Given the following information, formulate an inventory management system. The i
ID: 422358 • Letter: G
Question
Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year. Standard deviation of weekly demand Lead time Service probability 25 per week Item cost Order cost Annual holding cost (%) $ 8.00 $178.00 4 weeks 98% 29% of item cost Annual demand Average demand 28,100 562 per week a. Determine the order quantity and reorder point. (Use Excel's NORMSINV) function to find your z value and then round that z-value to 2 decimal places. Do not round any other intermediate calculations. Round your final answers to the nearest whole number.) Optimal order quantity Reorder point units units b. Determine the annual holding and order costs. (Do not round any intermediate calculations. Round your final answers to 2 decimal places.) Holding cost Ordering costExplanation / Answer
a.
Optimal Order quantity = Q* = ?(2AS/(I x C))
A = Annual Demand = 28,100 units
S = Order cost = $178 per order
I = annual holding cost = 29% per year per unit
C = unit cost of material = $8 per unit
Q* = ?(2*28,100*178/(0.29 x 8))
Q* = 2077 units
Optimal Order quantity = 2077 units
d= average weekly demand = 562 per week
L = lead time = 4 weeks
?d = standard deviation in average weekly demand = 25 units per week
Service level = 98%
z-score for 98% CSL is 2.05
Safety Stock = z?d?L = 2.05 x 25 x ?4 = 102.5
Safety stock = 102.5 units
Reorder Quantity level for Q-model:
R = monthly demand during lead time + Safety stock
R = dL + z?d?L
R = (562)(4) + 102.5
R = 2350.5 units
Reorder point = 2350.5 units
b.
Annual Holding Cost
AHC = (Q/2 + SS) x C x I
(2077/2 + 102.5)x 0.29 x $8
= $2647.12
Annual Ordering
AOC = D/Q x S
28100/2077 x $178
$2408.18
Total annual Cost
TC = AHC + AOC
$2647.12 + $2408.18 = $5055.30
ANS:
Holding Cost = $2647.12
Ordering Cost = $2408.18
Total inventory cost = $5055.30
C.
With price break of $50 per order for order quantity of 2100 units, the cost calculation is as follows:
Annual Holding Cost
AHC = (Q/2 + SS) x C x I
(2100/2 + 102.5)x 0.29 x $8
= $2673.8
Annual Ordering
AOC = D/Q x S
28100/2100 x $50
= $669.05
Total annual Cost
TC = AHC + AOC
$2673.8 + $669.05
= $3342.85
Inventory cost without discount = $5055.30
Inventory cost as per price break = $3342.85
Total Cost saving = 5055.30 – 3342.85 = $1712.45
Total Cost Saving = $1712.45
Annual Holding Cost
AHC = (Q/2 + SS) x C x I
(2077/2 + 102.5)x 0.29 x $8
= $2647.12
Annual Ordering
AOC = D/Q x S
28100/2077 x $178
$2408.18
Total annual Cost
TC = AHC + AOC
$2647.12 + $2408.18 = $5055.30
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