1. OPSM 301 Operations Management
Class 15:
Safety Inventory

2. Levers for Managing Inventories
Theoretical Inventory (In-process) Ith=R x T th
Reduce critical activity times
Eliminate non-value added work
Move work from critical to non-critical activities
Redesign process to replace serial with parallel processing
Cycle inventory
Average cycle inventory=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. Demand-Supply Mismatch
Apples’s iPhone broke sales record when it sold 1.7 million units on release day. Yet people were lining up to buy the gadget a week later. It is estimated that Apple could have sold upto million if could produce more units.
Financial Times, January 2011
During 2007, Ninentdo’s game system Wii was hard to get due to supply shortages. Analysts estimate that the company was leaving close to $1.3 billion on the table in unmet demand.
techspot.com, December 17, 2007
Mumbai’s real estate is said to be hot property. However, in the last quarter, sales have dipped so low that builders are getting worried ... At the current pace of consumption, it will take two years and four months to exhaust this stock. This is alarming because, a healthy market is supposed to have only an eight month inventory pile-up.
MumbaiMirror.com, February 8, 2011
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

5. The Basic Trade-off Key question: How much inventory? Inventory Costs
Efficiency
Responsiveness
Inventory Costs
Ordering cost
Carrying cost
Obsolescence
Damage
Shortage Costs
Lost margin
Customer goodwill
Lost customer
Key question: How much inventory?

6. Safety Inventory: Demand is uncertain
We may use historical data to forecast demand
Some truths about forecasts
They are always wrong(should measure error of forecast)
Aggregate forecasts are more accurate than individual forecasts
Long range forecasts are less accurate than short-range forecasts

7. 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?

8. How often to review
Continuous review
Periodic review

9. Inventory Cycle Stock Safety Stock Receive order Place an order Q Q/2
Inventory on hand
Çevrim
Stoğu
Cycle Stock
Safety Stock
Emniyet Stoğu
Lead time
Time Q
Pipeline stock
Time

10. Safety Inventory
Safety Inventory (Safety Stock): Inventory in excess of the average or (forecast) demand
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
or Probability that there will be no stock-out in a cycle

11. Reminder: The Normal Distribution
Standard Deviation = 5
Standard Deviation = 10
Average = 30

12. Safety Stocks & Service Levels: The relationship
Raise ROP until we reach appropriate Service Level (CSL):
To do numbers, we need:
Mean and stddev s of demand during lead time
Use Excel (or Standard Normal Table)
such that CSL = normsdist(z) or z = normsinv(CSL)
Cycle Service Level (CSL)
Stock-out probability
F(z)
Is = z s
demand during
supply lead time
mean
ROP
Standard Normal demand z
Avg Leadtime
Demand (LTD)
ROP= LTD+zs
Leadtime Demand
Reorder Point = Mean Demand During Lead Time + Safety Stock
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall
J.A. Van Mieghem/Operations/Supply Chain Mgt

13. Probabilistic Models When to Order?
Reorder Point (ROP)
Optimal
Order Quantity X
Safety Stock (SS)
Time
Inventory Level
Lead Time SS
ROP
Service Level
P(Stockout)
Place order
Receive order
Frequency 32

14. Stochastic Model: Fixed-Order Quantity
Order Quantity = same as before (EOQ)
Safety stock
Avg Inventory= Cycle Inventory + Safety stock
= Q/2 + zsL

15. Safety stock: How find s of lead time demand
Safety stock: How find s of lead time demand? A Fundamental Statistics Result: The Portfolio Effect sR sR … sR
Sum of N independent random variables, each with
identical standard deviation sR, has
standard deviation =
Applications:
Demand over the leadtime L has standard deviation = sR  L
Pooled demand over N regions or products has standard deviation = sR  N
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

16. The Standard Normal Distribution
Transform
X = N(mean,s.d.) to
z = N(0,1)
z = (X - mean) / s.d.
F(z) = Prob( N(0,1) < z)
Transform back, knowing z*:
X* = mean + z*s.d.
F(z) z

17. Example If we want to have probability of not stocking out=95%
(SL=95%)
z=1.64
ROP=mean+1.64
Assume that for daily demand:
Mean=20
std dev=10
Lead time=L=5 days
Then:

18. Learning Objectives: safety stocks
Safety stock is a hedge against uncertainty
Which factors drive safety stock ?
level of service z
Impact of increased service level on required safety stock
demand variability or forecast error sR,
delivery lead time L for the same level of service,
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall
J.A. Van Mieghem/Operations/Supply Chain Mgt

19. Example
The Home and Garden (HG) chain of superstores imports decorative planters from Italy. Weekly demand for planters averages 1500 with a standard deviation of 800. Each planter costs $10. HG incurs a holding cost of 25% per year to carry inventory. Each order shipped from Italy incurs a fixed transportation and delivery cost of $10,000. Consider 52 weeks in a year.
Determine the optimal order quantity of planters for HG
If the delivery lead time from Italy is 4 weeks and HG wants to provide its customers a cycle service level of 90%, how much safety stock should it carry? What would be the reorder point in that case?
A new shipping company(Fastship) promises to reduce the delivery lead time for planters to 1 week. But the cost of each planter will increase by $0.2 Should HG accept this offer? Quantify the impact of the change.

20. Safety stock = NORMSINV(0.9) x sqrt(4) x 800 = 2050
ROP=LTD+Safety Stock=4x
1.28
Additional cost per year = 1500*52*.2 = $15,600
Savings in holding cost = Savings in safety stock holding cost
= NORMSINV(.9)*800*(sqrt(4)-sqrt(1))*10*0.25 = $2562.5
Thus Fastship should not be used.