A Multiperiod Newsvendor Problem with Partially Observed Demand

Abstract

We consider a newsvendor problem with partially observed Markovian demand. Demand is observed if it is less than the inventory. Otherwise, only the event that it is larger than or equal to the inventory is observed. These observations are used to update the demand distribution from one period to the next. The state of the resulting dynamic programming equation is the current demand distribution, which is generally infinite dimensional. We use unnormalized probabilities to convert the nonlinear state transition equation to a linear one. This helps in proving the existence of an optimal feedback ordering policy. So as to learn more about the demand, the optimal order is set to exceed the myopic optimal order. The optimal cost decreases as the demand distribution decreases in the hazard rate order. In a special case with finitely many demand values, we characterize a near-optimal solution by establishing that the value function is piecewise linear.

Dynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability

“…Ding et al (2002) and Lu et al (2005Lu et al ( , 2006 extend this "stock more" result to perishable inventory systems with a general continuous demand distribution. Bensoussan et al (2005) study a similar problem with Markovian demand.…”

Optimal inventory control in a multi-period newsvendor problem with non-stationary demand

“…Bensoussan et al [17] proposes an estimation method based on observed demands using dynamic programming and probability theory. Levi et al [18] use the Monte Carlo simulations to estimate the demand distribution for both single newsvendor and multi-period newsvendor problems.…”

Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models

“…The (discrete) multiperiod newsvendor problem has been studied in detail by many authors, Matsuyama (2004), Berling (2006), Bensoussan et. al (2007Bensoussan et.…”