QUESTION 13 Gringo Inc is an electronics store specializing in flat-screen TVs.

Question

QUESTION 13 Gringo Inc is an electronics store specializing in flat-screen TVs. The store is open for 50 weeks in a year. Sales of a popular TV model are 25 units per week on average, with a standard deviation of 8. Ordering cost is $200 and annual holding cost for TVs held in inventory is 25% Gringo has the option of buying that TV model from 1 of two wholesalers that operate in the area. The cost of a TV (i.e. the wholesale price for Gingo) is 325$ no matter which wholesaler is selected The wholesaler lead times are given below: Wholesaler #1 | Wholesaler #2 Lead Time (in weeks) Std. deviation of lead time (in weeks) 2 3 As per companu policu a service level of 95% (z= 1.65) must be maintained, and a continuous review (0) sustem must be used to manage inventory. Also as per policy it is not allowed to split the purchasing between two wholesalers. All purchases for a given product must come from one wholesaler only The above policy results in two options: Option 1: purchase exclusively from wholesaler #1 Option 2: purchase exclusively from wholesaler #2

Explanation / Answer

(a)

d = weekly demand = 25
d = standard deviation of weekly demand = 8
L = average lead time = 2 weeks (WS1) and 3 weeks (WS2)
L = standard deviation of lead time = 2 weeks (WS1) and 1 week (WS2)

Wholesaler 1: Safety Stock = Z.LT = Z.sqrt(d2.L + L2.d2) = 1.65*sqrt(64*2+4*625) = 84.59

Wholesaler 2: Safety Stock = Z.LT = Z.sqrt(d2.L + L2.d2) = 1.65*sqrt(64*3+1*625) = 47.16

(b)

Wholesaler 1: ROP = d.L + Safety Stock = 25*2 + 84.59 = 134.59

Wholesaler 2: ROP = d.L + Safety Stock = 25*3 + 47.16 = 122.16

(c)

D = annual demand = 50 x 25 = 1250
S = ordering cost = $200
H = inventory holding cost = $325 x 25% = $81.25

Wholesaler 1

EOQ = (2.D.S / H)1/2 = sqrt(2*1250*200/81.25) = 78.45

Total inventory holding cost = holding cost of cycle stock + holding cost of safety stock

= EOQ x H/2 + Safety Stock x H = (78.45*81.25/2) + (84.59*81.25) = $10,059.97

Wholesaler 2

EOQ = (2.D.S / H)1/2 = sqrt(2*1250*200/81.25) = 78.45

Total inventory holding cost = holding cost of cycle stock + holding cost of safety stock

= EOQ x H/2 + Safety Stock x H = (78.45*81.25/2) + (47.16*81.25) = $7,018.78

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