Final answer:
Comparing CSL when a brush is backlogged versus when there is a lost sale involves understanding the implications of customer willingness to wait versus immediate lost revenue. A backlog can lead to a lower cycle stock and different costs as compared to a lost sale, which may cause the company to maintain higher stock to avoid losing sales. Without specific data, we cannot compute exact CSL values, only infer inventory strategy differences.
Step-by-step explanation:
The question asks to compare the Cycle Service Level (CSL) when a paintbrush is backlogged versus when there is a lost sale. CSL is an important metric in inventory management and represents the probability of not running out of stock in any given inventory cycle. Benjamin Moore Paints sells 150 paint brushes per week and has an order size of 1000 brushes. The cost of holding one brush for a year is 20% of its unit cost, which is $3, leading to a holding cost of $0.60 per brush per year. The cost of understocking, or Cu, is $0.50.
To compare the CSL when a brush is backlogged or when a sale is lost, we need to understand that with backlogging, customers are willing to wait for the item to be restocked, while a lost sale means the customer will not purchase the item if it's not in stock. The cost of understocking would be the main factor differentiating the two scenarios. In the case of a backlog, the cost involves potential customer dissatisfaction and delay costs, whereas a lost sale directly results in lost revenue.
The exact calculation of CSL would depend on the demand distribution, the lead time for restocking, and the inventory policy of the company. Generally, if a company can backlog, it maintains a lower cycle stock, assuming customers are willing to wait. In contrast, if sales are lost, then a company might decide to keep more stock to prevent losing sales, resulting in a higher CSL, but also higher holding costs.
To summarize, without additional specific data (like demand distribution and lead time), we cannot compute the exact CSL values, but we can infer the differences in inventory strategy based on the concept of backlogging versus lost sales and their associated costs.