A shipping company needs to purchase a fleet of ships to carry cargo between six cities...
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A shipping company needs to purchase a fleet of ships to carry cargo between six cities along four specific routes. The following table provides the routes and the number of ships required for each route. Route 1 2 3 4 Origin Dhahran Marseilles Naples New York Istanbul Mumbai New York Marseilles Destination Number of Ships Required per Day 8 8 321 All cargo can be moved on the same type of ship. The following table provides the travel time between the various cities in days: 1 Naples Marseilles Istanbul New York Dhahran Mumbai 0 Naples 1 2 7 Marseilles 1 0 3 8 Istanbul 2 3 0 5 14 New York 13 15 20 Dhahran 7 5 3 Mumbai 7 5 0 14 13 15 0 17 20 71003 8 It takes one day to unload and one day to load each ship. (a) Model the problem is deciding how many ships to purchase as a linear program. Hint: You'll need two families of constraints. One to model the requirement that each ship is reassigned to a new route after completing a route and second to ensure that each route gets its required number of ships each day. Hint: I suggest using the decision variable xi; to represent the number of ships reassigned from route i to route j. You'll need to associate a cost for each (i, j) pair with the number of ships needed to ensure that daily demand is continuously met along route j by taking ships from route i. A shipping company needs to purchase a fleet of ships to carry cargo between six cities along four specific routes. The following table provides the routes and the number of ships required for each route. Route 1 2 3 4 Origin Dhahran Marseilles Naples New York Istanbul Mumbai New York Marseilles Destination Number of Ships Required per Day 8 8 321 All cargo can be moved on the same type of ship. The following table provides the travel time between the various cities in days: 1 Naples Marseilles Istanbul New York Dhahran Mumbai 0 Naples 1 2 7 Marseilles 1 0 3 8 Istanbul 2 3 0 5 14 New York 13 15 20 Dhahran 7 5 3 Mumbai 7 5 0 14 13 15 0 17 20 71003 8 It takes one day to unload and one day to load each ship. (a) Model the problem is deciding how many ships to purchase as a linear program. Hint: You'll need two families of constraints. One to model the requirement that each ship is reassigned to a new route after completing a route and second to ensure that each route gets its required number of ships each day. Hint: I suggest using the decision variable xi; to represent the number of ships reassigned from route i to route j. You'll need to associate a cost for each (i, j) pair with the number of ships needed to ensure that daily demand is continuously met along route j by taking ships from route i.
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Lets go through the workings of the linear program step by step Decision Variables Let ri j represent the number of ships reassigned from route i to r... View the full answer
Related Book For
Essentials of Business Analytics
ISBN: 978-1285187273
1st edition
Authors: Jeffrey Camm, James Cochran, Michael Fry, Jeffrey Ohlmann , David Anderson, Dennis Sweeney, Thomas Williams
Posted Date:
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