Improving Productivity by Periodic Performance Evaluation: A Bayesian Stochastic Model

We model the situation where the productivity of members of a group, such as a salesforce, is periodically evaluated; those whose performance is sub-par are dismissed and replaced by new members. Individual productivity is modeled as a random variable, the distribution of which is a function of an unknown parameter. This parameter varies across the members of the group and is specified by a prior distribution. In this manner, the heterogeneity in the group is explicitly accounted for. We model the situation as a parameter adaptive Bayesian stochastic control problem, and use dynamic programming techniques and the appropriate optimality equations to obtain solutions. We prove the existence of an optimal policy in the general case. Further, for the case when the sales process can be characterized by a Beta-Binomial or a Gamma-Poisson distribution, we show that the optimal policy is of the threshold type at each evaluation period, depending only on the accumulated performance up to a given period. We present a computational procedure to solve for the optimal thresholds. Results of computational experiments show that an increase in the heterogeneity of the group can lead to more stringent levels of minimal acceptable performance.