Task Completion
In the Generalized Assignment Problem (GAP), we have a set of m 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 bi units of one specific resource, i = 1, . . . ,m. When machine i performs task j, the machine faces a cost equal to cij and consumes a, 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 die 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.
The curriculum is some chapters in the two following books: Wisniewski, M. (2016), Quantitative methods for decision makers, 6th edn. Pearson Albright, S.C., Winston, W.L. and Zappe, C. (2011), Data Analysis, Optimization, and Simulation Modeling (UK: Thomson Southwestern). ISBN 978-0538476768. Chapter 2.
Attachment:- Assignment Files.rar