Inventory and (Yield) ManagementInventory Management - Victor Araman Best Buy’s Lesson In the 1990s, Eric Morley, Best Buy’s director of transportation, remembers $15 million worth of personal computers were on the way to stores in time for the holidays when chip maker Intel Corp. unexpectedly announced it was going to introduce a new Pentium processor, which wouldn’t be available until after the New Year. “We were stuck,” Morley says. It became the Christmas without a PC. That’s when we learned that you don’t buy inventory just in case - you buy it just in time” Inventory Management – Victor Araman 1 Agenda A First Look at Inventory Management – Motivation Continuous Replenishment Model – Economic Order Quantity (EOQ) – EOQ variants Periodic Review Model – News Vendor – LL Bean (see other slides) Supply Chain Inventory Inventory Management – Victor Araman Agenda A First Look at Inventory Management – Motivation Continuous Replenishment Model – Economic Order Quantity (EOQ) – EOQ variants Periodic Review Model – News Vendor – LL Bean (see other slides) Supply Chain Inventory Inventory Management – Victor Araman 2 What Is Inventory? Inventory is the stock or store of an item or a resource used by an organization. Different types of inventory Finished Goods (FGI) | Work in Process (WIP) | Raw Material Examples Cash in an ATM/bank Half assembled engines in a car manufacturing plant Phones in a retail store Silicon in a semiconductor manufacturing plant Seats in a plane Advertising slots for a TV broadcaster Inventory Management – Victor Araman Inventory Management – Victor Araman 3 000 1.000 - 10.823.000 336.000 Net Receivables 2.486.473.000 5.000 359.070.897.000 30-36% of Total Assets Total Current Assets Other Current Assets 10.335.000 403.000 3.000 - 22.000 18.000 1.000 5.079.000 2.000 2.288.000 435.000 Inventory Inventory 5.454.566.000 324.000 3.000 328.000 2.486.731.Inventory Management – Victor Araman Period Ending Assets Current Assets Cash And Cash Equivalents Short Term Investments 2-Mar-12 25-Feb-11 26-Feb-10 1.103.000 - 10.000 5.000 140.897.731.000 - Long Term Investments Property Plant and Equipment Goodwill Intangible Assets Accumulated Amortization Other Assets Deferred Long Term Asset Charges Total Assets 16.005.826.020.348.000 5.000 17.302.471.000 438.849.000 4.103.297.000 90.000 1.000 1.000 Inventory Management – Victor Araman 4 .199.000 2.000 5.000 1.144.000 452.000 1.452. Zara Inventory Management – Victor Araman 5 .Importance of Inventory Inventory Management – Victor Araman Importance of Inventory Inventories represent a major commitment of monetary resources Inventories affect virtually all aspects of a company’s daily operations Inventories represent a lethal “weapon” Example: Dell. Wal-Mart. Why Do Companies Hold Inventory? To meet anticipated customer demand To protect against stock-outs To take advantage of economic order cycles To maintain independence of operations To allow for smooth and flexible production operations To hedge against inflation and price increases To take advantage of quantity discounts Inventory Management – Victor Araman Inventory Sales Ratio Inventory Management – Victor Araman 6 . On year ahead earnings Inventory Management – Victor Araman 7 .Inventory Sales Ratio Inventory Management – Victor Araman Impact of Inventory on Valuation Abnormal inventory growth vs. Why Do Companies Hold Inventory? WSJ-09-09-04 Inventory Management – Victor Araman Inventory Measures Average aggregate inventory value: – Average of the total value of all items held in inventory Weeks of supply = Average aggregate inventory value Cost of Goods Sold per week Cost of Goods Sold per week Inventory turns = Average aggregate inventory value Some of these measures can be customized for specific settings/industry – Retail: sales per sqm of shelf space – Restaurant: sales per available seat-hour – Media: sales per slot per impression Inventory Management – Victor Araman 8 . the cost that the retailer incurs just due to holding inventory is 30/4 = 7.7 Inventory Management – Victor Araman Inventory Turns: Importance Consider a retailer whose inventory holding cost is 0.825 B $ – Cost of Goods Sold = 26.258 year = 0. incur 30 cents to hold one unit of a good that costs 1 $ for 1 year – Say.Inventory Turns Common industry benchmark Example (K-Mart: 2002) – Inventory value = 4. each unit stays in inventory for (1/4) of a year – So.5 are paid towards the retailer’s inventory holding costs Inventory Management – Victor Araman 9 . COGS = 171.3 $/$/year (we will discuss the components of inventory costs later) – That is.75 B$.183) = 5.44 Turns/year Example (Walmart: 2002) – Inventory value = 22.56 B $ – Time to turn a dollar = 43 days – Inventory Turns = 7. (Little’s law) • • What is the financial significance of this time? Kmart improved this figure from 88 days in 1998. $7. – Kmart Inventory Turns in 2002 = (1/0. on average.5 cents per dollar – In other words.183 years = 67 days. when we buy a product for $100 at this retailer.258 B $/year – Average time to turn a dollar (cost) to a dollar = 4. this retailer turns inventory 4 times per year – So.825/26. 