1. OPSM 301 Operations Management Class 16: Inventory Management: safety inventory Koç University Zeynep Aksin zaksin@ku.edu.tr

2. Levers for Managing Inventories  Theoretical Inventory I th =R x T th –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. Demand is uncertain  We may use historical data to forecast demand  Recall QMBU 301?  Some truths about forecasts –They are always wrong-measure error of forecast –Aggregate forecasts are more accurate than individual forecasts –Long range forecasts are less accurate than short- range forecasts

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

6. How often to review  Continuous review  Periodic review

7. 7 Inventory Lead time Place an order Receive order Çevrim Stoğu Emniyet Stoğu Q Q/2 Inventory on hand Pipeline stock Q Time

8. 8 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

9. 9 Reminder: The Normal Distribution Average = 30 Standard Deviation = 5 Standard Deviation = 10

10. 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

11. Stochastic Model: Fixed-Order Quantity Order Quantity = same as before (EOQ) Safety stock

12. Reorder Point and Desired Stockout Probability Mean Demand During Lead Time Reorder Point (ROP) 1.0-(Desired Service Level) Reorder Point = Mean Demand During Lead Time + Safety Stock Desired Service Level

13. 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. The Standard Normal Distribution F(z) z 0

14. 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: