Newsvendor Order Quantile

Problem

Compute the newsvendor optimal order quantity as the sample quantile of demands at the critical fractile (price - cost) / (price - salvage). Use linear interpolation between order statistics, with the critical fractile clamped to the interval from 0 to 1.

Return 0.0 for empty demand, the sole value for a single demand, and use 0.5 when price equals salvage.

Hint

A higher unit margin relative to salvage pushes the critical fractile toward 1.

Test cases

case 1

in: [[10,20,30,40],10,4,1]

expected: 30

case 2

in: [[10,20,30,40],8,3,2]

expected: 35

case 3

in: [[5],10,4,0]

expected: 5

case 4

in: [[1,2,3,4,5],10,5,5]

expected: 5

case 5

in: [[10,20,30,40],5,4,1]

expected: 17.5

Starter codePython

def newsvendor_order_quantile(demands, price, cost, salvage):
    # Your code here
    pass

5 test cases · run your code against them in the editor