5 cents is the inventory cost/$.75 % higher than A! – Typically. – If Retailer B turns 8 times per year. 7.75 cents is the inventory cost per $ (by better Inventory management) – All else being the same.Inventory Turns: Importance Think about profit margins for two Retailers (A and B) in the same market (selling the same products) – If Retailer A turns 4 times per year. net profits in the retail industry can be as low as 2 % ! Inventory Management – Victor Araman Inventory Turns in the Retail Sector Gross Margin Compare: Wal-Mart : 7. only 3. the profit margin of B is 3.44 turns per year 45% 40% 35% 30% 25% 20% 0 5 10 Inventory Turns 15 Inventory Management – Victor Araman 10 .54 turns per year K-Mart : 5. ABC Analysis Divides on-hand inventory into 3 classes – A class. C class Basis is usually annual $ volume – $ volume = Annual demand x Unit cost Policies based on ABC analysis – Develop class A suppliers more – Give tighter physical control of A items – Forecast A items more carefully Inventory Management – Victor Araman Classifying Items as ABC 80-20 rule % Annual $ Usage 100 80 60 40 20 0 0 50 100 Class A B C % $ Vol 80 15 5 % Items 15 30 55 A B C % of Inventory Items Inventory Management – Victor Araman 11 . B class. 10%) 3% (1 . (per unit of inventory per unit time) – cost associated with maintaining an item in inventory until it is used or sold Stockout or shortage cost. and obsolescence Cost as % of Inventory Value 6% (3 .24%) 3% (2 . (per order/transaction) – cost incurred each time an order is placed with a supplier or production is ordered with its own shop Holding cost.5%) 11% (6 .5%) 3% (3 .5%) (Approximate Ranges) Inventory Management – Victor Araman 12 .3. (per unit of inventory) – Under constant demand: becomes relevant if a quantity discount is available Inventory Management – Victor Araman Inventory Holding Costs Category Housing costs Material handling costs Labor cost from extra handling Investment costs Pilferage. scrap. (per unit of lost sale) – occurs when the demand for an item exceeds its supply Item cost.Inventory Decisions Driven by Cost Ordering cost. EOQ Inventory Level Time Inventory Management – Victor Araman 13 .Agenda A First Look at Inventory Management – Motivation Continuous Replenishment Model – Economic Order Quantity (EOQ) – EOQ variants Periodic Review Model – News Vendor – LL Bean (see other slides) Supply Chain Inventory Inventory Management – Victor Araman Economic Order Quantity . or purchased in orders Each lot or order received in single delivery Lead time known and constant Ordering.Economic Order Quantity (EOQ) Model Assumptions Single product or item Demand rate known and constant Item produced in lots. or setup costs are constant No backorders are allowed No quantity discounts are allowed Inventory Management – Victor Araman Data & Costs Formulation Demand = D units per year Ordering cost = S dollars per order placed Holding cost = H dollars per unit per year Order quantity = Q units – – – Holding Cost = H Q/2 per year Ordering Cost = S D/Q per year Total Cost = H Q/2 + S D/Q Inventory Management – Victor Araman 14 . EOQ Model: How Much to Order? Annual Cost H Q/2 Order (Setup) Cost Curve S D/Q Q* Optimal Order Quantity Order Quantity (Q) Inventory Management – Victor Araman EOQ: When to Order? Inventory Level Average Inventory Q* / 2 ROP Reorder Point LT Lead Time Time Inventory Management – Victor Araman 15 . Solution of the EOQ Problem Total Cost TC(Q ) DS QH Q 2 Optimal Quantity Q* 2DS (EOQ solution) H Inventory Management – Victor Araman EOQ Model Equations D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day LT = Lead time in days Optimal Order Quantity Q* = 2×D×S H Reordering Point ROP = d × LT d = D Working days / Year Expected Number of Orders D N = Q* Expected Time between orders T = Working Days per year N Inventory Management – Victor Araman 16 . What if? What if management is concerned by costs of emissions? What if there are discounts based on the order quantity? What if demand or/and lead times are NOT deterministic? Inventory Management – