Jobs at Indiana University are rated on three factors:
■ Factor 1: Complexity of duties
■ Factor 2: Education required
■ Factor 3: Mental and/or visual demands
For each job at IU, the requirement for each factor has been rated on a scale of 1 to 4, with a 4 in factor 1 representing high complexity of duty, a 4 in factor 2 representing high educational requirement, and a 4 in factor 3 representing high mental and/or visual demands. IU wants to determine a formula for grading each job. To do this, it will assign a point value to the score for each factor that a job requires. For example, suppose that level 2 of factor 1 yields a point total of 10, level 3 of factor 2 yields a point total of 20, and level 3 of factor 3 yields a point total of 30. Then a job with these requirements has a point total of 10 + 20 + 30 = 60. A job’s hourly salary equals half its point total. IU has two goals (listed in order of priority) in setting up the points given to each level of each job factor.
■ Goal 1: When increasing the level of a factor by 1, the points should increase by at least 10. For example, level 2 of factor 1 should earn at least 10 more points than level 1 of factor 1. Goal 1 is to minimize the sum of deviations from this requirement.
■ Goal 2: For the benchmark jobs referred to in the file P16_38.xlsx, the actual point total for each job should come as close as possible to the point total listed in the table. Goal 2 is to minimize the sum of the absolute deviations of the point totals from the desired scores.
Use goal programming to find appropriate point totals. What salary should a job with skill levels of 3 for each factor be paid?