?

5.  X ij = Quantity of product to be delivered from i to j  C ij = Transportation cost from i to j  a i = Supply of i  b j = Demand of j

7.  In a transportation model, as seen previous slide, there are m sources and n destinations, each represented by a node. The arcs represent the routes linking the sources and destinations.  Arc(i,j) joining source to destination j carries two pieces of information.  The transportation cost from i to j : C ij  The transportation quantity from i to j : X ij

8.  The amount of supply at source i : a i  The amount of demand at destination j : b j  The objective : To Determine the unknowns X ij that will minimize the total transportation cost by satisfying all the supply and demand constraints.

9.  MG Automative has 3 factories in İzmir, Edirne and Bursa and 2 distribution centers in Ankara and Mersin.  In coming 3 months term, the capacities of factories: İzmir: 1,500pcs. Edirne: 1,000pcs. Bursa: 1,200pcs.  In coming 3 months term,the demands of centers: Ankara: 2,300 Malatya: 1,400  The distances (km.) between factories and centers: AnkaraMersin İzmir579892 Edirne6831,162 Bursa384831

10.  Transportation outsourcing company serves a price as 0.08 TL/km.  Construct the transportation model.

11.  Demand = Supply, The model is BALANCED  Demand = Supply, we have to balance the model by adding dummy demand or dummy supply points in solution.

12.  In MG Automative Model, Let’s assume that Izmir Factory has a capacity of 1,300(instead of 1,500). In this case Supply = 3,500pcs.and demand = 3,700pcs.  Assume that Ankara Distribution Center has a demand of 1,900 pcs.(instead of 2,300)

13. C1C2C3Capacity F1 152018200 F2 162217300 Demand 180150175 Construct the transportation model.