Final answer:
To calculate the number of kanban cards needed, we considered the production rate, the lead time demand, and the safety stock. The plant requires 8 containers to cover the lead time demand and an additional 2 containers for safety stock, totaling 10 containers. Hence, 10 kanban cards are required.
Step-by-step explanation:
The question involves calculating the number of kanban cards required for a bottling plant operation. To determine the number of kanban cards, we need to understand the rate of production, the demand during lead time, and the safety stock. The plant fills 3,600 bottles every three hours, equating to 1,200 bottles per hour. Given the lead time is 45 minutes, the demand during lead time is 1,200 bottles/hour * 0.75 hours = 900 bottles.
A container holds 120 bottles, so during the lead time, the demand will be 900/120 = 7.5 containers. Since we cannot have a fraction of a container, we round up to 8 containers needed during lead time. However, this does not include safety stock. The safety stock is 20 percent of the expected demand during lead time, which is 20% of 900 bottles = 180 bottles, or 1.5 additional containers. Again, rounding up, we require 2 containers for safety stock.
Thus, the total number of containers required is 8 containers for lead time demand + 2 containers for safety stock = 10 containers. Therefore, we need 10 kanban cards, with one card representing each container required to meet the lead time demand and the safety stock.