Harley Davidson has its engine assembly plant in Milwaukee and its motorcycle assembly
plant in Pennsylvania. Engines are transported between the two plants using trucks. Each
truck trip costs $1,800. The motorcycle plant assembles and sells 3200 motorcycles each
week. Each engine costs $600 and Harley incurs a holding cost of 20 percent per year.
How many engines should Harley load onto each truck? What is the cycle inventory of
engines at Harley?
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To determine how many engines Harley Davidson should load onto each truck and the cycle inventory of engines, we need to consider the production and transportation costs, as well as the holding cost. Here's how we can calculate these values:
1. Calculate the weekly demand for engines:
- Harley Davidson assembles and sells 3200 motorcycles per week.
- Assuming each motorcycle requires one engine, the weekly demand for engines is also 3200.
2. Determine the optimal order quantity for engines:
- The Economic Order Quantity (EOQ) formula can be used to calculate the optimal order quantity.
- The EOQ formula is √((2DS) / H), where D is the demand (3200 engines per week), S is the setup or ordering cost ($1800 per truck trip), and H is the holding cost (20% per year, or 0.2 as a decimal).
- Since we are calculating the optimal order quantity for each truck trip, D and H need to be converted to match the truck trip time frame.
- Since the demand and holding cost are all per week, we can keep them as is.
- Plugging the values into the formula, we get: √((2 * 3200 * $1800) / (0.2)) ≈ 320 engines per truck.
3. Calculate the cycle inventory of engines:
- The cycle inventory is the average quantity of inventory carried between two successive deliveries.
- In this case, it represents the average number of engines held at the motorcycle assembly plant while waiting for trucks.
- The cycle inventory can be calculated as 1/2 of the order quantity, since, on average, half of the order is in transit and half is held in inventory.
- Therefore, the cycle inventory of engines would be 320/2 = 160 engines.
In summary, Harley Davidson should load 320 engines onto each truck, and the cycle inventory of engines at Harley is approximately 160 engines.