The robust min-max newsvendor problem with balking under a service level constraint

In this paper we study an extension of a classic newsvendor model with balking under a service-level constraint. We also relax the assumption that the demand distribution is fully available to a decision-maker; we assume that only the mean and variance of the demand distribution are known, and discuss the procedure for determining the optimal order quantity for the concomitant model. We further extend our base model to two different cases: (i) when the fixed ordering cost is included, and (ii) when yield is uncertain. We illustrate the solution procedures for each case with numerical examples. Moreover, we discuss the performance and robustness of the approach through randomly generated test instances, and perform a numerical sensitivity analysis to evaluate the impact of the changes of a targeted fill-rate and variances of a demand distribution.