[Solved]1 Application Branch Bound Algorithm Given Set Machines 1m 2m 3m 4m 5m Set Cost Process Ma Q37218303
1. This is an application of the Branch and Bound algorithm. Given a set of Machines, (1M, 2M, 3M, 4M, 5M, and a set of Cost: Process to Machine Processes, (A, B, C, D, E), with the cost of assigning Process P to Machine M as shown in the table at right, the assignment prob- lem requires finding a one-to-one matching of these 5 processes to the 5 machines which minimizes the sum of the costs. A 4 8 13 2 3 B2 610 12 9 CII 10 | 5 | 6 | 4 | 18 Table I below represents the left-most branch of a search space tree where we assign Process A to Machine 1, Process B to Ma D 8 4 13 54 chine 2, and so on. Eİİ 4 | 7 | 1 | 15 | 3 Directions: First, determine the cost of the assignments in the first row of Table I below and use it as the initial bounding value. Then apply the Branch & Bound algorithm to subsequent rows, circling the assignment (letter and cost) which causes the algorithm to prune a branch. When a branch is pruned, do not record the total In Table II, use the last bound obtained in Table I to continue the process. Table I Table I 1 2 3 4 5 Total ABIC D E 1 23 4 5 Total BDİA C E 2 4 13 4 3 BDİA EC 2 4 13 15 18- BDİC AE ABIC E D 4 6 6 15 4 A B D C E 4 6 13 4 3 BİDE BDİC E A 2 4 6 15 3 461131518= ABİE CD 2 4 1 2 18 BDİE C A ABİE DC Show transcribed image text 1. This is an application of the Branch and Bound algorithm. Given a set of Machines, (1M, 2M, 3M, 4M, 5M, and a set of Cost: Process to Machine Processes, (A, B, C, D, E), with the cost of assigning Process P to Machine M as shown in the table at right, the assignment prob- lem requires finding a one-to-one matching of these 5 processes to the 5 machines which minimizes the sum of the costs. A 4 8 13 2 3 B2 610 12 9 CII 10 | 5 | 6 | 4 | 18 Table I below represents the left-most branch of a search space tree where we assign Process A to Machine 1, Process B to Ma D 8 4 13 54 chine 2, and so on. Eİİ 4 | 7 | 1 | 15 | 3 Directions: First, determine the cost of the assignments in the first row of Table I below and use it as the initial bounding value. Then apply the Branch & Bound algorithm to subsequent rows, circling the assignment (letter and cost) which causes the algorithm to prune a branch. When a branch is pruned, do not record the total In Table II, use the last bound obtained in Table I to continue the process. Table I Table I 1 2 3 4 5 Total ABIC D E 1 23 4 5 Total BDİA C E 2 4 13 4 3 BDİA EC 2 4 13 15 18- BDİC AE ABIC E D 4 6 6 15 4 A B D C E 4 6 13 4 3 BİDE BDİC E A 2 4 6 15 3 461131518= ABİE CD 2 4 1 2 18 BDİE C A ABİE DC
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Answer to 1. This is an application of the Branch and Bound algorithm. Given a set of Machines, (1M, 2M, 3M, 4M, 5M, and a set of … . . .
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