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 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 projects is 6 days.
Please formulate an LP model that helps the project manager assign the employees. Please use GAMS to find the optimal solution and optimal value.
|
Projects
|
A
|
B
|
C
|
|
Maximum Number of Employees
|
5
|
6
|
3
|
|
Reduction Of Completion Time(days/employee)
|
3
|
9
|
3
|