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...
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| Vydáno v: | Annals of operations research Ročník 302; číslo 1; s. 327 - 338 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.07.2021
Springer Springer Nature B.V |
| Témata: | |
| ISSN: | 0254-5330, 1572-9338 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Audience | Academic |
| Author | Ninh, Anh |
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| CitedBy_id | crossref_primary_10_1007_s10479_025_06738_x crossref_primary_10_1016_j_tre_2023_103365 crossref_primary_10_1007_s10479_022_04789_y crossref_primary_10_1016_j_tre_2025_103990 crossref_primary_10_1007_s10479_023_05167_y crossref_primary_10_1016_j_cor_2024_106870 crossref_primary_10_1007_s10479_024_06276_y |
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| DOI | 10.1007/s10479-021-03996-3 |
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| Keywords | Compound Poisson Discrete moment problem Newsvendor Panjer’s recursion |
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| SubjectTerms | 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 |
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| Title | Robust newsvendor problems with compound Poisson demands |
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