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Sweet cider is delivered weekly to Cindy’s cider bar. Demand varies uniformly between 100 liters and 200 liters per week. Cindy pays 30 cents per liter for the cider and charges 90 cents per liter for it. Unsold cider has no salvage value and cannot be carried into the next week due to spoilage. Find the optional stocking level and its stockout risk for that quantity.
Expert Answer
Ce = Cost per unit – Salvage value per unit
= $0.30 -$0
= $0.30
Cs = Revenue per unit – Cost per unit
= $0.90 – $0.30
= $0.60 per unit
SL= Cs / [Cs + Ce]
SL = $0.60 / [$0.60 + $0.30]
SL = $0.60 / $0.90
SL= 0.67
Thus optimal stocking level must satisfy demand 67% of the time. For the uniform distribution, this will be at a point equal to the minimum demand plus 67% of the difference between maximum and minimum demand.
So = 100 +0.67( 200-100) = 167 ltr.
The stock out risk is = 1 – 0.67 = 0.33
