1. OPSM 501: Operations Management
Koç University Graduate School of Business
MBA Program
OPSM 501: Operations Management
Week 12:
Inventory Management
Order-up-to model
Zeynep Aksin

2. Levers for Managing Inventories
Theoretical Inventory Ith=R x Tth
Reduce critical activity times
Eliminate non-value added work
Move work from critical to non-critical
Redesign process to replace serial with parallel processing
Cycle inventory
Average inventory per cycle=Q/2
Reduce set-up to reduce cycle inventory

3. Levers for Managing Inventories
Seasonal Inventory
Use pricing and incentive tactics to smooth demand
Increase resource flexibility
Safety inventory-this is next!

4. A Multi-Period Inventory Model
Often, there are multiple reorder opportunities
Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The distributor periodically places orders to replenish its inventory

5. Set Up: Simple Supply Chain
orders
Pipeline
stock
Supply
On-hand
inventory
Inventory position
Three key questions:
How often to review?
When to place an order?
How much to order?

6. Timing in the order up-to model
Time is divided into periods of equal length, e.g., one hour, one month.
During a period the following sequence of events occurs:
A replenishment order can be submitted.
Inventory is received.
Random demand occurs.
Lead times:
An order is received after a fixed number of periods, called the lead time.
Let l represent the length of the lead time.
An example with l = 1
13-6

7. Order up-to model vs. newsvendor model
Both models have uncertain future demand, but there are differences…
Newsvendor applies to short life cycle products with uncertain demand and the order up-to applies to long life cycle products with uncertain, but stable, demand.
Newsvendor
Order up-to
Inventory obsolescence
After one period
Never
Number of replenishments
One (maybe two or three with some reactive capacity)
Unlimited
Demand occurs during replenishment No
Yes
13-7

8. Periodic Review, Order-up-to Policy
Inventory Position = Quantity + Quantity
on hand on order
S - Base stock level/Order-up-to Point
p - Review period; l - Replenishment lead time
 - Demand per unit time
ss - Safety stock
Ordering Rule:
Place an order every p periods so as to bring your
inventory position to the Base Stock Level, S.

9. Periodic review with no demand variability
Inventory Level
time
(p+l) p l l
p+l
2p+l
3p+l p 2p 3p 4p
On-hand inventory
Inventory position

10. Periodic review with no demand variability
Order Quantity, Q = p
Average Cycle stock = Q/2 = p / 2
Pipeline stock =  l
Order-up-to point, S =  (p + l)

11. Why hold Safety Inventory?
Demand uncertainty
Supply uncertainty
Measures of product availability
Product fill rate (f): fraction of demand that is satisfied from product in inventory
Cycle service level (CSL): fraction of replenishment cycles that end with all the customer demand being met

12. Periodic review with variable demand
Order-up-to point (S) =  (p+l) + Safety Stock (ss)
Average Order Quantity (Q) = p
Average Pipeline stock =  l
Average Cycle stock = Q/2 = p / 2
Safety Stock = ss = ?

13. Determination of the Safety Stock
Inventory Level
p+ss
l+ss ss
time
On-hand inventory
Inventory position
p+l+ss l
p+l
2p+l
3p+l p 2p 3p 4p

14. Probabilistic Models + = S
Key idea: Order-up-to target covers demand over time period of p+l X +
= S

15. Designing for a target CSL
Safety Stock (ss) =
Choosing z:
a=CSL= P(demand during p+l <= S)
z= Fs-1(CSL)

16. Example #1 Given: p = 2 weeks l = 3 weeks  = 1.5 units per week
Target service level, CSL=95%
Solve:
Safety stock =
Base stock level =
so from table, z = 1.64
Average on-hand inv= 1.5x2/2 + safety stock= =8.86

17. Example #2 Given: p = 2 weeks l = 1 week  = 1.5 units per week
Target service level, CSL=95%
Solve:
Safety stock =
Base stock level =
so from table, z = 1.64

18. Computer example continued
Suppose we do not know the base-stock level S
We know the company uses a periodic-review, order-up-to policy
From company data we know that average on-hand inventory is 12.6 units
What service level is the store providing?

19. Example #3
12.6= (1.5 x 2)/2 + z x 2 x
z =2.48
F(2.48)=0.993

20. Computer store: determining policy parameters
Store wants to re-evaluate order frequency
Retain service level of 95%
Apple charges a fixed fee of $25 for shipping and handling of order
Store’s order processing cost is $15
The model being considered has wholesale price of $3000
Holding cost rate is estimated to be 20%

21. Example #4 Compute EOQ h= (3000x0.2)/52weeks/yr=$11.5 K=15+25=40
p = Q*/m=3.2/1.5=2.15

22. Delayed Product Differentiation
Products start off undifferentiated; at some point, product variety explodes
Trade-off between product variety vs. inventory and service levels
Design the product so the point of differentiation is delayed as much as possible
Don’t commit to FGI early on

23. DPD- Standardization Using common components or processes Examples:
Reduces complexity of manufacturing
Increases “flexibility” of work-in-process
Improves service level
Examples:
standardizing head driver board & print mechanism interface in b&w and color printers
generic printer for Mac and Windows users

24. DPD-Modular Design
Decomposing the complete product into submodules that are easily assembled; delay assembly of product specific modules
Can increase no. of modules
Same benefits as standardization
Examples:
Power supply module in the HP Deskjet printer
Inserting plastic color panel to generic products
Channel assembly in PC industry

25. DPD – Process Restructuring
Postponing (if necessary) reverse operations
Operation divided into two steps, first step common to all products
Reverse the order of two operations with first operation common to all products
Example:
Benetton (dye & knit  knit & dye)

29. When is DPD appropriate?
High uncertainty in demand mix
Long lead times
Short product life cycle
High inventory /stock out costs
Not too costly/time consuming to customize
High value to core component
Low variable cost of differentiating components

30. Announcement 1 Next week field trip to Mercedes coach plant
Departure from campus 8:10-visit 9:30
Bus info: MUHAMMET GÜLER ZP 4194
Intermediate stop at Ataturk Oto Sanayi: 8:35
HOŞDERE OTOBÜS FABRİKASI-check web site for directions
Sanayi Mah. Mercedes Bulvarı No. 5, Esenyurt / İstanbul Tel: (0 212) Pbx Fax: (0 212)

31. Announcement 2 Read the Temsa case before the trip
Bonus assignment-can be done in pairs (5%):
Take notes-ask questions-take photos if allowed to
Strategy: Comment on the 4 product attributes for Mercedes: PQTV
Process documentation: Provide a high level process flow chart
Process Selection: Analyze volume, variety level and its fit with the type of process (position the plant on the product-process matrix based on this analysis)

32. Announcement 3 Last session: will play the beer game in-class
Need to read the handout that I will distribute before coming to class
Need to be on time since we will start at 11:00 sharp-aim for arrival at 10:45.
Final exam on January 10:00
Room will be announced