Problem 10-27 (Algorithmic) A perishable dairy product is ordered daily at a par

Question

Problem 10-27 (Algorithmic) A perishable dairy product is ordered daily at a particular supermarket. The product, which costs $1.23 per unit, sells for $1.74 per unit. If units are unsold at the end of the day, the supplier takes them back at a rebate of $1 per unit Assume that daily demand is approximately normally dstributed with -145 and -25. Note: Use Appenidix 8 to identify the areas for the standard narmal distribution a. What is your recomemended daily arder quantbity for the supermarket? Round your answer to the nearest whole number b. What is the probability that the supermarket will sell all the units it orders? Round your answer to three decimal places. P(Stockout) t. In problems such as these, why would the suppler ofter a rebate as high as $1? For sxampla, why not ofter a nominal rebate of, say, 25c per unit? what happens to the supermarket arder quantity as the rebate is reduced? The higher rebate decreases the quantity that the supermarket should order. Previous Next

Explanation / Answer

Shortage or Underage cost, Cu = Selling price - cost = 1.74 - 1.23 = 0.51

Excess or Overage cost, Co = Cost - Salvage (rebate price) = 1.23 - 1 = 0.23

Optimal service level for the supermarket, or Critical ratio F(z) = Cu/(Cu+Co) = 0.51/(0.51+0.23) = 0.6892

Corresponding to F(z), value of z = NORMSINV(0.6892) = 0.4936

a) Recommended daily order quantity, Q* = + z = 145+0.4936*25 = 157

b) Probability = 1 - F(z) = 1 - 0.6892 = 0.3108

c) The higher rebate increases the quantity that the supermarket should order.

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