Question

Toyota imports batteries for its famous sedan Camry from a supplier in Japan every month. Each Camry requires a battery, and Toyota at a unit cost of $1200 (including tariff, shipment and material cost). It takes 2 months to receive the delivery. The monthly demand for Camry (and hence for the battery) is approximately normally distributed with a mean of 1000 units and a standard deviation of 250 units. The inventory holding cost for a battery is $100 per unit per month.

a. What is the safety stock for the battery if Toyota wants to maintain a service level of 95%?

b. What is the annual holding cost for this safety stock?

c. What is the average inventory on order/ in transit?

d. How much additional safety stock does Toyota have to carry to reach a service level of 98%?

Answer 1

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

=
`1.645 * 250 * √(2) = 581.595`

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

=
`2.053 * 250 * √(2) = 725.84`

Additional stocks needed = 726 - 582 = 144

Thus, Toyota needs to keep additional safety stock of 144 units to maintain 98% serviceability