INAR implementation of newsvendor model for serially dependent demand counts

The classic newsvendor model was developed under the assumption that period-to-period demand is independent over time. In real-life applications, the notion of independent demand is often challenged. In this paper, we propose a dynamic implementation of the newsvendor model based on a class of integer-valued autoregressive (INAR) models when facing correlated discrete demand. Motivated by application, we consider INAR models with underlying Poisson error innovations and with underlying negative-binomial error innovations to accommodate overdispersion scenarios. We numerically compare our proposal with the standard newsvendor solution and with a standard autoregressive-based newsvendor solution. Our results show that an appropriately specified INAR-based newsvendor solution not only outperforms the standard case but also the approximating forecasting approaches. Moreover, even in the presence of autocorrelation, the use of the standard autoregressive model as an approximating approach can lead to increased costs over and above the standard implementation of the newsvendor model based on no forecasting.