Question 8 (4 points) A liner shipping company operates three routes as follows. 2 days 3 days 6 days 5 days Route 1: Nansha Chiwan Hong Kong - Singapore Nansha 3 days 2 days 5 days Route 2: Tianjin Shanghai Hong Kong Tianjin 3 days 4 days 6 days 9 days Route 3: Karachi - Nhava Sheva Colombo - Singapore Karachi The sailing time between two ports on each route is also shown in the above figure, and the time spent at each port is assumed to be 0. Each route will serve only once. Ships 1, 2, and 3 with the same capacity of 5000 containers are deployed on Routes 1, 2, and 3, respectively, and each ship will depart from the first port of each route at day 0. The company receives some container shipment requests, and each request corresponds to an origin-destination (OD) pair of ports. The OD pairs, the demand, and the freight rate are shown in Table 8.1. Table 8.1: OD pair information Origin port Destination port Demand (container) Freight rate per container ($) Chiwan Singapore 1500 50 Shanghai Nansha 1000 65 Colombo Karachi 800 45 Nansha Karachi 1200 70 Tianjin Hong Kong 2000 45 The containers in Ships 1 and 2 can be transshipped to each other when they visit Hong Kong port. The containers in Ship 1 can also be transshipped to Ship 3 at Singapore port, while the containers in Ship 3 cannot be transshipped to Ship 1, because Ship 1 will visit Singapore port earlier than Ship 3. The transshipment cost is $10 per container (other costs will not be considered here). Formulate an LP/IP/MIP model that can be used to determine the volume of accepted containers for the demand of each OD pair to maximize the expected profit of the liner shipping company. (4 points) Question 8 (4 points) A liner shipping company operates three routes as follows. 2 days 3 days 6 days 5 days Route 1: Nansha Chiwan Hong Kong - Singapore Nansha 3 days 2 days 5 days Route 2: Tianjin Shanghai Hong Kong Tianjin 3 days 4 days 6 days 9 days Route 3: Karachi - Nhava Sheva Colombo - Singapore Karachi The sailing time between two ports on each route is also shown in the above figure, and the time spent at each port is assumed to be 0. Each route will serve only once. Ships 1, 2, and 3 with the same capacity of 5000 containers are deployed on Routes 1, 2, and 3, respectively, and each ship will depart from the first port of each route at day 0. The company receives some container shipment requests, and each request corresponds to an origin-destination (OD) pair of ports. The OD pairs, the demand, and the freight rate are shown in Table 8.1. Table 8.1: OD pair information Origin port Destination port Demand (container) Freight rate per container ($) Chiwan Singapore 1500 50 Shanghai Nansha 1000 65 Colombo Karachi 800 45 Nansha Karachi 1200 70 Tianjin Hong Kong 2000 45 The containers in Ships 1 and 2 can be transshipped to each other when they visit Hong Kong port. The containers in Ship 1 can also be transshipped to Ship 3 at Singapore port, while the containers in Ship 3 cannot be transshipped to Ship 1, because Ship 1 will visit Singapore port earlier than Ship 3. The transshipment cost is $10 per container (other costs will not be considered here). Formulate an LP/IP/MIP model that can be used to determine the volume of accepted containers for the demand of each OD pair to maximize the expected profit of the liner shipping company. (4 points)
