12.49 The propane reseller (jaslan sells an average of 219 propane sy linders pe
ID: 352173 • Letter: 1
Question
12.49 The propane reseller (jaslan sells an average of 219 propane sy linders per day during peak seisson, opurating 300 days per year. The reseller sources propane cylinders from the main plant in Winterthur, from where cylinders are always delivered one day after an order has been placed. For cach delivery the reseller is charged S50. Each cylinder has a value of Sbá Analysis of the sales shows that the standard deviation of the sales per day, orp, equals l 7.6 a) Calculate the optimal order quantity, assuming an annual holding cost of 5% of hold inventory b) Gatan wants to have a service level of 99%. Recommend a inventory control strategy that will support this goalExplanation / Answer
d = average daily demand = 71.9
D = annual demand = 71.9 x 300 = 21,570
L = average lead time = 1 day
S = fixed ordering cost = $50
H = annual carrying cost per item = 15% x $64 = $9.6
= std. deviation of daily demand = 17.6
(a)
Optimal order quantity (Q*) = (2.D.S/H)1/2 = SQRT(2*21570*50/9.6) = 474
(b)
Service level = In-stock probability = 99%
Z = NORMSINV(0.99) = 2.33 where Z ~ Normal(0,1)
Safety stock (SS) = Z..L = 2.33*17.6*SQRT(1) = 41
Reorder point = avergae lead time demand + safety stock = d.L + 41 = 71.9*1 + 41 = 112.9 or 113
The sutiable inventory control strategy is a (Q=474, R=113) strategy i.e. an ordr of 474 units will be placed when the inventory falls below 113 units.
(c)
First, calculate the exisitng total relevant cost under optimality.
Cycle stock carrying cost = Q*.H/2 = 474*9.6/2 = $2275.2
Ordering cost = (D/Q*) x S = (21570/474)*50 = $2275.2
Safety stock carrying cost = SS x H = 41*9.6 = $393.6
Total relevant cost = $2275.2 + $2275.2 + $393.6 = $4,944
With 12 cylinders per pallet, the oder quantity will be multiples of 12 i.e. either 468 or 480. Also, it si given that the lead time is L=2, so SS = Z..L = 2.33*17.6*SQRT(2) = 58
For Q=468
Cycle stock carrying cost = Q.H/2 = 468*9.6/2 = $2246.4
Ordering cost = (D/Q) x S = (21570/468)*50 = $2304.5
Safety stock carrying cost = SS x H = 58*9.6 = $556.8
Total relevant cost = $2246.4 + $2304.5 + $556.8 = $5,108, So, % increase =($5,108 - $4,944) / $4,944 = 3.3%
For Q=480
Cycle stock carrying cost = Q.H/2 = 480*9.6/2 = $2304
Ordering cost = (D/Q) x S = (21570/480)*50 = $2246.9
Safety stock carrying cost = SS x H = 58*9.6 = $556.8
Total relevant cost = $2304 + $2246.9 + $556.8 = $5,108, So, % increase =($5,108 - $4,944) / $4,944 = 3.3%
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