Needless Markup (NM), a famous “high end” department store, must decide on the q

Question

Needless Markup (NM), a famous “high end” department store, must decide on the quantity of a high-priced woman’s handbag to procure in Spain for the coming Christmas season. The unit cost of the handbag to the store is $28.50 and the handbag will sell for $150.00. Any handbags not sold by the end of the season are purchased by a liquidator for $10.00 each. In addition, the store accountants estimate that there is a cost of $0.40 for each dollar tied up in inventory, as this dollar invested elsewhere could have yielded a gross profit. Assume that this cost is attached to unsold bags only.

The optimal number of bags to purchase is 272.

Another supplier in the US. offers the same product but at a higher price of $35 due to its higher production cost. For this supplier, Needless Markup only needs to place the order 3 months in advance which results in a much better forecast. Past data shows if ordering 3 months in advance, the number of bags sold can be described by a normal distribution, with mean 150 and standard deviation 20. Which supplier should NM choose?

Explanation / Answer

So the order size is 169 vs 272.

Hence the new supplier is better (It helps to match the demand), Has better cost and profit attached.

M mean M S Std Dev S C Cost 28.5 P Price 150 V Salvage 10.4 Formula used Cu Cost of under order 121.5 (P-C) Co Cost of over order 18.1 (C-V) CR Critical ratio 0.8703 (Cu/(Cu+Co) So actual order m+Z*s 272 Other Supplier M mean 150 S Std Dev 20 C Cost 35 P Price 150 V Salvage 10.4 Formula used Cu Cost of under order 115 (P-C) Co Cost of over order 24.6 (C-V) CR Critical ratio 0.8238 (Cu/(Cu+Co) So actual order m+Z*s 168.598 169

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