Question

An electronics retailer sells LED TVs with a normally distributed daily demand with a mean of 150 and a standard deviation of 75. The lead time to receive a replenishment from their supplier is 2 days. They review their inventory and place orders every two days. They operate 7 days a week.

A.) If they were to implement an order-up-to model, what base stock level should they choose if they want to achieve a 99.3% in-stock probability?
B.) When they check their inventory level to place new orders, they find that they ran out of stock completely. In addition, they find that there are 5 customers who paid for the products and are waiting to receive the products. How many LED TVs should they order?

Answer 1

The base stock level for the order-up-to model should be set at 407 TVs to achieve a 99.3% in-stock probability. If the store runs out of stock completely with 5 customers waiting, they should order at least 305 TVs to cover the lead time demand and the additional demand from the customers waiting.

Step-by-step explanation:

In order to determine the base stock level for the order-up-to model, we need to find the reorder point. The reorder point is the level of inventory at which a new order should be placed. To calculate the reorder point, we need to consider the lead time demand, which is the average demand during the lead time. In this case, the lead time is 2 days and the mean demand is 150 TVs per day, so the lead time demand is 150 x 2 = 300 TVs.

The safety stock is the additional inventory held to protect against uncertainties such as demand variability and lead time variability. In this case, we want to achieve a 99.3% in-stock probability, which means that we want to have enough inventory to cover 99.3% of the demand during the lead time. We can use the z-score formula to calculate the safety stock:

Safety Stock = (Z-Score) x Standard Deviation x Square Root of Lead Time,

Substituting the given values, we get:

Safety Stock = 2.57 x 75 x √2 ≈ 107 TVs.

To calculate the reorder point, we add the lead time demand and the safety stock:

Reorder Point = Lead Time Demand + Safety Stock = 300 + 107 = 407 TVs.

Therefore, the base stock level they should choose for the order-up-to model is 407 TVs.

Since they have completely run out of stock and there are 5 customers waiting, they should order enough TVs to cover the lead time demand and also the additional demand from the customers waiting. The total demand will be the lead time demand (300 TVs) plus the demand from the customers waiting (5 TVs), which gives a total demand of 305 TVs. Therefore, they should order at least 305 TVs.

Answer 2

To achieve a 99.3% in-stock probability in an order-up-to model, the base stock level should be 343 LED TVs. If the retailer is out of stock completely and has 5 customers waiting, they should order 455 LED TVs.

Step-by-step explanation:

To determine the base stock level for an order-up-to model, we need to calculate the safety stock level. In this case, the lead time is 2 days and the desired in-stock probability is 99.3%. Using the Z-score formula, we can find the corresponding Z-score for this probability, which is approximately 2.57. We then calculate the safety stock as the product of the Z-score and the standard deviation: 2.57 * 75 = 192.75. The base stock level is the sum of the average daily demand (150) and the safety stock: 150 + 192.75 = 342.75. Therefore, the electronics retailer should choose a base stock level of 343 LED TVs.

In the given scenario, the retailer is completely out of stock and has 5 customers waiting for the products. To fulfill the demand, the retailer should order enough LED TVs to cover the average daily demand (150) plus the outstanding demand (5) and the lead time demand (2 days * 150 TVs/day = 300 TVs). Therefore, the number of LED TVs that should be ordered is 150 + 5 + 300 = 455.