You have a one-time chance to purchase an item for $8. The item can be sold to c

Question

You have a one-time chance to purchase an item for $8. The item can be sold to customers for $46. After one day, the item has no salvage value because it becomes rotten at the end of the day. It will then cost you $19 to properly dispose of any unsold items. You think you can sell 1,900 units in one day, but you also know that the standard deviation of demand for the item is 50 units. Use Appendix A.

How many units should you order? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)

Number of units ____________ units

Explanation / Answer

The cost for a stockout (Cso) of the item = Unit selling price – unit cost = $46 - $8 = $38

The cost of overstock (Cos) of the item is= Unit cost + Disposal cost –Salvage value = $8+ 19 -$0 = $27

Target service level = Cso/(Cso + Cos)

the target service level (TSL) = $38/($38 + $27) = 0.5846

This TSL will provide a 58.46% probability of meeting all demand for the item. From the table of cumulative probability in Appendix A, we see that this target probability is closest to 0.21 standard deviations. Therefore, the target order quantity is

Order Quantity = Expected demand + Safety stock = 1,900 + 0.21(50) = 1,910 units

number of units 1910 units

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