Costs involved in Inventory
Models
•
•
•
•
•
Ordering (Setup) cost
Unit purchasing (Production) cost
Holding (Carrying) cost
Shortage (Penalty) cost
Revenue (Selling price)
Basic EOQ Model
• EOQ: Economic Order Quantity
• Assumptions of EOQ models:
– Demand is constant (unvarying ), expressed as
annual demand (units per year ).
– Models use continuous review, not periodic review.
– Lead time is constant & known.
– Quantity discounts are not possible.
– 2 variable costs: setup cost and holding cost.
Inventory Levels
• Inventory vs. time.
Usage rate (D)
Reorder Point
(ROP)
Lead time ( L, l )
Cycle time (T)
time
Symbols in EOQ models
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•
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•
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Order quantity:
Optimal order quantity:
Annual demand (units):
Setup cost per order:
Holding cost (per unit):
Q
Q*
D
K
H
Annual Cost
Total Cost vs. Order Quantity.
Combined curve:
holding & setup.
Minimum
annual
cost We’ll find
an equation
for this amount
Optimal order quantity
Holding cost curve
Setup cost curve
Order Quantity
Annual setup cost: equation
• What is related to it? Q, K, & D
demand / quantity per order = # of orders.
# of orders * K = annual setup cost.
D
Annual setup cost =
*K
Q
Annual holding cost: equation.
• Q: order quantity Q & H.
• inventory is replenished precisely when no
inventory remains.
• Average inventory = Q/2 Constant
slope
Q
time
Annual holding cost: equation.
Q
Annual holding cost =
*H
2
Q
time
Finding where they are equal.
• The minimum cost of the system will be
found where ASC = AHC.
D
ASC = *K
Q
Q
AHC = *H
2
Solve for Q
• The minimum cost of the system will be
found where ASC = AHC.
D
*K =
Q
Q
*H
2
Solve for Q
• The minimum cost of the system will be
found where ASC = AHC.
2DK = Q2
H
Solve for Q
• The optimal order quantity that results in
the lowest system cost is called Q*
2DK = Q*
H
Holding costs
• Total annual holding cost: inc. monetary
value of inventory, annual cost of capital,
storage costs:
Hc =
cQ
2
Holding costs
• Total annual holding cost: inc. monetary
value of inventory, annual cost of capital,
storage costs:
Hf =
i * cQ
2
Holding costs
• Total annual holding cost: inc. monetary
value of inventory, annual cost of capital,
storage costs:
Hs =
sQ
2
Total holding costs
• Total annual holding cost: inc. monetary
value of inventory, annual cost of capital,
storage costs:
(s+ic)Q
Ht =
2
Other factors
(lurking in the shadows)
• Unit cost (production cost): cost per unit to
buy the inventory: symbol “c”
• Annual unit cost = cD
Other factors
(lurking in the shadows)
• Revenue: profit per unit of inventory sold:
symbol “r”
• Annual revenue = rD
Total Cost of the System
DK ( s + i c ) Q
Total cost = cD +
+
Q
2
Cost of the
products
Cost of
ordering
Cost of
inventory
Determine reorder point
• Demand is constant. Lead time is known.
ROP
L
=
Q
T
Q
ROP
time
L
MS Excel example
• (Go to it)
Homework: due Thursday
• p. 470, #1, 2, 4 - turn in ON PAPER
(preferably computer printouts, each on 1 sheet of
paper that can be understood by someone who
WASN’T there when you set it up.)
Preview of Thurs.: 2 other
models (ind. D)
• Production Order Quantity Model
• Quantity Discount Model