数学建模竞赛1995 B O The World’s Most Complicated Payroll定稿.pdfVIP

The World’s Most Complicated Payroll 275 The World’s Most Complicated Payroll Frank Thorne W. Garrett Mitchener Marci Gambrell North Carolina School of Science and Mathematics Durham, NC 27705 Advisor: Dot Doyle Introduction We present a model for paying the faculty that we believe is fair and consistent with the requirements, as well as ways of dealing with cost-of- living increases, budget shortages, and the transition process. We use a two-track salary model: All of the instructors are on one track while all of the Ph.D.s are on the other. To accommodate both seniority and rank elements into our model, we make salary a function of “quality points,” an index that incorporates both seniority and rank for Ph.D.s but just seniority in instructors. We use part of a root function as our salary function for both tracks and make the slope of the instructor function half that of the Ph.D. function. Furthermore, we designed a transition process for instructors promoted to assistant professor. To incorporate cost-of-living raises, our salary func- tions work in constant dollars. To deal with budget deficits, we let pro- motions happen as normally but also give out fractional quality points and make up the difference later. Our model does not provide for drastic deficits; these would require major changes, such as cuts or layoffs, which we leave as the business of the administration. To create a transition process, we give all faculty making more money than they should (as determined by the model) a minimum $100 raise each year (in real, not constant, dollars) until they are on the track as they should be, and divert the remaining money into extra raises for the financially challenged. Estimating some data that were not provided, we determined that 95% of the overpaid faculty would be on the proper payroll track within 4.6 years, meaning that with the exc