1. Inventory Stock of items or resources used in an organization.
Manufacturing inventory refers to materials that contribute or become part of a firm’s product output.
raw materials
component parts or supplies
work-in-process
finished goods

2. Purpose of Inventory meet variation in product demand
provide safeguard for variation in raw material delivery
maintain independence of operations
allow flexibility in production scheduling
take advantage of quantity discounts

3. Inventory Costs storage handling insurance and taxes
pilferage and breakage
obsolescence and depreciation
opportunity cost of capital
order processing
shipping and receiving
production setup and changeover
lost sales
backorders
lateness penalties

4. Inventory System
Set of policies and controls that monitor levels of inventory (for all items).. .
determine what levels should be maintained
when stock should be replenished
how large an order should be
keep track of orders sent and received
reconcile records with physical inventory

5. Economic Order Quantity (EOQ) Model
Assumptions:
demand rate constant
instantaneous replenishment
price per item independent of order size
no backorders allowed
Questions:
When to order?
How much to order?

6. EOQ Model Notation: D = demand rate per unit time (year)
Inventory
level
Time
Notation:
D = demand rate per unit time (year)
C = cost per unit item
S = setup/order cost
H = holding cost per unit item per unit time
I = inventory holding percentage
(H = IC)
Q = quantity to be ordered

7. Total Cost (per unit time)
= purchase cost + ordering cost
+ holding cost
TC = DC + SD/Q + HQ/2
Best Q? or
EOQ formula

8. Annual Product Costs, Based on Size of the Order
TC (total cost)
HQ/2
(holding cost)
Cost
DC (annual
cost of items)
SD/Q
(ordering cost)
Qopt
Order quantity size (Q)

9. Basic Fixed-Order Quantity Model with Lead Time
Order when inventory drops to
R = DL where L = lead time L Q
Number
of units
on hand R
Time

10. Inventory position = on-hand + on-order inventoryL

11. EOQ with Usage p = replenishment rate d = demand rate L Buildup =
Production
rate minus
usage rate
(p-d)
taking place
Usage
rate d Q
No production;
usage only L
Number
of units
on hand R

12. EOQ vs. JIT EOQ: JIT: Who is right? Who is wrong?
order quantity set according to EOQ formula
JIT:
reduce inventory as much as possible
Who is right? Who is wrong?
What is the “right” order quantity?
What is the “true” cost of inventory?

13. Inventory Pooling
What happens to the optimal order quantity when the demand rate doubles? Triples?
Consequences?
Large supermarkets vs. mom-&-pop stores
“backup” agreements between stores

14. Global Supply/Distribution Chains
Decentralized System:
Centralized System:
Retailers
Factory
Depot
Factory
Retailers

15. Inventory Management-Single Period Model
order placed (and delivered) before demand is known
unmet demand is lost
unsold inventory at the end of the period is discard (or salvaged at lower value)
How much to order?
Newsboy Model

16. Newsvendor Model Marginal Profit = MP
= profit resulting from last unit sold
Marginal Loss = ML
= loss from last unit unsold
Stock one unit if ...
MP Pr(D > 0) > ML Pr(D < 0)
Stock 2 units if ...
Stock 1 Stock 2
D = 0
D = 1
D = 2
D = 3
D = 4

17. Prob(Demand > n) < MP ML + MP
Newsvendor Model
keep order size at 1
-ML
1 more unsold
order 2
instead of 1 MP
1 fewer lost sale
Additional
Benefit
Order 2 if
Pr(D<1) (-ML) + Pr(D>1) MP > 0
or Pr(D<1) (-ML) + [1-Pr(D<1)] MP > 0 or
Pr(D<1) < MP
ML + MP
Increase order to n+1 if
Prob(Demand > n) < MP
ML + MP

18. EXAMPLE / Salvage Value A product is priced to sell at $100 per unit, and its cost is constant at $70 per unit. Each unsold unit has a salvage value of $30. Demand is expected to range between 35 and 40 units for the period: 35 units definitely can be sold and no units over 40 will be sold. The demand probabilities and the associated cumulative probability distribution (P) for this situation are shown below.
The marginal profit if a unit is sold is the selling price less the cost, or MP = $100 - $70 = $30.
The marginal loss incurred if the unit is not sold is the cost of the unit less the salvage value, or ML = $70 - $30 = $40.
How many units should be ordered?
SOLUTION The optimal probability of the last unit being sold is

19. According to the cumulative probability table (the last column in table below, 37 units should be stocked. The net benefit from stocking the 37th unit is the expected marginal profit minus the expected marginal loss.
EXHIBIT Demand and Cumulative Probabilities
(p) CPn
Number of Units Probability of
Demanded This Demand to
or more 1.00

20. Marginal Inventory Analysis for Units Having Salvage Value
EXHIBIT 14.13
Marginal Inventory Analysis for Units Having Salvage Value
(N) (p) (P) (MP) (ML)
Units of Probability CPn Expected Marginal Expected Marginal
Demand of Demand Profit of n-th Unit Loss of n-th Unit (Net)
(100-70)(1- CPn-1) (70-30)CPn (MP)-(ML)
$30 $0 $30.00
(5.00)
(22.50)
(33.00)
(40.00)
Note: Expected marginal profit is the selling price of $100 less
the unit cost of $70 times the probability the unit will be sold.
Expected marginal loss is the unit cost of $70 less the salvage
value of $30 times the probability the unit will not be sold.
Net = (MP)(1 - CPn-1 ) - (ML) CPn-1
= ( )($100 - $70) - (0.75) ($70 - $30)
= $ $10.00 = $12.50
For the sake of illustration, Exhibit shows all possible
decisions. From the last column, we can confirm that the
optimum decision is 37 units.

21. Newsvendor Model- Demand Distribution Continuousy
Order y such that
Prob(Demand < y) = MP .
ML+MP

22. Summary Uses and Costs of inventory EOQ Model Demand Stochastic?
lead time OK
non-instantaneous replenishment OK
constant demand rate
no backorders
Demand Stochastic?
Newsvendor model