Question

Store A uses the newsvendor model to manage its inventory Demand for its product is normally distributed with a mean of 500 and a standard deviation of 300 How many units should be ordered to achieve a 99.7% in-stock probability? Use Table 13.4 Multiple Choice o 1310 o 1340 o 1050 o 1695

Answer 1

To achieve a 99.7% in-stock probability using the newsvendor model, 1050 units should be ordered.

Step-by-step explanation:

The newsvendor model is used to determine the optimal order quantity in order to achieve a desired in-stock probability. In this case, the question is asking how many units should be ordered to achieve a 99.7% in-stock probability.

The newsvendor model takes into account the mean demand (500 units) and the standard deviation of demand (300 units). The desired in-stock probability of 99.7% corresponds to a z-score of approximately 2.75.

Using the z-score formula: z = (x - mean) / standard deviation, we can solve for x to find the optimal order quantity. Rearranging the formula, x = z × standard deviation + mean. Substituting the values, x = 2.75 × 300 + 500 = 1,025.

Therefore, the correct answer is 1050.

Answer 2

The number of units to be ordered to achieve a 99.7% in-stock probability is 1,340 units. The Option B is correct.

To get this number of unit to order, we need to apply the Newsvendor Model which is a a mathematical inventory management model. Its takes into account how much it costs to order too little (stockouts) against too much (excess inventory).

Given data:

• Mean demand (μ): 500 units
• Standard deviation of demand (σ): 300 units
• Desired in-stock probability: 99.7%

To get the value of z for responding service level, we wil use NORMSINV (Z) function using 99.7% as the parameter.

NORMSINV (Z):

= NORMSINV (0.997)

= 2.747781385445

= 2.8

Optimal order quantity = μ + z * б

= 500 + 2.8*300

= 1340

Therefore, the number of units to be ordered to achieve a 99.7% in-stock probability is 1,340 units