Dyson specializes in repairing vacuum cleaners. Dyson receives weekly deliveries
ID: 378851 • Letter: D
Question
Dyson specializes in repairing vacuum cleaners. Dyson receives
weekly deliveries from its vacuum cleaner belt supplier, who replenishes belts up to a level
that Dyson appliance is free to specify. Dyson buys a very popular belt at a unit price of
$17.50. The annual inventory carrying charge is 20%. Weekly demand for belts is normally
distributed with mean 86 and standard deviation 24. Dyson management wants to limit
the probability of a stock-out on any given week not to exceed 1%.
(a) What replenishment level would you recommend?
(b) What is Dyson' average level of safety stock?
(c) What is Dyson annual cost of holding cycle stock?
Explanation / Answer
Since probability of stockout not to exceed 1%, service level = 99% ( 0.99)
Corresponding Z value for probability 0.99 = NORMSINV ( 0.99) = 2.326
Given. Lead time of delivery ( Dyson receives weekly delivery ) = 1 week
Mean Weekly demand = m = 86
Standard deviation of weekly demand = Standard deviation of demand during lead time = S = 24
Thus average safety stock = ZxS = 2.326 x 24 = 55.82 ( 56 rounded to nearest whole number )
Thus , Replenishment stock = Mean weekly demand x Lead time ( weeks) + Safety stock
= 86 x 1 + 56
= 86 + 56
= 142
Given above replenishment quantity,
Cycle stock will fluctuate at steady rate between 86 and 0. Thus average cycle stock = 86/2 = 43
Annual Unit inventory holding cost = 20% of $17.50 = $3.5
Thus, Dyson’s annual cost of holding cycle stock
= Annual unit inventory holding cost x Cycle stock
= 3.5 x 43
= $150.5
REPLENISHMENT LEVEL = 142 VACUUM CLEANER
AVERAGE LEVEL OF SAFETY STOCK = 56 VACUUM CLEANER
ANNUAL COST OF HOLDING CYCLE STOCK = $150.5
REPLENISHMENT LEVEL = 142 VACUUM CLEANER
AVERAGE LEVEL OF SAFETY STOCK = 56 VACUUM CLEANER
ANNUAL COST OF HOLDING CYCLE STOCK = $150.5
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