The Censored Newsvendor and the Optimal Acquisition of Information

This paper investigates the effect of demand censoring on the optimal policy in newsvendor inventory models with general parametric demand distributions and unknown parameter values. We show that the newsvendor problem withobservable lost sales reduces to a sequence of single-period problems, while the newsvendor problem withunobservable lost sales requires a dynamic analysis. Using a Bayesian Markov decision process approach we show that the optimalin ventory level in the presence of censored demand ishigher than would be determined using a Bayesian myopic policy. We explore the economic rationality for this observation and illustrate it with numerical examples.

[1]  S. Karlin.  Dynamic Inventory Policy with Varying Stochastic Demands , 1960 .

[2]  H. Scarf.  Some remarks on bayes solutions to the inventory problem , 1960 .

[3]  J. J. Florentin,et al.  Optimal, Probing, Adaptive Control of a Simple Bayesian System† , 1962 .

[4]  Robert Bartle,et al.  The Elements of Real Analysis , 1977, The Mathematical Gazette.

[5]  D. Iglehart.  The Dynamic Inventory Problem with Unknown Demand Distribution , 1964 .

[6]  S. A. Conrad,et al.  Sales Data and the Estimation of Demand , 1976 .

[7]  K. M. vanHee,et al.  Bayesian control of Markov chains , 1978 .

[8]  R. L. Winkler,et al.  Learning, Experimentation, and the Optimal Output Decisions of a Competitive Firm , 1982 .

[9]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[10]  Katy S. Azoury,et al.  A Comparison of the Optimal Ordering Levels of Bayesian and Non-Bayesian Inventory Models , 1984 .

[11]  Katy S. Azoury.  Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution , 1985 .

[12]  W. Lovejoy.  Myopic policies for some inventory models with uncertain demand distributions , 1990 .

[13]  William S. Lovejoy,et al.  Suboptimal Policies, with Bounds, for Parameter Adaptive Decision Processes , 1993, Oper. Res..

[14]  G. Gallego,et al.  The Distribution Free Newsboy Problem: Review and Extensions , 1993 .

[15]  David J. Braden,et al.  Nonlinear Pricing to Produce Information , 1994 .

[16]  S. Nahmias.  Demand estimation in lost sales inventory systems , 1994 .

[17]  E. Silver,et al.  Preventive maintenance with limited historical data , 1995 .

[18]  Stephen A. Smith,et al.  Estimating negative binomial demand for retail inventory management with unobservable lost sales , 1996 .

[19]  Ananth V. Iyer,et al.  Improved Fashion Buying with Bayesian Updates , 1997, Oper. Res..

[20]  David F. Pyke,et al.  Inventory management and production planning and scheduling , 1998 .

[21]  Evan L. Porteus,et al.  Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales , 1999 .

[22]  Graham K. Rand,et al.  Inventory Management and Production Planning and Scheduling (Third Edition) , 2001, J. Oper. Res. Soc..