The customers and the potential facilities of a country have been aggregated in seven regions as...

 

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The customers and the potential facilities of a country have been aggregated in seven regions as shown in Figure 1. Figure 1: A B с D E F G A 0 7 4 5 12 7 14 B 7 0 11 12 12 14 11 A A company would like to open three facilities among these regions to supply all the customers. The unit shipping costs between all regions are given in Table 1. Table 1: F B C D Region EFG C 4 11 0 7 D 16 3 11 D 5 12 7 The demand in each region is known and given in Table 2. Table 2: 0 15 5 9 B G E Demand in tons 100 200 120 45 250 80 75 E 12 12 16 15 0 14 6 F 7 14 3 5 14 0 8 G 14 11 11 9 6 8 00 0 If a facility is decided to be opened in a region, its capacity is determined beforehand and is given in Table 3. Table 3: Region A B с D E F A Fixed Cost 1000 Capacity in tons 225 500 B 1500 300 900 The final key body of data involves the fixed costs of opening a facility in each region. The fixed cost of setting up a facility is different in each region as shown in Table 4. Table 4: 600 130 110 D E F с 1200 2500 1800 800 G 750 The objective is to determine the overall distribution plan that minimizes the total annual cost. You are the head of the OR team that has been assigned the task of determining the shipping plan for each of the following options. Option 1: The new facilities are opened in region B, C, and F. Option 2: The new facilities are opened in region A, D, and F. Option 3: The new facilities are opened in region A, E, and G. Analyze the company's distribution strategy and suggest possible improvements. You should answer the following questions when you work on the case: Question 1. Present your results for each of the three options. (40 pts) Hint: Optimize the distribution plan by formulating and solving a linear programming model for each option. Develop three distribution plans that minimizes total shipping and fixed costs while satisfying demands at the regions (Use GAMS to develop the models). Discuss the resulting benefits of the suggested plans. Answer Questions 2, using the best option obtained while solving Question 1. Question 2. If the company would like to ship all the required demand of region G only from one open facility, can the shipment plan be still improved? (15 pts) Hint: Modify your model and resolve. The customers and the potential facilities of a country have been aggregated in seven regions as shown in Figure 1. Figure 1: A B с D E F G A 0 7 4 5 12 7 14 B 7 0 11 12 12 14 11 A A company would like to open three facilities among these regions to supply all the customers. The unit shipping costs between all regions are given in Table 1. Table 1: F B C D Region EFG C 4 11 0 7 D 16 3 11 D 5 12 7 The demand in each region is known and given in Table 2. Table 2: 0 15 5 9 B G E Demand in tons 100 200 120 45 250 80 75 E 12 12 16 15 0 14 6 F 7 14 3 5 14 0 8 G 14 11 11 9 6 8 00 0 If a facility is decided to be opened in a region, its capacity is determined beforehand and is given in Table 3. Table 3: Region A B с D E F A Fixed Cost 1000 Capacity in tons 225 500 B 1500 300 900 The final key body of data involves the fixed costs of opening a facility in each region. The fixed cost of setting up a facility is different in each region as shown in Table 4. Table 4: 600 130 110 D E F с 1200 2500 1800 800 G 750 The objective is to determine the overall distribution plan that minimizes the total annual cost. You are the head of the OR team that has been assigned the task of determining the shipping plan for each of the following options. Option 1: The new facilities are opened in region B, C, and F. Option 2: The new facilities are opened in region A, D, and F. Option 3: The new facilities are opened in region A, E, and G. Analyze the company's distribution strategy and suggest possible improvements. You should answer the following questions when you work on the case: Question 1. Present your results for each of the three options. (40 pts) Hint: Optimize the distribution plan by formulating and solving a linear programming model for each option. Develop three distribution plans that minimizes total shipping and fixed costs while satisfying demands at the regions (Use GAMS to develop the models). Discuss the resulting benefits of the suggested plans. Answer Questions 2, using the best option obtained while solving Question 1. Question 2. If the company would like to ship all the required demand of region G only from one open facility, can the shipment plan be still improved? (15 pts) Hint: Modify your model and resolve.