costs involved in inventory models ordering (setup) cost unit purchasing (production) cost holding...
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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.
Inve
ntor
y (
Q )
time
Usage rate (D)
Cycle time (T)Lead time ( L, l )
Reorder Point (ROP)
Symbols in EOQ models
• Order quantity: Q
• Optimal order quantity: Q*
• Annual demand (units): D
• Setup cost per order: K
• Holding cost (per unit): H
Total Cost vs. Order Quantity.A
nnua
l Cos
t
Order Quantity
Holding cost curve
Setup cost curve
Combined curve:holding & setup.
Minimumannual
cost
Optimal order quantity
We’ll findan equationfor this amount
Annual setup cost: equation• What is related to it?
Annual setup cost = DQ
K*
Q, K, & Ddemand / quantity per order = # of orders.# of orders * K = annual setup cost.
Annual holding cost: equation.• Q: order quantity Q & H.
• inventory is replenished precisely when no inventory remains.
• Average inventory =
Q
time
Constant slope
Q/2
Annual holding cost: equation.
Q
time
Annual holding cost = Q2
H*
Finding where they are equal.• The minimum cost of the system will be
found where ASC = AHC.
AHC = Q2
H*ASC = DQ
K*
Solve for Q• The minimum cost of the system will be
found where ASC = AHC.
Q2
H*DQ
K* =
Solve for Q• The minimum cost of the system will be
found where ASC = AHC.
Q2
H2DK =
Solve for Q• The optimal order quantity that results in
the lowest system cost is called Q*
Q*H
2DK =
Holding costs
• Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs:
cQ2
Hc =
Holding costs
• Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs:
i * cQ2
Hf =
Holding costs
• Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs:
sQ2
Hs =
Total holding costs
• Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs:
( s + i c ) Q2
Ht =
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
( s + i c ) Q2
Total cost = cD + + DKQ
Cost of theproducts
Cost of ordering
Cost of inventory
Determine reorder point• Demand is constant. Lead time is known.
Q
time
ROP
L
ROPQ
LT
=
MS Excel example
• (Go to it)
Preview of Thurs.: 2 other models (ind. D)
• Production Order Quantity Model
• Quantity Discount Model
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.)