Bayesian and Adaptive Controls for a Newsvendor Facing Exponential Demand

Abstract

The newsvendor problem is relatively easy to solve when the distribution of demand for newspapers is known. When the demand is unknown, the newsvendor faces a dual problem in the sense of Feldbaum (1960): to choose a decision variable that maximizes profit in the present period, and choose a large enough "observation window" to be able to view the process correctly so that consistent parameter estimation can occur. This is a difficult problem in general. In this paper, we treat a special case when the newsvendor faces exponential demand, independently and identically distributed with unknown mean.

Keywords: Consistent estimators, censored data, Bayesian control, adaptive control, Newsvendor model, unnormalized probability, optimal control, incomplete information, partial observations

JEL Classification: C61, M11, D81, D83