OPSM 301 Operations Management Class 15: Safety Inventory

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

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

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 2-2.5 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

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?

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

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?

How often to review Continuous review Periodic review

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

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

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

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

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

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

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

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

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:

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

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.

Safety stock = NORMSINV(0.9) x sqrt(4) x 800 = 2050 ROP=LTD+Safety Stock=4x1500+2050 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.