Deterministic conversion of uncertain manpower planning optimization problem

Abstract

Manpower planning is a very important component of human resource management. However, there are many indeterminate factors that should be taken into consideration in manpower planning. For example, the decision of employees to quit the job is determined by their preference, which is beyond the control of human resource department. It can be realistically modeled as a random variable when the historical data of quitting rate is large enough. Otherwise, it can only be regarded as an uncertain variable when the historical data is inadequate. In this paper, we discuss a manpower planning optimization problem for a manufacturing company with hierarchical system, where the quitting rate of employees is modeled as an uncertain variable. First, we formulate a mathematical model for this uncertain manpower planning optimization problem, where the influence on the production outputs by employees is taken into consideration. Second, we present a deterministic conversion method to transform this uncertain manpower planning optimization problem into an equivalent deterministic discrete-time optimization problem. It is further converted into an equivalent linear programming model with an equality constraint and an inequality constraint. Finally, we use the real data from Singapore, Denmark and China to carry out a numerical simulation and make a comparison with the results obtained based on stochastic model to show the advantages of our method.