Poor and Sick Newsboy Model : A Robust Generalisation with Misspecified Demand

Newsboy problem is one of the most widely discussed inventory control problems. We start with a generalisation of the newsboy problem for critical perishable commodities, where the shortage and excess are of much higher importance than merely the quantity lost. In particular, we develop the parametric optimal order quantity estimation method in the generalised newsboy problem with log-Normal and Gamma demand distributions. We also construct the maximum likelihood estimators using the first order condition of the stochastic optimisation problem based on uncensored sample data. We present the performance study of the maximum likelihood estimators using Monte-Carlo simulation experiments. We have also discussed the nonparametric estimator of the optimal order quantity. Another important contribution of this paper is the detailed study of the impact of misspecified demand distribution. In this regard, we assume a popular demand model, viz. uniform or exponential, as the misspecified demand distribution in place of log-Normal and Gamma one of the true densities. We consider two types of misspecifications, namely complete and partial misspecification. We present the estimates of the optimal order quantity under complete misspecification. For partial misspecification, we present an extensive Monte-Carlo simulation based performance study of the non-parametric estimator of optimal order quantity with its misspecified counterparts. Our extensive simulation study shows that the non-parametric estimator performs quite well than its parametric counterpart under partial misspecification