Question

Soap and Towels is a retailer of home goods.... Use Appendix 14A, Soap and Towels is a retailer of home goods. They receive inventory from their supplier with a 3-week lead time. Assume they order weekly, and they use the order-up-to model for choosing base stock levels. A peppermint soap sells on average two boxes every 4 weeks. (Round your answer to 2 decimal places. Use the Poisson distribution and Appendix 14A.) How many boxes of the peppermint soap do they order on average each week?

Answer 1

The retailer should order 1.5 boxes of peppermint soap on average each week, based on the product selling 2 boxes every 4 weeks and a 3-week lead time.

Step-by-step explanation:

The student's question revolves around determining the average number of boxes of peppermint soap a retailer should order weekly using the order-up-to inventory model, and Poisson distribution based on given conditions such as a 3-week lead time and average sales of two boxes every 4 weeks.

To find the average weekly order amount, we need to consider the average demand over the lead time. Given that the product sells two boxes every 4 weeks, we can calculate the weekly demand and then multiply by the lead time (3 weeks) to find the lead time demand. Using Poisson distribution, we can then adjust the order level to ensure a certain service level is maintained, but we are not given a service level or variability in demand, so we'll just calculate the average.

Here's the calculation:

1. Find the weekly demand: 2 boxes per 4 weeks equals 0.5 boxes per week.
2. Calculate the demand over the 3-week lead time: 0.5 boxes per week × 3 weeks equals 1.5 boxes.
3. Since they order weekly, the average number of boxes ordered each week would be 1.5 boxes to cover the 3-week lead time demand.

Therefore, the retailer should order on average 1.5 boxes of peppermint soap each week.