Central Perk’s owner decides to stock the Harvard Business Review in hopes of at

Question

Central Perk’s owner decides to stock the Harvard Business Review in hopes of attracting Wallstreet bankers to its store. Since the owner has been so impressed by your knowledge of logistics, he asks for you to determine the how many magazines they should order every 2 months. You are able to sell the magazines for $18.95. It costs Central Perk $12.00 to buy the magazine. Unsold magazines are able to be salvaged for $10.00. You forecast that Central perk would be able to sell 60 magazines every 2 months with a standard deviation of 10.

Explanation / Answer

Here the bimonthly demand of megazines are expected to be 60 with standard deviation of 10.

Cost of megazine = $ 12.00

Selling price p = $ 18.95

salvage value s = $ 10.00

Here the overage cost = c -s = 12 - 10 = $ 2 per unit

Underage cost = p - c = 18.95 - 10 = $ 6.95 per unit

So , we choose the first Q such that

Pr[ DO not sell Q + 1 unit] = F(Q) >= underage cost / (underage cost + overage cost)

F(Q) >= 6.95/ (6.95 + 2) = 6.95/8.95 = 0.77654

Here As the demand is normal distribution

Pr(Q< Qoptimal ; 60 ; 10 ) = 0.77654

So, as per normal distribution table we will get the z value.

Z = 0.76056 = (Qoptimal - 60)/10

Qoptimal  = 60 + 10 * 0.76056 = 67.7056 or say 68 megazine

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