Question

A perishable dairy product is ordered daily at a particular supermarket. The product, which costs $1.2 per unit, sells for $1.64 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 distributed with u = 145 and 6 = 30. Note: Use Appendix B to identify the areas for the standard normal distribution. a. What is your recommended daily order quantity for the supermarket? Round your answer to the nearest whole number. Q* = b. What is the probability that the supermarket will sell all the units it orders? Round your answer to three decimal places. P(Stockout) = c. In problems such as these, why would the supplier offer a rebate as high as $1? For example, why not offer a nominal rebate of, say, 250 per unit? What happens to the supermarket order quantity as the rebate is reduced? The lower rebate decreases the quantity that the supermarket should order.

Answer 1

1. COST PRICE = 1.2
SALES PRICE = 1.64
SALVAGE VALUE = 1

Cost of shortage(Cs) = sales price - cost price = 1.64 - 1.2 = 0.44
Cost of overage(Co) = Cost price - salvage value = 1.2 - 1 = 0.2

Service level = Cs / (Cs + Co) = 0.44 / (0.44 + 0.2) = 0.6875
The Z value that corresponds to a service level of 0.6875 is = 0.49

Mean demand = 145
Standard deviation = 30

Optimal stocking level = Mean demand + (Z * Standard deviation)

= 145 + (0.49 * 30) = 160

2. Probability of stockout = 1 - Service Level = 1 - 0.6875 = 0.3125 or 31.25%

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