1. Inventory Control Model
Kusdhianto Setiawan
Gadjah Mada University

2. Inventory Planning & Control
Planning on what
Inventory to stock
And how to acquire it
Forecasting
Parts/Product
Demand
Controlling
Inventory
Levels
Feedback Measurements
To revise plans and forecasts

3. Importance of Inventory Control
The Decoupling Function….. Inventory as a buffer
Storing Resources…. Where JIT is not possible
Irregular Supply and Demand
Quantity Discount
Avoiding stockouts and shortages

4. Inventory Decision How much to order When to order
With respect to (constraint) inventory cost:
Cost of the items
Cost of ordering
Cost of carrying/holding
Cost of safey stock
Cost of stockouts

5. Inventory Cost Factors
Ordering Cost Factors
Carrying Cost Factor
Developing & Sending Purchase Order (PO)
Cost of Capital
Processing & inspecting incoming iventory
Taxes
Bill Paying
Insurance
Inventory Inquiries
Spoilage
Utilities, phone bills, etc for the purchasing dept.
Theft
Salaries & wages for purchasing dept. employees
Obselescence
Supplies e.g: paper, toner printer, billing form, etc. for the purchasing dept.
Salaries & wages for warehouse employees
Utilities & building cost for the warehouse
Supplies such as forms & papers for the warehouse.

6. Economic Order Quantity (EOQ)
Objective: Determining how much to order
Assumptions:
Demand is known and constant
Lead time, the time between the placement of the order and the receipt of the order, is known and constant
The receipt of inventory is instantaneous
Quantity discount are not possible
Variable costs: ordering cost and holding/carrying cost
If orders are placed at the right time, stockouts/shortages can be avoided completely

7. EOQ Continued…. Order Quantity = Q = Maximum inventory level
Minimum Inventory Level
Time

8. EOQ Continued…. Cost Minimum Total Cost Carrying Cost Curve
Ordering Cost Curve
Optimal Order Quantity
Order Quantity

9. Computing Average Inventory
Day
Inventory Level
Beginning
Ending
Average
1 (order received) 10 8 9 2 6 7 3 4 5 1
Demand: Constant, 2 units/day
Ending Inventory is assumed to be always zero
Maximum level = 10 units
Total of Daily average = = 25
Number of days = 5
Average inventory level = 25/5 = 5 …… Q/2

10. Finding the EOQ Expression: Q = number of pieces per order
Q* = optimal number of pieces per order
D = annual demand in units for the inventory items
C0 = ordering cost for each order
Ch = holding cost per unit per year

11. Finding the EOQ Annual Ordering Cost
= no. of order placed per year x order cost per order
Annual Holding or Carrying Cost
= Average inventory level x carrying cost per unit per year
= (Q/2) Ch
Optimal Order Quantity
ordering cost = carrying cost
(D/Q)Co = (Q/2)Ch 4.

12. Finding Reorder Point (ROP)
ROP = (demand/day) x (lead time for a
new order in days)
ROP = d x L
Inventory Level (Units) Q*
Slope = units/day = d
Lead Time = L
Time
(days)
ROP
(units)

13. EOQ Without The Instantaneous Receipt Assumption
Inventory Level
Part of inventory cycle during which
Production is taking place
There is no production
During this part of the inventory cycle
Maximum Inventory
time t
Production Run Model

14. Annual Carrying Cost New terms:
t = length of the production run (days)
p = daily production rate
Annual inventory holding/carrying cost
= average inventory level x carrying cost/unit/year
= average inventory level x Ch
Average inventory level = ½ Maximum inventory level
Maximum inventory level
= (total produced during the production run)
- (total used during the production run)
Q = pt  t = Q/p
Max Inv. Level = p(Q/p) – d(Q/p) = Q – (d/p)Q = Q(1-d/p)
Annual Inventory carrying cost
= ½ (max. inv. Level) x Ch
= ½ Q(1-d/p)Ch

15. Annual Setup/Ordering Cost
Annual setup cost
= (no. of setup/year) x (setup cost/setup)
= (D/Qp)Cs
where:
D = annual demand in units
Qp = Quantity produced in one batch
Cs = setup cost per setup
Annual Ordering Cost
= (D/Q)Co

16. Optimal Order Quantity for Production Run Model
Ordering Cost = Carrying Cost
(D/Q)Co = ½ ChQ(1-d/p)
Optimal Order Quantity
Optimal Production Quantity, Q*p

17. Quantity Discount Model
Quantity Discount Schedule
Discount Number
Discount Quantity
Discount (%)
Discount Cost ($) 1
0-999
5.00 (normal cost) 2
1,000 – 1,999 4
4.80 3
2,000 – over 5
4.75
Total Cost = material cost + ordering cost + carrying cost
= DC + (D/Q)Co + ½ QCh

18. Total Cost Curve Total Cost TC for Disc. 1 TC for Disc. 3
Q* for Disc. 2
Order Quantity
1,000
2,000

19. Use of Safety Stock
Safety stock: additional stock that is kept on hand
It is used only when demand is uncertain
Main purpose: to avoid stockouts when the demand is higher than expected
ROP = d x L (normal condition)
ROP = d x L + SS (demand is uncertain)
Because it is dealing with decision under risk, knowing the probability of demand is necessary.

20. Safety Stock with Known Stockout Costs
Case of ABCO
ROP = 50 units (= d x L)
Ch = $5 (per unit per year)
Cso = $40/unit (stockout cost)
Optimal number of orders per year is 6
Objective: to find the reorder point, including safety stock, that will minimize total expected cost
Total expected cost is the sum of expected stockout cost plus expected additional carrying cost

21. Probability of Demand for ABCO
Number of Units
Probability 30
0.2 40
50 (ROP)
0.3 60 70
0.1
Total
1.0

22. Annual Expected Stockout Cost
When the ROP < demand over lead time
Total Cost = Stockout Cost
= no. of units short x stockout cost/unit x
no. of orders per year
When the ROP > demand over lead time
Total Cost = total additional carrying cost
= no. of surplus units x carrying cost

23. ABCO’s Stockout Costs Probability 0.20 0.30 0.10 State of Nature
Alternative 30 40 50 60 70
EMV
2,400
4,800
7,200
9,600
4,320
2,410
100
990
150
305
200
110

24. Safety Stock with Unknown Stockout Cost
There are many situation when stockout cost are unknown or extremely difficult to determine, i.e: major stockout cost is the loss of goodwill, how to measure it?
Alternative approach: using service level
Service level = 1 – probability of a stockout or
Probability of a stockout = 1 – service level

25. Hinsdale Company Example
Average demand = 350 units
Standard Deviation = 10
Hinsdale wants to follow a policy that result in stockout occuring only 5% of the time.
How much safety stock should be maintained?

26. Safety Stock & Normal Distribution
σ=10
X = mean + safety stock
SS = safety stock = X – μ
Z = (X – μ) / σ = SS/ σ
Z value for an area under the normal curve of 0.95 (=1-0.05) is 1,65 (see appendix A)
SS = 1.65 (10) = 16.5 units or 17 units
SS = Z σ SS
μ=350
X=?