Inventory Control System

Inventory control system
[Document subtitle]
[DATE]

Question 1
Number of batches = 100
Costs of cutting = $14
Sell price = $30
Number of trees that should be cut down by the company =?
Expected profit =?
Assuming zero salvage value and hence,
Shortage cost = sell price – Cost of cutting = 30-14= $16
Overstocking cost = Cost of cutting – Salvage value = $14 – 0 = $14
Now,
Critical ratio = Shortage cost / (Shortage cost + Overstocking cost) = 16 / (16+14) = 0.53
Probability distribution
It can be seen based on the above table that the critical ratio falls at the cumulative
probability of 0.62 which means the corresponding batches would be 5.
Thereby, the total number trees = 5
Hence, it can be concluded that optimal number of trees that should be cut would be 5 trees.
1

Average demand = 4.83
Expected shortage = 0.71
Now,
Expected Sales = (Avg. demand) – (Exp. Sales) = 4.83 – 0.71 = 4.12
Expected overage =5 – 4.22 = 0.88
Expected revenue = {(Sell price * Expected sales) + (Expected overage* Salvage value)} *
Total batches = {(30*4.12) + (0.88*0)} * 100 = 12360
Expected cost = Cost of cutting * Optimal number of trees * Total batches = 14 *5*100 =
7000
Expected profit = Expected revenue – Expected cost = 12360 – 7000 = $5360
Therefore, the company would get an expected profit of $5360.
2

Question 2
D = 12.5
R = $65
S = $170
H = $7
L= 1
Optimal Value of Order Quantity ¿ ( 2∗D∗S
H )
0.5
Optimal Value of Order Quantity=( 2∗12.5∗170
7 )0.5
=24.64∨25
Reorder Level = DL = 12.5 * 1 = 12.5
Question 3
Service level = 95%
Mean demand of the company = 280 units a week
Standard deviation = 38 units
lead time = 2.2 weeks (Constant)
Company’s practice for this item would constitute the ROP and safety stock.
Safety Stock
Safety stock=Z∗standard deviation∗( Lead time ) 0.5
z value for 95 % service level=1.65
Safety stock=1.65∗38∗( 2.2 ) 0.5=92.9∨93
ROP
3