Consider a producer who can receive shipments by sea or air. The mean demand is
ID: 446688 • Letter: C
Question
Consider a producer who can receive shipments by sea or air. The mean demand is 5000/week, H = 0.50 $/unit/year, S= 20000/order. L=2 weeks if they ship by air. Standard deviation of damnd = 1500 per week. Suppose we have the following extra information: if they ship by sea instead of air, L=3 weeks. It saves $5000 per year in transportation cost. Assume service level needed is 95%.
a). Note that if lead time increases safety stock will increase. Compute by how much.
b). Should they ship by sea ? (Hint; Compute the change in safety stock if they ship by sea. Then see if the cost of carrying this additional stock is worth the saving in transportation cost.)
Explanation / Answer
a)
Safety Stock is given as
= Z(@ 95% service level) * SQRT[ Expected Lead time * Standard deviation of demand ^2 + (Expected Demand*Standard deviation of Lead time)^2]
In case of Air
Lead time = 2 , Standard deviation of demand = 1500, Mean demand = 5000,
At 95 % service level , z = 1.65, as no change in lead time, Stddev of lead time = 0
Safety Stock , Air = 1.65 * SQRT( 2*1500^2+0) = 1.65 * 2121.32 = 3500.17 ~= 3500
For the Ship, Lead time = 3 and other units remain the same
Safety Stock , Ship = 1.65 * SQRT( 3*1500^2+0) = 1.65 * 2598.07 = 4286.82 ~= 4287
We see Safety Stock Ship 4287 is higher than safety stock, Air, 3500
The safety Stock is higher by 787 Units
b) Yes they should ship by sea because the savings in Transportation costs supersedes the Holding cost beacuse of additional Inventory
Holding Cost = 0.5 $/Unit/year
Holding cost of increased Safety Stock = 787 * 0.5$/Unit/Year = 393.5$/year
The Holding Cost of Additional Safety Stock is way less than 5000 $ saved in Transportation. Hence it should be shipped by Sea
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