Robust newsvendor problems with compound Poisson demands

We consider the robust newsvendor problem where the demand follows a compound Poisson distribution, but its distribution is only partly known. This assumption means that customers arrive according to a Poisson process with a given intensity, while the size of customer demand is another random variab...

Full description

Saved in:
Bibliographic Details
Published in:Annals of operations research Vol. 302; no. 1; pp. 327 - 338
Main Author: Ninh, Anh
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2021
Springer
Springer Nature B.V
Subjects:
Analysis
Analysis of variance
Business and Management
Combinatorics
Constraint modelling
Customers
Demand
Demand (Economics)
Operations research
Operations Research/Decision Theory
Optimization
Order quantity
Poisson density functions
Poisson distribution
Random variables
Robustness (mathematics)
Short Note
Statistical analysis
Theory of Computation
United States
Compound Poisson
Discrete moment problem
Newsvendor
Panjer’s recursion
ISSN:0254-5330, 1572-9338
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider the robust newsvendor problem where the demand follows a compound Poisson distribution, but its distribution is only partly known. This assumption means that customers arrive according to a Poisson process with a given intensity, while the size of customer demand is another random variable. Yet, the newsvendor only knows the expectation and variance of the demand sizes. Given limited information, a plausible approach, put forth in prior work, is to evaluate the moments of the aggregate demand (from all customers) and then determine the respective order quantity. Instead, this paper suggests to make the best use of all the information contained in the first few moments of demand sizes as well as the structural properties of a compound demand distribution to compute a better ordering quantity. To achieve this goal, we propose a new decision model employing Panjer’s recursion as constraints. The attendant optimization problem is then solved via convex relaxation using McCormick envelopes. Numerical results confirm that the newsvendor can gain a significant increase in expected profit using the new modeling approach to make his/her ordering decision.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-021-03996-3