Costs involved in Inventory Models

1
Costs involved in Inventory Models

• Ordering (Setup) cost
• Unit purchasing (Production) cost
• Holding (Carrying) cost
• Shortage (Penalty) cost
• Revenue (Selling price)

2
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.

3
Inventory Levels

• Inventory vs. time.

Usage rate (D)
Inventory ( Q )
Reorder Point (ROP)
time
Cycle time (T)
Lead time ( L, l )
4
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

5
Total Cost vs. Order Quantity.
Combined curve holding setup.
Annual Cost
Minimum annual cost
Holding cost curve
Well find an equation for this amount
Setup cost curve
Optimal order quantity
Order Quantity
6
Annual setup cost equation
Q, K, D demand / quantity per order of
orders. of orders K annual setup cost.

• What is related to it?

7
Annual holding cost equation.

• Q order quantity Q H.
• inventory is replenished precisely when no
  inventory remains.
• Average inventory

8
Annual holding cost equation.
Q 2
Annual holding cost
H

9
Finding where they are equal.

• The minimum cost of the system will be found
  where ASC AHC.

Q 2
D Q
AHC
ASC
H
K


10
Solve for Q

• The minimum cost of the system will be found
  where ASC AHC.

Q 2
D Q
H
K



11
Solve for Q

• The minimum cost of the system will be found
  where ASC AHC.

2DK
Q2

H
12
Solve for Q

• The optimal order quantity that results in the
  lowest system cost is called Q

2DK
Q

H
13
Holding costs

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

cQ 2
Hc
14
Holding costs

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

i cQ 2
Hf
15
Holding costs

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

sQ 2
Hs
16
Total holding costs

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

( s i c ) Q 2
Ht
17
Other factors (lurking in the shadows)

• Unit cost (production cost) cost per unit to buy
  the inventory symbol c
• Annual unit cost cD

18
Other factors (lurking in the shadows)

• Revenue profit per unit of inventory sold
  symbol r
• Annual revenue rD

19
Total Cost of the System
( s i c ) Q 2
DK Q
Total cost cD
Cost of inventory
Cost of the products
Cost of ordering
20
Determine reorder point

• Demand is constant. Lead time is known.

21
MS Excel example

• (Go to it)

22
Preview of Thurs. 2 other models (ind. D)
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 WASNT there
  when you set it up.)

• Production Order Quantity Model
• Quantity Discount Model