Question

You are a newsvendor selling San Pedro Times every morning. Before you get to work, you go to the printer and buy the day’s paper for $0.30 a copy. You sell a copy of San Pedro Times for $1.50. Daily demand is distributed normally with mean = 285 and standard deviation = 57. At the end of each morning, any leftover copies are worthless and they go to a recycle bin. How many copies of San Pedro Times should you buy each morning?

Answer 1

The newsvendor should buy approximately 323 copies of the San Pedro Times each morning using the Newsvendor model, which accounts for overage and underage costs, and the critical ratio to maximize expected profit.

Step-by-step explanation:

To determine the optimal number of copies of San Pedro Times that the newsvendor should buy each morning, we use the Newsvendor model. The Newsvendor model is a mathematical model that balances the cost of ordering too many items (overage) against the cost of ordering too few (underage).

The cost to the vendor for each unsold newspaper is $0.30 (since they are worthless at the end of the day and that is the purchase cost). The profit for each newspaper sold is the selling price minus the purchase price, which is $1.50 - $0.30 = $1.20. This gives us the overage cost of Co=$0.30 and the underage cost of Cu=$1.20 - $0.30 = $0.90.

The critical ratio is then calculated as Cu / (Cu + Co), which simplifies to $0.90 / ($0.90 + $0.30) or 0.75. Looking at the standard normal distribution table, we find the z-score that corresponds to a cumulative probability nearest to 0.75 is approximately 0.67.

To find the optimal order quantity Q*, we apply the formula: Q* = mean + (z-score * standard deviation). Plugging in the numbers: Q* = 285 + (0.67 * 57), we get Q* approximately 323 copies. Therefore, the newsvendor should buy about 323 copies of San Pedro Times each morning to maximize expected profit.