Markovian Approach to Forecasting Personnel Populations and Costs

The Board of Education in New York City typically negotiated three-year contracts with their staff. It was found that costs over the three-year period invariably exceeded projections by 10%–20%. An analysis showed that although the number of employees was relatively constant, the distribution of employees with respect to salary levels had changed significantly. As a result, projections of salary costs were substantially understated. Over the course of the contract term, salaries increased due to longevity and additional employee education. Classic methods for forecasting costs include regression analyses, time series analysis, and simulation methods. Markov chains have also been used to project population changes over time. In this paper, we present a Markov chain model that was successfully used to forecast teacher populations as well as costs with much greater precision than had been possible previously. The model incorporated personnel as well as cost projections. For a given total salary budget, management was thus able to place salary increases in levels so as to keep costs to a minimum. As a result, management was able to obtain significant reductions in labor costs. In addition, the model can help by incorporating issues of diversity and inclusion in the workplace. By being able to track where employees would likely be down the line, a fairer distribution could be achieved.