DFCivil is a Turkish company located in istanbul (i). DFCivil is considering sending orders to customers...

  

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DFCivil is a Turkish company located in istanbul (i). DFCivil is considering sending orders to customers in Los Angeles (LA) through Milano (M) and Rotterdam (R) route. Hence the route is istanbul-Milano-Rotterdam-Los Angeles. The company has the option to choose a different mode of transportation for each segment of the route. The costs for each mode of transportation used at each segment are given below. These costs are total costs for shipments between segments and do not depend on the volume of the shipment. Note that some of the modes are not available (NA) for some segments. City Pair Mode İ-M M-R R-LA $500 $400 $600 $400 Rail NA Highway NA Sea NA NA $2400 Moreover, there is a cost for changing the transportation mode at each city. These costs are given in the table below. The costs of initial loading at istanbul and final unloading at Los Angeles are assumed to be zero. To Rail Highway $150 $0 Sea Rail $0 $200 5 Highway $100 $200 $150 Sca $100 $0 The company wants to minimize its shipment cost by using the appropriate modes of transportation at each segment. a) (15 points) Formulate a mathematical model in open form that can be used to minimize the total cost of the shipment. Define your decision variables. Discuss the objective function and each constraint. DFCivil is a Turkish company located in istanbul (i). DFCivil is considering sending orders to customers in Los Angeles (LA) through Milano (M) and Rotterdam (R) route. Hence the route is istanbul-Milano-Rotterdam-Los Angeles. The company has the option to choose a different mode of transportation for each segment of the route. The costs for each mode of transportation used at each segment are given below. These costs are total costs for shipments between segments and do not depend on the volume of the shipment. Note that some of the modes are not available (NA) for some segments. City Pair Mode İ-M M-R R-LA $500 $400 $600 $400 Rail NA Highway NA Sea NA NA $2400 Moreover, there is a cost for changing the transportation mode at each city. These costs are given in the table below. The costs of initial loading at istanbul and final unloading at Los Angeles are assumed to be zero. To Rail Highway $150 $0 Sea Rail $0 $200 5 Highway $100 $200 $150 Sca $100 $0 The company wants to minimize its shipment cost by using the appropriate modes of transportation at each segment. a) (15 points) Formulate a mathematical model in open form that can be used to minimize the total cost of the shipment. Define your decision variables. Discuss the objective function and each constraint.