asap Problem 2: Inventory Management A distributor uses a continuous review syst
ID: 422241 • Letter: A
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Problem 2: Inventory Management A distributor uses a continuous review system to manage its inventory. Parts are purchased with the entire order arriving at the same time (instantaneous replenishment). The information belovw represents one SKU, stock keeping unit, of critical importance. Unit Cost of Material Annual Demand Standard Deviation of Daily Demand Business Days Per Year Average Material Lead Time Standard Deviation of Lead Time $250 100,000 units 20 250 7 days 2 days $500 per orde 40% per year Cost Annual Holding Cost As % of Purchase C 2A. Determine the reorder point, assuming that there is NO safety stock. (3 points) 2B. Determine the optimal order quantity. (4 points) of the ndivid 20. Determine the safety stock for a service level of 97.5%. The demand is normally distributed and the safety stock must protect against uncertainties in both lead time and daily demand. (4 points) eterr whic ry, 20. The suppler offered a 15% discount if the company orders a minimum of 2000 units each time Determine if it is an economically attractive offer. (3 points) 7 of 10 in a w the fc assembly plant uses a variety of nuts, bolts, screws,. euor thuto the point of use on the assembly line anaExplanation / Answer
2A.
Without safety stock the reorder point quantity is determined as follows:
Reorder point = Daily demand x lead time
Daily demand = d = Annual Demand/days per year = 100,000/250 = 450 units
Lead time = L = 7 days
Reorder point = d x L = 400 x 7 = 2800 units
Reorder point = 2800 units
2B.
Optimal Order quantity = Q* = ?(2AS/(I x C))
A = Annual Demand = 100,000 units
S = setup cost = $500 per order
I = annual holding cost = 40% per year per unit
C = unit cost of material = $250 per unit
Q* = ?(2*100,000*500/(0.4 x 250))
Q* = 1000 units
Optimal Order quantity = 1000 units
2c.
Cycle Service Level = 97.5%
z-score for CSL = 0.975 is 1.96
The Safety stock is given as follows:
SS = z?(L?d2 + d?L2)
?d = SD of daily demand = 20 units
?L = SD of Lead time = 2 days
SS = 1.96 x ?((7)(20)2 + (400)(2)2)
SS = 1.96 x 66.33
SS = 130 units
Safety Stock = 130 units
2D.
For the given problem quantity discount or price-volume range model is applied.
Quantity Discount Model
1. For each price range (C), compute EOQ
2. If EOQ < Minimum quantity for price range, adjust the quantity to Q = Minimum for discount. If the EOQ > Maximum quantity for discount, adjust the quantity to Q = Maximum for discount. If the EOQ is within the range, then adjust Q = EOQ.
3. For each EOQ or adjusted Q, compute Total cost
4. Choose the lowest-cost quantity.
Price 15% discount of actual price if the order quantity is 2000 units
Discounted price = (1 – 0.15) x 250 = $212.5
Annual Demand
A
100000.00
Setup cost
S
500.00
Holding cost per month
I
40%
Option
Unit Price (C)
EOQ
Optimal order quantity
Annual Material Cost
Annual Ordering Cost (AOC)
Annual Carrying Cost (ACC)
Total Material Cost
= Material Cost + AOC + ACC
?(2*A*S/C*I)
(Q)
A*C
(A/Q)*S
(Q/2)*H
Actual plan
250
1000
1000
$25,000,000
$50,000
$50,000
$25,100,000
Discount Plan
212.5
1085
2,000
$21,250,000
$25,000
$85,000
$21,360,000
The lowest cost is for Discount plan, thus the economic order quantity is 2000 units per order.
Annual Demand
A
100000.00
Setup cost
S
500.00
Holding cost per month
I
40%
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