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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:

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costs involved in inventory models
Costs involved in Inventory Models
  • Ordering (Setup) cost
  • Unit purchasing (Production) cost
  • Holding (Carrying) cost
  • Shortage (Penalty) cost
  • Revenue (Selling price)
basic eoq model
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 Levels

Usage rate (D)

  • Inventory vs. time.

Inventory ( Q )

Reorder Point

(ROP)

time

Cycle time (T)

Lead time ( L, l )

symbols in eoq models
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
Total Cost vs. Order Quantity.

Combined curve:

holding & setup.

Annual Cost

Minimum

annual

cost

Holding cost curve

We’ll find

an equation

for this amount

Setup cost curve

Optimal order quantity

Order Quantity

annual setup cost equation

D

Q

Annual setup cost =

K

*

Annual setup cost: equation

Q, K, & D

demand / quantity per order = # of orders.

# of orders * K = annual setup cost.

  • What is related to it?
annual holding cost equation

Q/2

Constant slope

Q

time

Annual holding cost: equation.
  • Q: order quantity Q & H.
  • inventory is replenished precisely when no inventory remains.
  • Average inventory =
annual holding cost equation1

Q

time

Annual holding cost: equation.

Q

2

Annual holding cost =

H

*

finding where they are equal
Finding where they are equal.
  • The minimum cost of the system will be found where ASC = AHC.

Q

2

D

Q

ASC =

AHC =

H

K

*

*

solve for q
Solve for Q
  • The minimum cost of the system will be found where ASC = AHC.

D

Q

Q

2

K

H

=

*

*

solve for q1
Solve for Q
  • The minimum cost of the system will be found where ASC = AHC.

2DK

=

Q2

H

solve for q2
Solve for Q
  • The optimal order quantity that results in the lowest system cost is called Q*

2DK

=

Q*

H

holding costs
Holding costs
  • Total annual holding cost: inc. monetary value of inventory,annual cost of capital, storage costs:

cQ

2

Hc =

holding costs1
Holding costs
  • Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs:

i * cQ

2

Hf =

holding costs2
Holding costs
  • Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs:

sQ

2

Hs =

total holding costs
Total holding costs
  • Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs:

( s + i c ) Q

2

Ht =

other factors lurking in the shadows
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 shadows1
Other factors (lurking in the shadows)
  • Revenue: profit per unit of inventory sold: symbol “r”
  • Annual revenue = rD
total cost of the system
Total Cost of the System

DK

Q

( s + i c ) Q

2

Total cost = cD + +

Cost of

inventory

Cost of the

products

Cost of

ordering

determine reorder point

ROP

Q

L

T

=

Q

ROP

L

time

Determine reorder point
  • Demand is constant. Lead time is known.
preview of thurs 2 other models ind d

Homework: due Thursday

Preview of Thurs.: 2 other models (ind. D)
  • 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.)
  • Production Order Quantity Model
  • Quantity Discount Model