(Part Assignment) As an illustration of the assignment model…
(Part Assignment) As an illustration of the assignment model, let us consider the case of Fix-It Shop, which has just received three new rush projects to repair: (1) a radio, (2) a toaster oven, and (3) a coffee table. Four workers, each with different talents and abilities, are available to do the jobs. The Fix-It Shop owner estimates what it will cost in wages to assign each of the workers to each of the three projects. The costs, which are shown in the below table, differ because the owner believes that each worker will differ in speed and skill on these quite varied jobs. The owner’s objective is to assign the three projects to the workers in a way that will result in the lowest total cost to the shop. Note that the assignment of people to projects must be on a one-to-one basis; each project must be assigned to one worker. Note that one worker will not be assigned. Person Project 1 2 3 David 8 14 6 Eve 9 10 11 Frank 8 12 7 Glory 4 10 8 We now develop the LP model for Fix-It Shop’s example. Let Xij = Flow on the arc from node denoting worker i to node denoting project j. The solution value will equal 1 if worker i is assigned to project j, and will equal 0 otherwise, where i = D (for David), E (for Eve), F (for Frank), G (for Glory). j = 1 (for project 1), 2 (for project 2), 3 (for project 3). For example, XD1 = Flow on the arc from worker David to Project 1. (Part Assignment) Write the objective function only (in terms of XD1, XD2, XD3, XE1, XE2, XE3, XF1, XF2, XF3, XG1, XG2, XG3). This is NOT an excel function.
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