Answer:
Check the explanation
Step-by-step explanation:
Given data :
1. Mean of monthly demand for batteries = 1000 units
2. The standard deviation of monthly demand for batteries = 250 units
3. The total unit cost of a single unit = $1200
4. Inventory holding cost for each unit = $100
5. Lead time = 2 months
Solutions
1. The Z-score for 95% service level is 1.645. Since we wish to calculate safe stock, we will be using the upper limit, i.e.
I= 1.645 *0* Total Leadtime
=

Thus, Toyota needs to keep a safety stock of 582 units to maintain 95% serviceability
2. In order to maintain 95% serviceability all year round, Toyota will have to maintain the required safety stock for all 12 months
\therefore Annual holding cost of this stock = No of units * Holding cost of each unit = 582 * $100*12 = $698,400
3. The time taken for delivery of a unit = 2 months
Thus, in any particular month, the items to be delivered in the next months as well as in the following month will be in transit.
Since average orders = 1000, the total numbers of orders in transit = 1000*2 = 2000
4. The Z-score for 98% service level is 2.053. Since we wish to calculate safe stock, we will be using the upper limit, i.e.
I= 2.053 *0* Total Leadtime
=

Additional stocks needed = 726 - 582 = 144
Thus, Toyota needs to keep additional safety stock of 144 units to maintain 98% serviceability