A study on the effect of yield uncertainty in price-setting newsvendor models with additive-multiplicative demand

Abstract

Random yield and uncertain demand usually both exist in many industries, such as the semiconductor industry. In this paper, the price-setting newsvendor model is studied which involves a single manufacturer and a single retailer with random yield and uncertain demand respectively. Under the condition of additive-multiplicative demand, we investigate the varying effects of random yield on the optimal price, order quantity, and expected profit in two situations with different cost structures. The first case is an in-house production case where the firm pays for the raw material quantity it has ordered, and the second one is a procurement case where the firm pays for the real product quantity it receives only. By using the theory of stochastic comparisons, we find that a less variable and a stochastically larger yield rate both lead to a lower optimal price and a higher expected profit for the in-house production case. Moreover, a less variable yield rate also results in a lower optimal price and a higher profit for the procurement case, but this is not true for a stochastically larger yield rate. Numerical examples illustrate that the effect of yield randomness on the optimal order quantity is not general.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 71501058, 71231004, 71601065, 71571058, 71690235, 71690230, 71531008), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), and Anhui Province Natural Science Foundation (No. 1608085QG167). Panos M. Pardalos is partially supported by the project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026).

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Correspondence to Wenjuan Fan.

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This paper is submitted to the special issue OCA6. Dr. Jun Pei registered and attended this conference, and Prof. Panos M. Pardalos attended this conference as a plenary speaker.

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Yu, L., Fan, W., Pei, J. et al. A study on the effect of yield uncertainty in price-setting newsvendor models with additive-multiplicative demand. Optim Lett 12, 1421–1441 (2018). https://doi.org/10.1007/s11590-017-1215-9

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Keywords

  • Random yield
  • Additive-multiplicative demand
  • Newsvendor model
  • Stochastic comparison