1. Inventory- a stock or store of goods
Dependent demand items- components or sub-assemblies (In a Roland piano, the bench, for example). Forecast is based on # of related finished goods
Independent demand items- finished goods that have their own demand curve (subject to randomness we discussed during forecasting section

2. Types of inventories- piano example
Raw materials & parts (e.g. piano keys)
Work In Process (keyboard assembly)
Finished Goods (keyboard, stand and bench)
Replacement items (keyboard cover handle)
In-transit inventory

3. Why keep inventory if it costs so much?
There are times in which the cost of keeping inventory is less than the benefits derived:
smooth production requirements as seen in Agg. Planning examples
decouple operations A distribution company wants to keep distributing even if the ship carrying the next shipment is late!

4. Why keep inventory if it costs so much?
To meet our stockout goals. Software is quick-decision purchase- many companies have 0% stockout strategies as a result (I.e. opportunity cost = 100%; inventory cost may equal 50%)
To capitalize on opportunities. If we have excess warehouse and staff capacity, we may save by buying a lot at a great price.

5. Ordering: quantity & timing Realities in the real world
Your order quantity may have to be done for political reasons (new product the president is behind- Edirol example)
We may not be able to affect the timing of orders. Distribution companies usually have to place 3 or even 6 month orders for highly technological products to smooth production planning. So fixed interval models are developed.

6. Counting Inventory
Periodic systems count physically at regular intervals and re-order when necessary. Your accounting audit will require this.
Perpetual systems (that count inventory as it changes in real time and re-ordering when we hit a reorder point) are almost universally used as the cost of computing has decreased.
Most companies combine use of both.

7. Adding math models to your tool kit
What is the lead time of your order (time between submission & receipt)
What is your holding cost (includes interest, insurance obsolescence, theft, wear, warehousing, etc.)
What is your ordering cost (including the cost of the transaction and receipt
What is your Shortage cost (opportunity)

8. What inventory do we evaluate?
Pareto principle tells us that 20% of our items will account for 80% of our orders/ supply requests
So, use the ABC system to classify value Item demand Unit Cost Annual $ value Class

9. More on ABC System
Can be used to determine number of re-counts in physical counts (e.g. A’s get 3; B’s get 2; C’s get 1)
Can also be used to determine who does counts (A’s counted by controller, staff & warehouse; B’s by staff & warehouse; C’s by warehouse only)

10. Profile of Inventory Level Over Time
The Inventory Cycle
Profile of Inventory Level Over Time Q
Usage
rate
Quantity
on hand
Reorder
point
Time
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time

11. So we’ve evaluated the right inventory. Now let’s order.
EO Q Model minimizes the sum of holding and ordering costs by finding the optimal order quantity.
Assumptions: 1) one product at a time; 2) we’re confident in our annual demand forecast; 3) demand is even; 4) lead time is constant (management issue); 5) orders received in one delivery; 6) no qty discounts

12. Getting to EOQ: we’re balancing...
ANNUAL CARRYING COST = (Q/2)*H (Q= order quantity units; H- carrying cost/unit)
ANNUAL ORDERING COST = (D/Q)*S (D= annual unit demand; Q= order size; and S= ordering cost
calculus then gives us EO Q, the optimal order quantity

13. Total cost = annual carrying cost + annual order cost
The Total-Cost Curve is U-Shaped
Ordering Costs QO
Order Quantity (Q)
Annual Cost
(optimal order quantity)
Carrying
Costs

14. Given that demand = 405/month
Carrying cost = $30/yr/unit Order Cost = $4/order
1) EOQ= SQR(2*(405*12)*4)/30)= 36
2)What is average # of bags on hand? Q/2= 18
3) # of orders per year= (405*12)/36 =135
4) Carrying cost = (36/2)*30=540; ordering cost= (4860/36)*4=540 total cost = =1080
**We need figures represented as annual costs.

15. Determining the economic run quantity of production
When company is producer and user, determines optimum production run size (since production usually happens faster than usage)
When we’re producing our own goods, assumes setup costs are the same as order costs in formula
so total cost = carrying cost +setup cost
TC = (Max. Inventory/2)*H + (D/Q)*S
Economic Run quantity = SQRRT(2DS/H)* SQRRT(p/(p-u)) where p=prod. Rate u=usage rate
cycle time =Q/u run time = Q/p

16. Quantity discounts if carrying costs are constant
Goal: minimize total cost, where TC = (Q/2)*H + (D/Q)*S + PD where P= unit price
Step 1: compute the common EOQ (if carrying cost is a constant $ figure, it won’t vary)
Step 2: compute total cost at EOQ and price breaks and compare

