Task completion

In the Generalized Assignment Problem (GAP), we have a set of in machines and a set of n tasks. The machines need to perform the tasks, while each task has to be performed by exactly one machine. Machine i has available b_i units of one specific resource, I = 1, ..., m. When machine i performs task j, the machine faces a cost equal to c_ij and consumes a_ij 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.