Willy Wonka Chocolate Factory produces chocolate bars from different ingredients like cocoa, cocoa butter, milk, sugar, hazelnut, pistachio etc. Willie Wonka has two cocoa butter plants located in Balkesir and Mula. Cocoa butter is produced from cocoa at these two plants or it is imported at the Izmir harbor. The produced and imported cocoa butter is transported to chocolate plants in stanbul and Adana, where chocolate bars are produced. Willy Wonka ships chocolate produced at the chocolate plants to its main distribution centers in Istanbul, zmir, Ankara, Bolu, Trabzon, and to the zmir harbor for export. WIN NKA Nutty Crunch Sumo The estimates on the transportation costs between the cocoa butter plants and the chocolate plants; and between the chocolate plants and the distribution centers are given in Table 1. Table 2 contains the chocolate demand forecast at the distribution centers for the next year. Table 3 shows the current cocoa butter and chocolate production capacities as well as cocoa butter yield. Table 4 summarizes the current distribution plan prepared for the next year. You have to figure out how many tons of cocoa butter to ship from each cocoa butter plant to each chocolate plant and how many tons of the chocolate to ship from each chocolate plant to each distributor. You have to make sure that none of the capacities of the plants is exceeded, and all the chocolate demand of the distributors is satisfied. The shipment plan that minimizes the total costs must be quite different from the current plant. Table 1: TRANSPORTATION COSTS: Annual cost of shipping 1000 tons of cocoa butter from cocoa butter plant i to chocolate plant j (Million $ /1000 ton) Destinations Cocoa butter plants Balkesir Chocolate Plants Istanbul Adana 0.026 0.017 0.037 0.017 0.032 0.033 Mula Import (Izmir) Annual cost of shipping 1000 ton of chocolate from chocolate plant j to distribution center k (Million $/1000 ton) Destinations Distribution Centers Plants Istanbul | 0.000 | 0.032 Istanbul Export (Izmir) 0.042 0.043 Izmir Ankara Bolu Trabzon 0.040 | 0.052 | 0.017 | 0.055 0.041 0.039 0.027 | 0.023 Adana Table 2: DEMAND: Annual demand at distribution centers Dist. Centers Next Year 103 Istanbul Izmir 74 Ankara 50 Bolu 60 Trabzon 102 Export(Izmir) 13 Total 402 Table 3: CAPACITY: Annual capacity of chocolate plants Annual capacity of cocoa butter plants (1000 tons/year) Balkesir (1000 tons/year) 30 Mula 68 Istanbul 220 Import (Izmir) 20 Adana 200 CHOCOLATE YIELD: 1000 tons of chocolate produced from 1000 ton of cocoa butter Domestic 8.333 9.091 Import Table 4: Single Period - Current Shipment Plan 0 Amount of cocoa butter shipped from plant i to chocolate plant j next year (1000 ton) Istanbul Adana Total Capacity Balkesir 24 24.00 30.00 Mula 2.42 0 2.42 68.00 0 20.00 20.00 Import Total cocoa butter 22.42 24 Total chocolate 202 200 (1000 tons) 20 Amount of chocolate shipped from chocolate plant j to distribution center k next year (1000 ton) Istanbul Istanbul 103 0 Izmir 49 25 Ankara 5 0 0 50 50 Bolu 0 60 Trabzon 0 102 Export (Izmir) 0 1 3 13 13 Total 202 200.00 Adana Capacity 220 200 Total 103 103 7 4 74 60 60 102 102 Demands Total shipping cost 11.244 (Million dollars) Question 3. Suppose Willy Wonka prefers to keep the existing relationship between Istanbul-Ankara and Adana-Bolu by sending at least some amount between these locations, and at the same time wants to minimize its shipment costs. What shipment costs would justify this? (10 pts) Hint: Use sensitivity information to answer Questions 3, 4 and 5. Willy Wonka Chocolate Factory produces chocolate bars from different ingredients like cocoa, cocoa butter, milk, sugar, hazelnut, pistachio etc. Willie Wonka has two cocoa butter plants located in Balkesir and Mula. Cocoa butter is produced from cocoa at these two plants or it is imported at the Izmir harbor. The produced and imported cocoa butter is transported to chocolate plants in stanbul and Adana, where chocolate bars are produced. Willy Wonka ships chocolate produced at the chocolate plants to its main distribution centers in Istanbul, zmir, Ankara, Bolu, Trabzon, and to the zmir harbor for export. WIN NKA Nutty Crunch Sumo The estimates on the transportation costs between the cocoa butter plants and the chocolate plants; and between the chocolate plants and the distribution centers are given in Table 1. Table 2 contains the chocolate demand forecast at the distribution centers for the next year. Table 3 shows the current cocoa butter and chocolate production capacities as well as cocoa butter yield. Table 4 summarizes the current distribution plan prepared for the next year. You have to figure out how many tons of cocoa butter to ship from each cocoa butter plant to each chocolate plant and how many tons of the chocolate to ship from each chocolate plant to each distributor. You have to make sure that none of the capacities of the plants is exceeded, and all the chocolate demand of the distributors is satisfied. The shipment plan that minimizes the total costs must be quite different from the current plant. Table 1: TRANSPORTATION COSTS: Annual cost of shipping 1000 tons of cocoa butter from cocoa butter plant i to chocolate plant j (Million $ /1000 ton) Destinations Cocoa butter plants Balkesir Chocolate Plants Istanbul Adana 0.026 0.017 0.037 0.017 0.032 0.033 Mula Import (Izmir) Annual cost of shipping 1000 ton of chocolate from chocolate plant j to distribution center k (Million $/1000 ton) Destinations Distribution Centers Plants Istanbul | 0.000 | 0.032 Istanbul Export (Izmir) 0.042 0.043 Izmir Ankara Bolu Trabzon 0.040 | 0.052 | 0.017 | 0.055 0.041 0.039 0.027 | 0.023 Adana Table 2: DEMAND: Annual demand at distribution centers Dist. Centers Next Year 103 Istanbul Izmir 74 Ankara 50 Bolu 60 Trabzon 102 Export(Izmir) 13 Total 402 Table 3: CAPACITY: Annual capacity of chocolate plants Annual capacity of cocoa butter plants (1000 tons/year) Balkesir (1000 tons/year) 30 Mula 68 Istanbul 220 Import (Izmir) 20 Adana 200 CHOCOLATE YIELD: 1000 tons of chocolate produced from 1000 ton of cocoa butter Domestic 8.333 9.091 Import Table 4: Single Period - Current Shipment Plan 0 Amount of cocoa butter shipped from plant i to chocolate plant j next year (1000 ton) Istanbul Adana Total Capacity Balkesir 24 24.00 30.00 Mula 2.42 0 2.42 68.00 0 20.00 20.00 Import Total cocoa butter 22.42 24 Total chocolate 202 200 (1000 tons) 20 Amount of chocolate shipped from chocolate plant j to distribution center k next year (1000 ton) Istanbul Istanbul 103 0 Izmir 49 25 Ankara 5 0 0 50 50 Bolu 0 60 Trabzon 0 102 Export (Izmir) 0 1 3 13 13 Total 202 200.00 Adana Capacity 220 200 Total 103 103 7 4 74 60 60 102 102 Demands Total shipping cost 11.244 (Million dollars) Question 3. Suppose Willy Wonka prefers to keep the existing relationship between Istanbul-Ankara and Adana-Bolu by sending at least some amount between these locations, and at the same time wants to minimize its shipment costs. What shipment costs would justify this? (10 pts) Hint: Use sensitivity information to answer Questions 3, 4 and 5