Question

1. California Health Ltd. delivers organic beetroot juice to Fresh Modern Restaurant each day. Demand varies uniformly between 900ml and 1,000ml per day. Fresh Modern Restaurant pays $0.30/ml of the organic beetroot juice and sells the organic beetroot juice for $0.80/ml. Unsold organic beetroot juice has no salvage value and cannot be carried over. Find the optimal stocking level and its stockout risk for that quantity.   

Answer 1

Cost Per ml of Beetroot Juice = $0.3

Revenue Per ml = $0.8

Salvage Value per ml = 0

Minimum Demand = 900 ml ; Maximum Demand = 1000 ml

Solution:

Cost of Overage, Co = Cost per ml - Salvage per ml

= $0.3 - $0

= $0.3 is the excess cost of having the juice stocks at the end of the period

Cost of Underage, Cu = Revenue per ml - Cost per ml

= $0.8 - $0.3

= $0.5 is the shortage cost or opportunity cost (for lost sales)

Service level is the in-stock probability that the demand will not exceed the stocking level during the given period. This is given by:

Service level= Cost of Underage / (Cost of Underage + Cost of overage)

= 0.5 / (0.5 + 0.3)

= 0.625 or 62.5% is the in-stock probability

Stock-out risk = 1 - Service level = 1- 0.625 = 0.375

37.5% is the stockout risk (Probability that it will be out of stock 37.5% of the time)

In other words, 62.5% of the time, the demand is being met.

So, Optimal stocking level = Minimum Demand + Service level (Maximum Demand - Minimum Demand)

= 900 ml + 0.625 (1000ml - 900ml)

= 962.5 ml