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.)