CHAPTER V Transportation Models Instructor : Lect.Volkan ÇETİNKAYA 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. SOURCES SUPPLY DESTINATIONS Thermal Power Plants Coal Mine 12 8 İSKENDERUN DEMAND 5 15 POLAND 15 10 ANTALYA 4 17 S. AFRICA 6 22 25 27 20 11 15 30 25 22 27 28 20 32 AUSTRALIA 2 21 3 23 BRAZIL 5 GÖKOVA 35 TEKİRDAĞ TRABZON 5 4 21 Xij = Quantity of product to be delivered from i to j Cij = Transportation cost from i to j ai = Supply of i bj = Demand of j Min 𝑖∈𝐼 𝑗∈𝐽 X𝑖𝑗 . C𝑖𝑗 𝑗∈𝐽 𝑋𝑖𝑗 ≤ ai (Supply Constraint for each factory) 𝑖∈𝐼 𝑋𝑖𝑗 ≥ bj (Demand Constraint for each customer) 𝑋𝑖𝑗 ≥ 0 and integer Number of constraints=Total of Fact. + Total of Dist.Centers 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 : Cij The transportation quantity from i to j : Xij The amount of supply at source i : ai The amount of demand at destination j : bj The objective : To Determine the unknowns Xij that will minimize the total transportation cost by satisfying all the supply and demand constraints. 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: İzmir Edirne Bursa Ankara 579 683 384 Mersin 892 1,162 831 Transportation outsourcing company serves a price as 0.08 TL/km. Construct the transportation model. Demand = Supply , The model is BALANCED Demand = Supply, we have to balance the model by adding dummy demand or dummy supply points in solution. 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) F1 F2 Demand C1 C2 C3 Capacity 15 16 180 20 22 150 18 17 175 200 300 Construct the transportation model.