Near optimality guarantees for data-driven newsvendor with temporally dependent demand: a Monte Carlo approach

We consider a newsvendor problem with stationary and temporally dependent demand in the absence of complete information about the demand process. The objective is to compute a probabilistic guarantee such that the expected cost of an inventory-target estimate is arbitrarily close to the expected cost of the optimal critical-fractile solution. We do this by sampling dependent uniform random variates matching the underlying dependence structure of the demand process -- rather than sampling the actual demand which requires the specification of a marginal distribution function -- and by approximating a lower bound on the probability of the so-called near optimality. Our analysis sheds light on the role of temporal dependence in the resulting probabilistic guarantee, which has been only investigated for independent and identically distributed demand in the inventory management literature.