Question

An auto manufacturer produces two different versions of a vehicle, Regular and Hybrid, in its plant in Kentucky. Both vehicles use the same kind of tires, and each vehicle requires 5 identical tires (one of which is a spare tire). The purchasing department of the plant uses a (Q, R)-policy to manage the inventory level of the tires. The tires are ordered from an external supplier with a lead time of 3 days. The purchasing departments goal is to limit stock-outs of tires to 3% of the ordering cycles. The supplier charges $200 per tires. In addition, there is a fixed cost of ordering a batch of tires, equal to $1,000 per shipment. The holding cost incurred by the plant is $0.2 per tire per day. The daily production rate of the regular vehicle is normally distributed with a mean of 20 and a standard deviation of 5. The daily production rate of the hybrid vehicle is normally distributed with a mean of 15 and a standard deviation of 3 (a) What are the mean and the standard deviation of the daily demand for the tires at this plant? How about the mean and standard deviation of demand for tires during the lead time of 3 days? (b) What are the order quantity (Q) and the reorder level (R) the purchasing department should use to achieve its service level goal for the tires?

Answer 1

Solution:-

(a)

Mean every day interest for standard vehicle = 20

Standard deviation of every day interest for ordinary vehicle = 5

Mean day by day interest for mixture vehicle = 15

Standard deviation of day by day interest for normal vehicle = 3

Mean every day interest for tires = 205 + 155

Therefore,Mean day by day interest for tires=175

Difference of day by day request of tires = 5(5^2) + 5(3^2)

= 5(25)+5(9)

= 170

Change of day by day request of tires = 170

Standard deviation = sqrt(170)

So,Standard deviation = 13.04

Normal interest of tires amid the lead time = 175 * 3

Normal interest of tires amid the lead time= 525 tires

Standard deviation of lead time request = 13.04 * sqrt(3)

Standard deviation of lead time request = 22.60

(b)

Normal day by day request, D = 175

Holding cost per unit, h = $0.2 every day

Requesting cost, K = $1,000

Along these lines, ideal request amount, Q = (2*D*K/h)1/2

Q= sqrt(2*175*1000/0.2)

Ideal request quantity,Q= 1,323 tires

The given administration level is 97 percent,

z = Normsinv (0.97)

z= 1.88

Security stock = z * Standard deviation of lead time request

z= 1.88,Standard deviation of lead time demand=22.60

Security stock=43 units

Reorder point, R = normal lead time request + safety stock

Normal lead time request =525

Security stock=43 units

Reorder point, R = 568 tires

Along these lines, the ideal (Q, R) = (1323, 568)