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9.2 Barge loading A shipper on the river Rhine owns a barge of carrying capacity 1500 m'. Over time he has specialized in the transport of wheat. He has seven regular customers who load and unload practically at the same places. The shipper knows his costs of transport from long experience and according to his personal preferences has concluded agreements with his clients for the price charged to them for the transport of their wheat. The following table summarizes the information about the seven clients. Every client wishes to tranport a certain number of lots, deciding himself the size of his lots in m'. The table lists the price charged by the shipper for every transported lot. The last column of the table contains the cost incurred by the shipper per transported m'. This cost differs depending on the distance covered. Client 2 3 4 5 6 Table 9.3: Lots to transport Available quantity Lot size Price per Transport (ne. of lots) (in m) lot (in cost in /m') 12 10 1000 80 600 70 20 6 600 85 25 9 800 BO 50 15 1200 73 40 10 800 70 12 1100 80 'The reader is reminded that it is possible to visualize the output of the optimizer by adding the line Betparan (XPRS_VERBOSE", true) before the optimization statement. In Xpress-IVE, the tree search can be w. sualized directly 126 Loading and cutting problems Applications of optimization with Xpress-MP The objective of the shipper is to maximize his profit from transporting the wheat with lots that may be divided Question 1: As a first step, assuming that every client has an unlimited quantity of wheat, which clients' wheat should be transported? Question 2: If in addition the actual availability of wheat lots from the customers is taken into account, which strategy should the shipper adopt? Question 3: What happens if the lots cannot be divided? 9.2 Barge loading A shipper on the river Rhine owns a barge of carrying capacity 1500 m'. Over time he has specialized in the transport of wheat. He has seven regular customers who load and unload practically at the same places. The shipper knows his costs of transport from long experience and according to his personal preferences has concluded agreements with his clients for the price charged to them for the transport of their wheat. The following table summarizes the information about the seven clients. Every client wishes to tranport a certain number of lots, deciding himself the size of his lots in m'. The table lists the price charged by the shipper for every transported lot. The last column of the table contains the cost incurred by the shipper per transported m'. This cost differs depending on the distance covered. Client 2 3 4 5 6 Table 9.3: Lots to transport Available quantity Lot size Price per Transport (ne. of lots) (in m) lot (in cost in /m') 12 10 1000 80 600 70 20 6 600 85 25 9 800 BO 50 15 1200 73 40 10 800 70 12 1100 80 'The reader is reminded that it is possible to visualize the output of the optimizer by adding the line Betparan (XPRS_VERBOSE", true) before the optimization statement. In Xpress-IVE, the tree search can be w. sualized directly 126 Loading and cutting problems Applications of optimization with Xpress-MP The objective of the shipper is to maximize his profit from transporting the wheat with lots that may be divided Question 1: As a first step, assuming that every client has an unlimited quantity of wheat, which clients' wheat should be transported? Question 2: If in addition the actual availability of wheat lots from the customers is taken into account, which strategy should the shipper adopt? Question 3: What happens if the lots cannot be divided