Managing Service Inventory Shin Ming Guo NKFUST Reasons to Hold Inventory Inventory Models ABC Classification News Vendor Problem Hospitals and Inventory Management Control Barcodes and computers keep track of every bottle of antibiotics and other supplies. Secure supply cabinets with thumbprint security technology Management Analyze how much is spent on every type of illness and surgical procedure. Computers keep track of stock and automatically reorder from suppliers 2 1
Focus: Matching Supply with Demand Demand can vary and is unpredictable. Supply is inflexible and maybe costly. Demand < Supply Stock may be perishable Demand > Supply Customers may not want to wait 3 Who Cares About Inventory? Acer reported its first ever quarterly loss yesterday. The Taiwanese PC maker suffered a net loss of 6.79 billion in Taiwanese dollars ($234.3 million) Acer has been hit hard by overestimating demand for its PCs. It has lost $150 million to get rid of excess inventory. 4 2
What About a Shortage of Vaccine? In 2006, Nintendo launched the Wii game console and could not make enough units to keep up with the demand. Some people would wait in long lines to purchase scarce units and resell them online for several hundred dollars over the retail price 5 Physical Goods Distribution 6 3
Reasons to Hold Inventory In transit Inventory Seasonal Inventory Cycle Inventory Decoupling Inventory/Buffers Safety Inventory Speculative Inventory 7 Reasons to Hold Less Inventory Inventory might become obsolete. Inventory might perish. Inventory might disappear. Inventory requires storage space and other overhead cost. Opportunity cost. 8 4
Inventory Costs Holding or Carrying cost Overestimate the demand storage cost: facility, handling risk cost: depreciation, pilferage, insurance opportunity cost Ordering cost cost placing an order: preparing, negotiating, receiving and inspection Shortage costs or Lost Sales costs of canceling an order or penalty Underestimate the demand Annual cost 20% to 40% of the inventory s worth 9 Inventory Performance How to calculate average Inventory value? Inventory turn = Cost of Goods Sold average inventory value Service level = in stock probability before the replenishment order arrives Fill rate = number of sales number of demands 10 5
Inventory Control Decisions Ordering of general merchandise, supplies When to order? Reorder point, order frequency How many to order? Order quantity, target inventory level Fixed Order Period P model Fixed Order Quantity Q model 11 Fixed Order Quantity Models 12 6
Economic Order Quantity D=annual demand, Q=order quantity, S=setup cost, H=unit holding cost D Q TC(Q) S H Q 2 Total annual cost =ordering cost + holding cost 2DS Economic Order Quantity Q* H Q d L d=daily demand L=lead time Reorder point =d L L 13 14 7
Inventory Control under Demand Uncertainty Place a new order whenever the inventory position drops to ROP (reorder point). ROP How to avoid possible stock out? d=daily demand L=lead time Reorder point =d L+ safety stock 15 Safety Stock amount of inventory carried in addition to the expected demand, in order to avoid shortages when demand increases Service level=probability of no shortage =P (demand inventory) =P(demand E(D)+safety stock) safety stock depends on service level, demand variability, order lead time service level depends on Holding cost Shortage cost 16 8
=daily demand =std dev. of daily demand ROP expected demand during L safety stock L z L Service level or probability of no shortage =95% (99%) z=1.64 (2.33) 17 P model: fixed time period RP RP RP RP is the review period. TIL is the target inventory level determined by the forecasts. We place an order to bring the inventory level up to TIL. 18 9
Timespan = length of review period + lead time = RP+ L Target Inventory = expected demand + safety stock (RP L) z RP L Order Quantity = target inventory inventory position 19 ABC Classification Pareto s 80/20 principle dollar usage=usage cost There are other ways to do ABC classification. Review ABC classification periodically. 20 10
ABC Classification for Inventory Control A Q model B P model with R=1 week C P model with R=1 month 21 Single Period Inventory Model Only one production or procurement opportunity. Stochastic demand leads to lost sales or leftover. There are losses of profit and goodwill for each unsatisfied customer. There is a salvage value for each unit of leftover. Forecasting helps balancing cost of ordering too much vs. cost of ordering too little. 22 11
Case : Order Management at Sport Obermeyer Klaus Obermeyer founded Obermeyer in 1947, when he was among the first ski instructors on Aspen Mountain. Customer service, marketing, design & research, accounting in Colorado Rockies. Contract manufacturers in Hong Kong and China. Long lead time, short sales period Increasing product variety, more marked downs Forecasting and Ordering at Sport Obermeyer Demands depend on weather, fashion trend, economy. Forecasts based on Panel Consensus. Dominant members have stronger influence on the outcome of a consensus forecast. Independent forecasts can provide an indicator of the forecast accuracy for each style. 24 12
Working with Customers to Improve Forecasts Obermeyer invites key customers to place early orders (20% of total sales) to get market information. Forecasts are updated based on those early orders. 25 News Vendor Problem D = boxes of donuts demanded Q = boxes of donuts stocked P = price of one box of donuts, $10 C = cost of one box of donuts, $4 S = salvage value of one box, $2 26 13
P = price of one box, $10 C = cost of one box, $4 S = salvage value of one box, $2 C u = unit contribution: P C = $6 C o = unit loss: C S = $2 27 Finding Optimal Order Quantity F(Q) = probability of having leftover inventory To maximize expected profit, we order Q units so that the expected loss on the Q th unit equals the expected gain on the Q th unit: C F( Q) C 1 F Q o u Cu Rearrange the above equation > F( Q) Co C C u / (C o +C u ) is called the critical ratio. Choose Q such that the probability of no lost sales (i.e., demand <Q) equals the critical ratio. u 28 14
29 Retail Discounting Model S = current selling price D = discount price P = profit margin on cost (% markup as decimal) Y = average number of years to sell entire stock of dogs at current price (total years to clear stock divided by 2) N = inventory turns (number of times stock turns in one year) Loss per item = Gain from revenue S D = D(PNY) D S ( 1 PNY) 30 15