17. Quantity discounts if carrying costs are constant
Assume: D5000,/yr h= $2/unit/yr s=$48
Units Price
$10 $9
600+ $8
STEP 1: compute the common EOQ= SQR ((2DS)/H) = SQR((2*5000*48)/2)=
STEP 2: compute the EOQ (490) = (Q/2)*H + (D/Q)*S + PD = (490/2)* /490)*48 + (9*5000) = $45980 (with rounding)
STEP 3: compare with TC at discount levels TC = (Q/2)*H + (D/Q)*S + PD = (600/2)*2 + (5000/600)*48 + (8*5000)= 41000
600 is the optimum order quantity account for discounts

18. We know how much to order… now, when do we reorder?
ROP: predetermined inventory level of an item at which a reorder is placed.
Demand (d) and Lead TIME (LT)
ROP= d*LT
Example: Monthly demand is 400. Lead Time is two weeks (.50 months). ROP= 400 *.50 =200
Reorder when inventory level reaches 200.
This model assumes static d and LT

19. What if demand or lead time is variable?
Then we add a safety stock to help us satisfy orders if demand is higher than expected.
Company policy: What is our service level? It is the number: 1- stock-out risk. “Our service level goal is 95%. In other words, there’s a 95% probability we won’t stock out.

20. Handling variability, 2
We assume the variability is characterized by the normal distribution.
Turn to page 889. The shaded area under the curve represents the probability of us having inventory, given the variability in the average demand or average lead time.
So let’s say we have a service level goal of 95%. What is the Z score that characterizes 95% of the area under the normal curve?
About 1.645

21. When lead time is variable:
First example: LEAD TIME variable.
When lead time is variable, ROP= d* avgLT + z*d(LT) where d= demand rate; LT= lead time; LT=std. Dev. Of lead time
Get the z score (based on your service level goal) from the table as we saw on the last slide based on company’s stockout policy..

22. ROP= d* avgLT + z*d(LT)
Given: demand during lead time =400/day
Lead Time = 5 days,  =2 acceptable stockout risk= 5%
STEP 1: get your Z score = z (.95) =1.65
STEP 2: plug in * *400*2= 3320
Reorder when inventory = 3320

23. If demand rate is variable:
ROP= avgd* LT + z* sqr.root of LT * (d)
assume: avg d =1000; d= 14; LT=4; company stockout policy = 10% risk.
Z score for .90 = 1.28
1000* * 2 * 14= = 4036
in real world, d is derived by managers keeping careful records to determine it.

24. For next time PROBLEMS (not questions) Ch 12 #s 1,6,13,19,
Page 587- know models 1,2,3, and 4a,b,c

25. Problem 1 Item Usage Unit Cost Value Class 4021 90 1400 126000 A

26. Problem 6 D=800/MO @ $10/UNIT S=$28 H= 35% OF UNIT COST/YR
D- 9600/YR H= $3.50/UNIT/YR
CURRENT TC = (q/2)*H + (D/Q)*S
CURRENT TC= (800/2)* (9600/800)*28 =1736
EOQ= square root of ((2DS)/H)
EOQ = SQR ((2*9600*28)/3.50) =SQR =391.91= 392
TC at 392= (392/2 )*3.5 + (9600/392)*28=
Cost savings = =364

27. Problem 13: carrying costs are constant
D=18000 H= $0.60/yr S=$96
STEP 1: Common EOQ= SQR ((2DS)/H) = SQR((2*18000*96)/.6)= 2400
STEP 2: = (Q/2)*H + (D/Q)*S + PD =(2400/2)* (18000/2400)*96 + (1.20*18000)=$23040
= (5000/2)* (18000/5000)*96 + (18000*1.15)=$
(10000/2)*.60 + (18000/10000)* *1.10=
5000 is the optimum order quantity account for discounts

28. Problem 19, page 597
see page 573, equation The estimate of standard deviation of lead time demand is available, so you can use this simpler equation
Expected demand during LT = Std dev of LT demand = 30
a) Step 1 z=2.33
a) step (2.33*30)=69.9=370
b) from a)--> 70 units
c)less safety stock is required because we’d be carrying an amount of inventory causing us to stock out more often.

29. Problem 23 625= 85*6 + z*85*1.10 solving for z, z=1.22
Hint: plot the information you do have under the equation, then solve for what you don’t have.
When the book says “the delivery time is normal” that means we’ve got a variable lead time problem.
When lead time is variable, ROP= d* avgLT + z*d(LT) where d= demand rate; LT= lead time; LT=std. Dev. Of lead time
625= 85*6 + z*85*1.10
solving for z, z=1.22
from table on p. 883, that shows an 89% probability of supply, implying an 11% probability the supply will be exhausted.