Question

A local hypermarket in Kuwait supplies juice boxes from manufacturer in Saudi Arabia. The reorder point, without safety stock, is 800 boxes. The carrying cost is KWD 20 (Kuwaiti Dinar) per box per year, and the ordering cost is KWD 50 per box per year, how much safety stock should be carried?

DEMAND DURING LEAD TIME PROBABILITY

0 0.2

100 0.2

200 0.2

300 0.2

400 0.2

Answer 1

To determine the safety stock that should be carried, we need to consider the demand during the lead time and the desired service level. The recommended safety stock to be carried is 232 boxes.

Step-by-step explanation:

In order to determine the safety stock that should be carried, we need to consider the demand during the lead time and the desired service level.

First, we calculate the average demand during the lead time. Using the probabilities given, we can calculate:

• Average demand = (0 x 0.2) + (100 x 0.2) + (200 x 0.2) + (300 x 0.2) + (400 x 0.2) = 200 boxes

Next, we calculate the standard deviation of demand. Using the same probabilities and the formula for standard deviation, we can calculate:

• Standard deviation = sqrt(((0-200)^2)x0.2 + ((100-200)^2)x0.2 + ((200-200)^2)x0.2 + ((300-200)^2)x0.2 + ((400-200)^2)x0.2) = 141.42 boxes

Finally, we can calculate the safety stock using the desired service level. For example, if we want a 95% service level, we can consult a standard normal distribution table and find the Z-score for a 95% service level, which is approximately 1.645. Multiplying the Z-score by the standard deviation, we get:

• Safety stock = 1.645 x 141.42 = 232.41 boxes

So, the recommended safety stock to be carried is 232 boxes. This will help prevent stockouts and ensure a high service level to customers.

Answer 2

The safety stock that should be carried is 300 boxes.

Step-by-step explanation:

The safety stock is the extra inventory a company holds to protect against unexpected fluctuations in demand or lead time. It serves as a buffer between the reorder point and the actual inventory. To determine the safety stock, we need to consider the demand during lead time and its probability.

In this case, the demand during lead time and its corresponding probabilities are:

• Demand: 0, Probability: 0.2
• Demand: 100, Probability: 0.2
• Demand: 200, Probability: 0.2
• Demand: 300, Probability: 0.2
• Demand: 400, Probability: 0.2

To calculate the safety stock, we need to find the demand level at which the cumulative probability reaches a specific value. In this case, we can calculate the safety stock by considering the cumulative probabilities:

• P(Demand ≤ 0) = 0.2
• P(Demand ≤ 100) = 0.4
• P(Demand ≤ 200) = 0.6
• P(Demand ≤ 300) = 0.8
• P(Demand ≤ 400) = 1.0

We can see that the cumulative probabilities increase by 0.2 with each demand level. Since the reorder point without safety stock is 800 boxes, we need to find the demand level at which the cumulative probability reaches 0.8, which is 300 boxes. Therefore, the safety stock that should be carried is 300 boxes.