Inventory ManagementCopyright 2011 John Wiley & Sons, Inc.
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Purpose of inventory management
when to order
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Bullwhip effect
demand information is distorted as it moves away from the end-use customer
higher safety stock inventories to are stored to compensate
Seasonal or cyclical demand
Inventory provides independence between stages and avoids work stoppages
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Quality Management in the Supply Chain
Customers usually perceive quality service as availability of goods they want when they want them
Inventory must be sufficient to provide high-quality customer service in QM
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Items being transported
Tools and equipment
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Dependent
Independent
Cars, appliances, computers, and houses are examples of independent demand inventory
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Ordering cost
Shortage cost
temporary or permanent loss of sales when demand cannot be met
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Periodic system (fixed-time-period)
order placed for variable amount after fixed passage of time
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A
B
C
$85,400
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C 6, 5, 10, 7 12.5 60.0
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EOQ
Basic EOQ model
Production quantity model
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Demand is known with certainty and is constant over time
No shortages are allowed
Order quantity is received all at once
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Annual ordering cost =
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TC = +
CoD
Q
CcQ
2
=
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Qopt =
2CoD
Cc
Qopt =
2(150)(10,000)
(0.75)
= 311/5
Order is received gradually, as inventory is simultaneously being depleted
AKA non-instantaneous receipt model
assumption that Q is received all at once is relaxed
p - daily rate at which an order is received over time, a.k.a. production rate
d - daily rate at which inventory is demanded
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Q(1-d/p)
Inventory
level
(1-d/p)
Q
2
Time
0
Order
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Maximum inventory level = Q - d
= Q 1 -
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Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day
Qopt = = = 2,256.8 gallons
Q
p
2,256.8
150
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D
Q
10,000
2,256.8
= 1,772 gallons
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Solution of EOQ Models With Excel
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=(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8))
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TC = + + PD
P = per unit price of the item D = annual demand
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Qopt
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Qopt = = = 72.5 TVs
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=IF(D10>B10,D10,B10)
Reorder Point
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R = dL
L = lead time
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Lead time = L = 10 days
R = dL = (32.154)(10) = 321.54 gallons
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Stockout
Service level
probability that the inventory available during lead time will meet demand
P(Demand during lead time <= Reorder Point)
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Reorder
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Reorder
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where
z = number of standard deviations
corresponding to the service level
probability
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Copyright 2011 John Wiley & Sons, Inc.
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The paint store wants a reorder point with a 95% service level and a 5% stockout probability
d = 30 gallons per day
L = 10 days
For a 95% service level, z = 1.65
R = dL + z d L
= 30(10) + (1.65)(5)( 10)
= (1.65)(5)( 10)
= 26.1 gallons
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where
L = lead time
zd tb + L = safety stock
I = inventory level
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sd = 1.2 packages
tb = 60 days
L = 5 days
I = 8 packages
Q = d(tb + L) + zd tb + L - I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 packages
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