Erica Zhang is the chief buyer for house wares at a large department store. Unfortunately, her store faces stiff competition from specialty retailers that carry imported cooking and dining articles. To meet this competitive challenge, Erica has reorganized her house wares department to create a "store within a store" that has the same ambiance as her competitors. To kick off her concept, she plans a one-month promotion that features a sale on several special items, including an imported Three Kings baking dish. (The Three Kings baking dish leaves a "crown" image on the top of the cake.) These baking dishes must be ordered six months in advance. Any leftover inventory at the end of the promotion will be sold to a discount chain at a reduced price.
Erica has collected some pricing and cost data, listed in the following table, to help her decide how many of the Three Kings baking dishes to order. Erica predicts total demand for the imported baking dish to be normally distributed with mean of 980 and standard deviation of 354. Leftover dishes will be sold to the discount chain for $15.
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Three Kings baking dish:
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Selling price
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$40.00
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Purchase price
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$16.00
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Shipping cost
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$3.00
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Handling cost*
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$0.80
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Warehouse surcharge**
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$1.10
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Total cost
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$20.90
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*Estimate of variable cost to uncrate, clean, and transport a dish to the house wares department.
**Allocation of fixed overhead expenses in the shipping and receiving department.
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For parts a through c, suppose 1,200 imported Three Kings baking dishes are ordered.
a. What is the fill rate?
b. What is the in-stock probability?
c. How many Three Kings cake dishes should she purchase?
d. Erica is concerned about customer service. Suppose she feels there is a loss of goodwill of $10 for every customer that wants to purchase the Three Kings dish but is unable to do so due to a stock out. Now how many Three Kings cake dishes should she purchase?