I need to find optimum weekly targets for an 8-week period for a group of employees. The end result expected is maximum of sum of percentage of times the employees met the goal in each week. I am doing the "percentage met" calculation on a dataset containing past performance of employees on the tasks.
My decision variable is the weekly improvement percentage (weekly_share). This will reduce the existing goals by the said percentage in each week, starting from 10% in Week 1 and ending at 100% in Week 8.
For each week, percentage of meeting revised goal calculated using
weekly improvement= 100 x (count of Tasks Completed x 3600) / (Total work time in week x existing goal x weekly_share)
I wanted to maximize the sum of these percentages for all 08 weeks
I have set the following constraints: a) for week 1, weekly_share>= 10% b) for all weeks from 2-8, weekly_share >= weekly_share in previous week (week 2>= week 2, etc) c) weekly_share for 8th week = 100%
When using Excel Solver, I do not get a solution in Simplex LP (error in either objective or constraint cell). With GRG Nonlinear and Evolutionary, the weekly_share are set to the lower limit (since it is in the denominator, the lowest value gives the highest ratio).
How can I solve this?