You are working as an Operations Research Intern at the European Headquarters of a single- type...

 

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You are working as an Operations Research Intern at the European Headquarters of a single- type car manufacturer. As today's task, you have been asked to model an IP which should be developed to minimize the annual cost of meeting the demand of cars where all parameters of the problem are deterministic. The company is currently discussing of producing the cars in four factories which are located in Riga, Bucharest, Berlin and London. Each facility can produce as many as 140,000 cars annually and have annual rents as 6.35, 5.69, 5.89, 4.13 Million Euros for Riga, Bucharest, Berlin and London facilities respectively. Therefore, these facilities may or may not be opened depending on your model. The project team that is formed by the members of Logistics and Production departments has given you the production costs per facility and the shipping costs as in table 1 below. Table 1. Production + Shipping Costs Eastern Europe Southern Europe Western Europe UK & Ireland Riga 312 446 464 398 Bucharest 377 336 367 410 Berlin 331 336 389 466 London 392 392 431 375 You have also requested the annual demand of each region and it is given in the table 2 below: Table 2. Annual Demand of Each Region Eastern Europe Southern Europe western Europe 110,000 UK & Ireland 120,000 140,000 50,000 Additionally, you have been requested to consider the following limitations. • Either London or Bucharest facilities must be opened. (Note: Both can be open at the same time) • If Riga and Bucharest facilities are opened, then Berlin facility cannot be opened. • If Berlin and London facilities are opened, then Bucharest must not be opened while Riga must be opened. Note: Formulate your IP in an open form and while formulating it, give index (or indices), decision variable(s) and parameter(s), explicitly to receive credits. Use f & g functions and find the values of M when necessary to receive credits. You are working as an Operations Research Intern at the European Headquarters of a single- type car manufacturer. As today's task, you have been asked to model an IP which should be developed to minimize the annual cost of meeting the demand of cars where all parameters of the problem are deterministic. The company is currently discussing of producing the cars in four factories which are located in Riga, Bucharest, Berlin and London. Each facility can produce as many as 140,000 cars annually and have annual rents as 6.35, 5.69, 5.89, 4.13 Million Euros for Riga, Bucharest, Berlin and London facilities respectively. Therefore, these facilities may or may not be opened depending on your model. The project team that is formed by the members of Logistics and Production departments has given you the production costs per facility and the shipping costs as in table 1 below. Table 1. Production + Shipping Costs Eastern Europe Southern Europe Western Europe UK & Ireland Riga 312 446 464 398 Bucharest 377 336 367 410 Berlin 331 336 389 466 London 392 392 431 375 You have also requested the annual demand of each region and it is given in the table 2 below: Table 2. Annual Demand of Each Region Eastern Europe Southern Europe western Europe 110,000 UK & Ireland 120,000 140,000 50,000 Additionally, you have been requested to consider the following limitations. • Either London or Bucharest facilities must be opened. (Note: Both can be open at the same time) • If Riga and Bucharest facilities are opened, then Berlin facility cannot be opened. • If Berlin and London facilities are opened, then Bucharest must not be opened while Riga must be opened. Note: Formulate your IP in an open form and while formulating it, give index (or indices), decision variable(s) and parameter(s), explicitly to receive credits. Use f & g functions and find the values of M when necessary to receive credits.

Answer rating: 100% (QA)

1 Producing all the quantity demanded from the production facilities costing least in terms of transportation which is calculated as below Region Annual Demand Eastern Europe 120000 Southern Europe 11... View the full answer