Question

A newspaper boy is trying to perfect his business in order to maximize the money he can save for a new car. Paper sales are normally distributed, with a mean of 100 and standard deviation of 10.He sells papers for $.50 and pays $.30 for them. Unsold papers are trashed with no salvage value.

A.) How many papers should he reorder each day?

B.) What percent of the time will he experience a stockout?

C.) Are there any drawbacks to the order size proposed? If so, how can they be addressed?

Answer 1

1. COST PRICE = 0.3
SALES PRICE = 0.5
SALVAGE VALUE = 0

Cost of shortage(Cs) = sales price - cost price = 0.5 - 0.3 = 0.2
Cost of overage(Co) = Cost price - salvage value = 0.3 - 0 = 0.3

Service level = Cs / (Cs + Co) = 0.2 / (0.2 + 0.3) = 0.4
The Z value that corresponds to a service level of 0.4 is = -0.25

Mean demand = 100
Standard deviation = 10

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

= 100 + (-0.25 * 10) = 98

2. Probability of stockout = 1 - Service Level = 1 - 0.4 = 0.6

3. Yes, the drawback is that he has a higher chance of stockout based on the service level. If the salvage value can be increased by opting for recycling the paper, or the cost of purchase could be decreased if more newspapers are ordered, the stock outs can be balanced since the cost of overage would reduce.

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