In the Generalized Assignment Problem (GAP), we have a set of machines and a set of...

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In the Generalized Assignment Problem (GAP), we have a set of machines and a set of tasks. The machines need to perform the tasks, while each task has to be performed by exactly one machine. Machine i has available b, units of one specific resource, i=1,..., m. When machine i performs taskj, the machine faces a cost equal to c, and consumes an units of resource, i=1,...,m, j-1,...,n. The goal of the GAP is to perform all the tasks at minimum cost, while not violating the capacities on the resources. Address the following questions, making sure to describe the modeling approach used: (i) Solve the GAP using the data provided in gap.xlsx, with m-3 and n=20. (ii) Perform a sensitivity analysis to the availability of the resource at the machines. (iii) Discuss the modeling of the version of the GAP, in which additional capacity on the resource can be acquired. (iv) Discuss the modeling of the version of the GAP, in which the cost faced by the machines when performing the tasks is uncertain. (v) Discuss the modeling of the multi-resource version of the GAP, in which while performing the tasks, we consume several resources. For simplicity, you can assume that two resources are being consumed. (vi) With the help of an example, illustrate how Business Analytics tools are used when managing human capital. Excel shoot for the task: 1 2 3 4 5 6 7 B 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A I 1 2 3 4 5 6 7 8 9 10 8555555 12 13 14 15 16 17 18 19 20 B e_(11) 2 10 4 4 6 9 6 6 2 8 2 7 5 9 4 8 10 1 7 1 С c_(21) 3 3 4 5 6 6 4 6 7 3 5 5 3 8 4 4 5 8 1 7 D *_(4)| 4 7 9 4 2 3 10 2 6 5 6 3 8 1 7 11 5 9 8 8 E a [18] 200 492 220 258 351 323 167 157 2:30 440 500 281 321 395 223 456 312 620 219 540 F (21) 240 600 220 190 351 365 176 157 165 540 340 432 345 395 198 643 600 300 340 339 G (31) 220 518 191 230 400 390 123 265 230 690 207 512 233 548 165 333 600 300 219 339 H E 1 1 2 3 J b_(1) 2000 2000 2000 In the Generalized Assignment Problem (GAP), we have a set of machines and a set of tasks. The machines need to perform the tasks, while each task has to be performed by exactly one machine. Machine i has available b, units of one specific resource, i=1,..., m. When machine i performs taskj, the machine faces a cost equal to c, and consumes an units of resource, i=1,...,m, j-1,...,n. The goal of the GAP is to perform all the tasks at minimum cost, while not violating the capacities on the resources. Address the following questions, making sure to describe the modeling approach used: (i) Solve the GAP using the data provided in gap.xlsx, with m-3 and n=20. (ii) Perform a sensitivity analysis to the availability of the resource at the machines. (iii) Discuss the modeling of the version of the GAP, in which additional capacity on the resource can be acquired. (iv) Discuss the modeling of the version of the GAP, in which the cost faced by the machines when performing the tasks is uncertain. (v) Discuss the modeling of the multi-resource version of the GAP, in which while performing the tasks, we consume several resources. For simplicity, you can assume that two resources are being consumed. (vi) With the help of an example, illustrate how Business Analytics tools are used when managing human capital. Excel shoot for the task: 1 2 3 4 5 6 7 B 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A I 1 2 3 4 5 6 7 8 9 10 8555555 12 13 14 15 16 17 18 19 20 B e_(11) 2 10 4 4 6 9 6 6 2 8 2 7 5 9 4 8 10 1 7 1 С c_(21) 3 3 4 5 6 6 4 6 7 3 5 5 3 8 4 4 5 8 1 7 D *_(4)| 4 7 9 4 2 3 10 2 6 5 6 3 8 1 7 11 5 9 8 8 E a [18] 200 492 220 258 351 323 167 157 2:30 440 500 281 321 395 223 456 312 620 219 540 F (21) 240 600 220 190 351 365 176 157 165 540 340 432 345 395 198 643 600 300 340 339 G (31) 220 518 191 230 400 390 123 265 230 690 207 512 233 548 165 333 600 300 219 339 H E 1 1 2 3 J b_(1) 2000 2000 2000

Answer rating: 100% (QA)

Here are the answers to the questions 1 Solve the GAP using the data provided in gapxlsx with 3 machines and 20 tasks To solve this GAP we can formulate it as an integer program Let xij be a binary de... View the full answer