Multi-location newsvendor problem with random yield: Centralization versus decentralization

We study a multi-location newsvendor problem with an additive or multiplicative random yield assump-tion. We derive the expected cost and variance of cost under both centralized and decentralized systems. Given the additive random yield, we show that centralization is better than decentralization if demand is deterministic, or demand is uncertain and service level is 0.5. This result is driven by the risk pooling effect, where risk refers to supply risk. Given the multiplicative random yield, we show that decentraliza-tion is better than centralization if demand is deterministic. This result is driven by the risk diversification effect, where risk refers to supply risk. Through numerical experiments, we find that in general there is no risk pooling effect nor risk diversification effect if demand is uncertain. Specifically, under additive random yield the cost variance of centralized system can be either higher or lower than the decentral-ized system. Under multiplicative random yield, centralization is better than decentralization in terms of the expected cost, while decentralization is better than centralization in terms of the cost variance. Both the analytical and numerical results suggest that, when considering supply uncertainty, the comparison between centralization and decentralization highly depends on demand uncertainty.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This study investigates a multi-location newsvendor problem with different random yield assumptions. Through cost analysis, the study compares centralized and decentralized systems and derives their expected costs and cost variances. The results suggest that centralization is better than decentralization when demand is deterministic or uncertain with a service level of 0.5, driven by the risk pooling effect. However, when demand is deterministic, decentralization is better due to the risk diversification effect. Numerical experiments show that there is generally no risk pooling effect or risk diversification effect when demand is uncertain. Specifically, under additive random yield, the cost variance of the centralized system can be either higher or lower than the decentralized system. Under multiplicative random yield, centralization is better in terms of the expected cost, while decentralization is better in terms of the cost variance. Both analytical and numerical results indicate that the comparison between centralization and decentralization depends heavily on the uncertainty of demand when considering supply uncertainty.