Product recall timing optimization using dynamic programming

In this paper we treat the optimal timing of product recall decisions as a dynamic process with defect rate as a random variable. We first develop an optimal stopping model where the defect rate is a beta random variable that is constant across all periods. We solve the problem using stochastic dynamic programming (DP) and develop thresholds for optimal stopping based on the observed value of the number of returns as a state variable. We then extend the model where the beta defect rate random variable is revised using Bayesian updating in each period after observing the number of product returns from the preceding period. Employing the conjugate property of the beta and binomial, we again solve the problem as a stochastic DP and determine the thresholds based on the values of the state vector with three variables. We show that for the more general version, the computational difficulty increases dramatically with problem size. For this problem we present a simulation optimization approach that selects the best functional form for the threshold curve. Several examples and managerial insights illustrate our findings.