Question

Cream Cakes makes and sells cakes daily. Based on past experience the owner has estimated the following probabilities for the daily demand for fresh cream cakes:Daily Demand (cakes)Probability 300.1400.2500.3600.3700.1 The cakes cost $12 to make and are sold for $22 per cake. Cream Cakes believes a lot of their success is because they only sell fresh cakes. Any cakes unsold at the end of the day is mashed up and sold to the local piggery for $7.00 If the proprietor follows the criterion of regret, how much would be ordered daily?

Answer 1

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Solution

The unit selling price per cake is given as Cs = $22. This represents the cost of understccking i.e. the cost of a lost sale due to lack of inventory. The cost of overstocking = Co = Unit Cost - Salvage value = 12 - 7 = $5. This represents the cost of overstocking i.e. having inventory without demand. The optimal service level is given by Cs/(Cs+Co) = 22/(22+5) = 0.814.

The optimal service level can be looked up under the CDF column in the table given below (CDF represents the cumulative distribution function as per the usual statistical definition) and we see that the applicable daily demand for such a case to be satisfied is 60 where the CDF = 0.9. The CDF immedietely preceding this is 0.6 which is less than our optimal service level of 0.814.

Demand	Probability	CDF
30	0.1	0.1
40	0.2	0.3
50	0.3	0.6
60	0.3	0.9
70	0.1	1.0

Optimal order quantity is 60