​Ebb&Flow (E&F) sells yoga supplies including their popular​ eco-friendly yoga mat design. The monthly demand for yoga mats follows a normal distribution with mean 540 mats per month and standard deviation 56 systems per month.​ E&F reviews its inventory every 24 days. It takes 18 days to receive an order delivery​ (assume 30 days per​ month). E&F would like to maintain a service level of 93​%. E&F purchases the systems from a supplier for $35 per system. Annual holding cost is 20​% of the purchase cost per audio system. You may use the following table of values for the Standard Normal distribution to find your z value. a) Compute the safety stock level you recommend for​E&F. b) Compute average inventory on order ​c) Compute the annual holding cost for carrying the safety stock ​(round your response to nearest​cent).

Monthly demand (D) ~ N(μD=540, σD=56)
P = review period = 24 days = 24/30 = 0.80 month
L = avergae lead time of delivery = 18 days = 0.60 month
CSL = 93%, so, Z = NORMSINV(0.93) = 1.48 where Z ~ N(0,1)
H = annual holding cost per part = $35 x 20% = $7

(a)

Safety stock (SS) = Z.σD.SQRT(P+L) = 1.48*56*SQRT(0.8+0.6) ≅ 98 (rounded off to nearest integer)

(b)

Target inventory level = μD.(P+L) + SS = 540*(0.8+0.6) + 98 = 854

Q = average order quantity = μD.P = 540*0.8 = 432

Average inventory on order = T – Q = 854 – 432 = 422

(c)

Annual holding cost for the safety stock = SS x H = 98 x $7 = $686

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