The local ACE Hardware store places a single order for Winter Sidewalk Salt to m

Question

The local ACE Hardware store places a single order for Winter Sidewalk Salt to meet its demand for the 12 week winter sales season. Based on the last 5 year data the demand is known to be normally distributed with a mean of 4800 bags and a standard deviation of 1625 bags. Bags are purchased wholesale for $3.20 and sold for $7.10. At the end of the season unsold bags have a salvage value of $1.45. (i)Using the News Vendor model derive the optimal service level and order quantity. (ii)If ACE places an order for 7500 bags what is the probability they will have a loss?

Explanation / Answer

Given C1 = Salvage loss = $1.45

C2 = Lost profit = 7.10 -3.20 = $3.90

i) Mean = 4800 and SD = 1625

Pc = C1 / (C1+C2) = 1.45 / (1.45+3.90) = 0.27103

The Z value corresponding to 0.27103 of the area under the normal curve can be read from tables as 0.3932

EOQ = mean - Z SD = 4800 - 0.3932*1625 = 4161.05 bags

ii) P(X>7500) = P(Z > (7500-4800)/1625) = P(Z>1.6615) = 0.04831

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