Assignment:
Q: A project manager is in charge of 3 ongoing projects, A, B, and C. Due to recent reorganization, the project manager can assign additional employees to the 3 projects. Each employee who is assigned to a project can reduce the time to complete the project. The table below summarizes the data for the 3 projects. For instance, at most 5 employees may be assigned to project A. Each employee assigned to project A reduces the completion time by 3 days. (For example, if 3 employees are assigned to project A, its completion time is reduced by 9 days.) Total 11 employees are available. The project manager must maximize the least reduction among all 3 projects. For instance, if we can reduce the completion time of projects A, B, and C by 6, 8, and 9 days, respectively, the least reduction among all 3 projects is 6 days. Please formulate an LP model that helps the project manager assign the 11 employees. Please use GAMS to find the optimal solution and optimal value.
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Projects
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A
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B
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C
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Maximum Number of Employees
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5
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6
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3
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Reduction of Completion Time (days / employee)
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3
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9
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3
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