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‘SuperMart, a newly established manufacturing company, would like to optimize its product and distribution system to cope with the increasing cost pressure. Currently, the company produces its products in four plants located in different areas and two distribution centres (DC) to store products. All products are produced in plants and transported to distribution centres to store after products are produced. Then, the products are transported to its three stores located in different areas. The product quality produced in different plants is the same, but the production unit costs are different due to the differences in labour and material costs. The production capacities in different plants are different as well. The unit transportation costs (from plants to distribution centres), production unit costs, and plant capacities of each plant are presented in the table below. Information related to plants Cost of transport to DC 5 Cost of transport to DC 6 Plant capacity Production unit costs Fixed costs 4 5 10 12 5 6 Plant 1 Plant 2 Plant 3 Plant 4 6,000 10,000 20,000 15,000 12,000 11,000 10,000 8,000 9 7 13 15 2 3 The unit transportation costs (from distribution centres to stores) presented in table below. The demand for Store 7, Store 8 and Store 9 are 5,000, 4,000, and 6,000 respectively. Information related to customers Cost of transport to Store 7 Cost of transport to Store 8 2 3 Cost of transport to Store 9 4 DC 1 5 DC 2 4 5 As for the manufacturing plants, if SuperMart decides to produce products in a plant, a fixed cost will be incurred. Formulate an integer linear programming (ILP) model that helps the company to decide the production and transportation plan. You do not need to solve the model.