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HW 4

This document calculates the optimal order quantity to minimize total costs for four different order quantities using data on range, price, holding cost, and demand. It determines that ordering 1000 units results in the lowest total cost of $25,490. It then evaluates two suppliers based on quantity ranges, unit prices and holding costs to determine the optimal order quantity that minimizes total costs for each supplier. For Supplier A, the optimal order quantity is 254 units with a total cost of $134,429.89. For Supplier B, the optimal order quantity is 252 units with a total cost of $136,715.38. Finally, it calculates the safety stock and reorder point needed to achieve a 4% stockout policy based on

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Manju Sree
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78 views6 pages

HW 4

This document calculates the optimal order quantity to minimize total costs for four different order quantities using data on range, price, holding cost, and demand. It determines that ordering 1000 units results in the lowest total cost of $25,490. It then evaluates two suppliers based on quantity ranges, unit prices and holding costs to determine the optimal order quantity that minimizes total costs for each supplier. For Supplier A, the optimal order quantity is 254 units with a total cost of $134,429.89. For Supplier B, the optimal order quantity is 252 units with a total cost of $136,715.38. Finally, it calculates the safety stock and reorder point needed to achieve a 4% stockout policy based on

Uploaded by

Manju Sree
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
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(0.

40P)
Range Price H
0-999 5 2 D 4900
1000-3999 4.95 1.98 S 50
4000-5999 4.9 1.96
6000 and more 4.85 1.94

EOQ = √2DS/H
Q5 494.9747
Q4.95 497.4683
Q4.9 500
Q1.94 502.5707

First one is feasible because it is in range compared to the others. This is feasible as it falls within the range of 0 to 999.
Thus, the EOQ is 495 units for the holding cost of $2.00

Total Cost = Holding cost + Ordering Cost + Purchase cost


= Q/2H + D/QS + PD

TC494.9 25489.95

Ordering 6000 units will result in:


TC6000 29625.83

Ordering 4000 units will result in:


TC4000 27991.25

Ordering 1000 units will result in:


TC1000 25490

Thus the optimal order quantity to minimize total cost is 1000 units
ange of 0 to 999.
SUPPLIER A SUPPLIER B
Quantity Unit Price H Quantity Unit Price H
1-199 14 3.5 1-149 14.1 3.525
200-499 13.8 3.45 150-394 13.9 3.475
500+ 13.6 3.4 350+ 13.7 3.425

SUPPLIER A
For holding cost of $3.40
EOQ = 257.751791767137
Not feasible

For holding cost of $3.45 Total cost of 254 units


EOQ = 254.01625855312 Total Cost = Holding cost + Ordering Cost
Feasible = $ 134,429.89

For holding cost of $3.50


EOQ = 250.387454859504
Not feasible

Thus the EOQ is 254 units

SUPPLIER B
For holding cost of $3.43
EOQ = 255.870391827231
Not feasible

For holding cost of $3.48 Total cost of 252 units


EOQ = 252.188803455616 Total Cost = Holding cost + Ordering Cost + Purchas
Feasible Total Cost $ 136,715.38

For holding cost of $3.53


EOQ = 248.611657307309
Not feasible
S 40
D 9600

t of 254 units
t = Holding cost + Ordering Cost + Purchase cost
134,429.89

its
cost + Ordering Cost + Purchase cost
Lead time Demand 600
Std. Dev of Lead Time demand 52
Stock out policy 4%
z score 1.75

a
Safety Stock = Z x SD during lead time = 1.76 x 52 = 91.52 = 92 units

b
Reorder point = Demand during lead time + Safety Stock = 600 + 92 = 692 units

c The average demand during lead time is is 600 pounds. This will result in a stockout probability of 50%
kout probability of 50%

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