A Markovian manpower planning, human resource valuation model

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Tech


The purpose of this dissertation is to formulate a quantitative model which can be used in two areas: (1) manpower planning, and (2) human resource valuation. The techniques used are based on an absorbing Markov model. A conceptual model is developed for any firm that has employees who normally move from one position to another within the firm.

The conceptual model is applied to a large Certified Public Accounting (CPA) firm. Some of the data used in the application were supplied by an actual firm. These data were used to develop a transition matrix for the firm. The transient states of the matrix correspond to the employment positions within the firm, i.e., staff, manager, and partner. The absorbing states of the matrix were for employees leaving the firm (1) before becoming a partner, or (2) after becoming a partner. The elements of the transition matrix are the probabilities of employees making certain movements (staff to staff, staff to manager, etc.) during each one-year transition period. These probabilities are based on historic data and must pass a stability test (Chi square) in order to be statistically valid. The original transition matrix covered a ten year time period (February 1, 1967 to January 31, 1977). However, the transition probabilities for staff and managers were found to be unstable according to the Chi square test. A matrix covering the nine year period from February 1, 1968 to January 31, 1977 was tested with the same results. After further tests, a transition matrix for the five-year period from February 1, 1972 to January 31, 1977, was found to be stable. This became the model transition matrix.

The transition matrix should also be tested for the Markov property, i. e., are the transition probabilities affected by the employee's time in grade at his present position? This test was only simulated for the CPA firm because the data needed for the test were not available.

After the tests, the model was extended into manpower planning and human resource valuation. Examples of model output that can be helpful for manpower planning include predicted numbers of employees at each level,during future transition periods t probabilities of employees rising to each level within the firm, steady-state information on manpower supply, and average employee tenure with the firm. For human resource valuation, the model is the basis for three methods for charging cost; based valuations against income. The first method is an amortization technique based on an employee's average tenure with the firm. The second method amortizes human resource costs over a period equal to average tenure plus three standard deviations.