Suppose that the newsvendor faces integer-valued demand and must choose an integer value of y. We make no assumptions about the demand distribution (other than that it is an integer) or about the relationship between h and p. Prove that y* is the smallest integer y such that F(y) ≥ (r − c)/(r − v) where F is the cdf of the demand distribution. (Hint: Consider calculating the cost difference between two consecutive integer values.)

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Suppose that the newsvendor faces integer-valued demand and must choose an integer value of y. We make no assumptions about the demand distribution (other than that it is an integer) or about the relationship between h and p. Prove that y* is the smallest integer y such that F(y) ≥ (r − c)/(r − v) where F is the cdf of the demand distribution. (Hint: Consider calculating the cost difference between two consecutive integer values.)

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