Question

A tire distribution centre supplies various mechanic shops around the province and sells on average 40 sets (4 tires to a set) of one specific tire each week. These tires are supplied by an overseas manufacturer. The following information is known about the tire sets:

Weekly average tire set demand (µ) 40

Weekly tire set demand standard deviation (σt) 8

Weekly holding cost per tire set $18.00

Order cost per order $45.00

Lead time 1 weeks

Working weeks per year 50 weeks

The company currently uses a periodic review inventory control system with a period (P) of 8 weeks.

(1) Given that the distribution centre wants a 99.5% service level, what is the required safety stock?

(2) What is the required target inventory level (T)?

(3) Calculate the annual inventory cost of this periodic review system.

(4) The company is committed to a periodic review system, but thinks it may be incurring unnecessary costs. Suggest a better period (P) that will decrease the annual inventory cost. What is the expected cost of your proposed P?

Answer 1

Weekly average tire set demand (µ) = 40

Weekly tire set demand standard deviation (σt) = 8

Weekly holding cost per tire set, H = $18.00

Order cost per order, S = $45.00

Lead time, L = 1 weeks

Working weeks per year, w = 50 weeks

Review period, P = 8 weeks

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(1)

z = NORMSINV(0.995) = 2.576

Required safety stock = z*σt*(sqrt(L+P)

= 2.576*8*sqrt(1+8)

= 62 (approx)

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(2)

Required target inventory level, T = µ*(L+P) + Safety stock

= 40*(1+8)+62

= 422  

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(3)

Number of orders = Number of weeks per years / Review period (P)

= 50/8

= 6.25

Average cycle inventory = µ*P/2

= 40*8/2

= 160

Annual inventory cost of periodic review system

= Ordering cost + Holding cost of average cycle inventory + Holding cost of safety stock

= 6.25*45 + 50*18*160 + 50*18*62 (holding cost is $ 18 per unit per week. So, it is multiplied by 50 to convert to annual holding cost)

= $ 200,081.3

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(4)

EOQ = sqrt(2µS/H)

= sqrt(2*40*45/18)

= 14

Optimal review period = Q/µ

= 14/40

= 0.35 weeks