Transcript Inventory Management

Inventory Management
Chapter 13
Inventory Costs
• Purchase cost
– The amount paid to buy the inventory
• Holding (carrying) costs
– Cost to carry an item in inventory for a length of time, usually a year
• Interest, insurance, taxes (in some states), depreciation, obsolescence,
deterioration, spoilage, pilferage, breakage, tracking, picking, and
warehousing costs (heat, light, rent, workers, equipment, security).
• Ordering costs
– Costs of ordering and receiving inventory
• determining how much is needed, preparing invoices, inspecting goods
upon arrival for quality and quantity, and moving the goods to temporary
storage.
• Shortage costs
– Costs resulting when demand exceeds the supply of inventory; often
unrealized profit per unit
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The Inventory Cycle
Profile of Inventory Level Over Time
Q
Usage
rate
Quantity
on hand
Reorder
point
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Time
Lead time
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Total Annual Cost
• Total Cost = Annual Holding Cost + Annual Ordering
Cost
Q
D
(TC) =
H
+
S
2
Q
Average number of
units in inventory
Number of
orders
where
• Q = order quantity in units
• H = holding (carrying) cost per unit, usually per year
• D = demand, usually in units per year
• S = ordering cost per order
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Deriving EOQ
• Using calculus, we take the derivative of the total
cost function and set the derivative (slope) equal
to zero and solve for Q.
• The total cost curve reaches its minimum where
the carrying and ordering costs are equal.
𝐻
−1 𝐷𝑆
𝑇𝐶 = +
=0
2
2
𝑄
′
𝑄∗
=
2𝐷𝑆
=
𝐻
→
𝐷𝑆 𝐻
=
2
𝑄
2
→
𝐷𝑆 𝐻𝑄
=
𝑄
2
2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡
𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
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EPQ: Inventory Cycle
Q
Production
and usage
Usage
only
Production
and usage
Usage
only
Production
and usage
Qp
Cumulative
production
Imax
Amount
on hand
Time
Instructor Slides
13-6
Time
• Cycle time
– The time between setups of consecutive runs
• Run time
– The production phase of the cycle
EPQ – Total Cost
TC min  Carrying Cost  Setup Cost
I
  max
 2
D

H

S

Q

where
I max  Maximum inventory

Qp
 p  u
p
p  Production or delivery rate
u  Usage rate
Instructor Slides
13-8
EPQ
2 DS
Qp 
H
p
p u
Optimal Batch size a.k.a Economic Produciton Quantity (EPQ)
Instructor Slides
13-9
Quantity Discount Model
• Quantity discount
– Price reduction for larger orders offered to customers
to induce them to buy in large quantities
Total Cost  Carrying Cost  Ordering Cost  Purchasing Cost
Q
D
 H  S  PD
2
Q
where
P  Unit price
Instructor Slides
13-10
Reorder-Point
ROP
= (Demand per day) * (Lead time for a new order in days)
=
d * L
where
d = (Demand per year) / (Number of working days in a year)
Example:
– Demand = 12,000 iPads per year
– 300 working day year
– Lead time for orders is 3 working days
In other words, the
manager should place the
order when only 120 units
left in the inventory.
d = 12,000 / 300 = 40 units
ROP = d * L = 40 units per day * 3 days of leading time = 120 units
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