Problem $14-17($Algo$)$

Meritor, a company that makes muffler assemblies for the automotive industry, is committed to the use of kanban to pull material through its manufacturing cells. Meritor has designed each cell to fabricate a specific family of muffler products. Fabricating a muffler assembly involves cutting and bending pieces of pipe that are welded to a muffler and a catalytic converter. The mufflers and catalytic converters are pulled into the cell based on current demand. The catalytic converters are made in a specialized cell.

Catalytic converters are made in batches of $10$ units and are moved in special hand carts to the fabrication cells. The catalytic converter cell is designed so that different types of catalytic converters can be made with virtually no setup loss.

Meritor hires a team of consultants. The consultants suggest a partial robotic automation as well as the safety stock to be $12\mathrm{.}5$ percent. Meritor implements these suggestions. The result is an increase in efficiency in both the fabrication of muffler assembly and the making of catalytic converters. The muffler assembly fabrication cell averages $20$ assemblies per hour and the lead time is three hours' response time for a batch of $10$ catalytic converters. How many kanban cards are needed? $($Round up your answer to the next whole number.$)$

Number of kanban card sets