3. (24 marks) Firelands Electronic has plants at two locations manufacturing heat sinks to be used in computers. The monthly production levels of the plants at location 1 and location 2 are 10,000 units and 8,000 units respectively. The units are shipped to one of the three warehouses at locations A, B and C and then to one of the three destinations at locations D, E and F. The monthly demands of these three destinations are 6,000, 6,500 and 5,000 units respectively. All possible shipping routes and the corresponding shipping costs (in dollars) per unit are shown in the tables below. A 1 N.A. ki B 5 6 2 4 3 D E F A 8 7 NA B NA 5 6 N.A. kz kg While each N.A. means the corresponding shipping route does not exist, it is possible to ship from location 1 directly to D at a unit shipping cost of $11, and from warehouse A to warehouse B (if need be) at a unit shipping cost of $4. (a) Draw a complete network representation of the problem. Label the nodes with 1, 2, A, B, C, D, E and F. (b) The objective is to minimize the total shipping cost. Let xij be the number of units to be shipped from node i to node j. Find the constraint associated with each node. (c) In addition to the constraints above, there are other constraints shown in the table below. Find a mathematical description for each of those constraints. Constraint Description ci Shipment from location 1 to B must be at least 4,000 units. D cannot receive more units directly from location 1 than from A A cannot handle more than 6,000 units at a time. B cannot handle more than 8,500 units at a time. C cannot handle more than 7,000 units at a time C2 C3 C4 CS 3. (24 marks) Firelands Electronic has plants at two locations manufacturing heat sinks to be used in computers. The monthly production levels of the plants at location 1 and location 2 are 10,000 units and 8,000 units respectively. The units are shipped to one of the three warehouses at locations A, B and C and then to one of the three destinations at locations D, E and F. The monthly demands of these three destinations are 6,000, 6,500 and 5,000 units respectively. All possible shipping routes and the corresponding shipping costs (in dollars) per unit are shown in the tables below. A 1 N.A. ki B 5 6 2 4 3 D E F A 8 7 NA B NA 5 6 N.A. kz kg While each N.A. means the corresponding shipping route does not exist, it is possible to ship from location 1 directly to D at a unit shipping cost of $11, and from warehouse A to warehouse B (if need be) at a unit shipping cost of $4. (a) Draw a complete network representation of the problem. Label the nodes with 1, 2, A, B, C, D, E and F. (b) The objective is to minimize the total shipping cost. Let xij be the number of units to be shipped from node i to node j. Find the constraint associated with each node. (c) In addition to the constraints above, there are other constraints shown in the table below. Find a mathematical description for each of those constraints. Constraint Description ci Shipment from location 1 to B must be at least 4,000 units. D cannot receive more units directly from location 1 than from A A cannot handle more than 6,000 units at a time. B cannot handle more than 8,500 units at a time. C cannot handle more than 7,000 units at a time C2 C3 C4 CS
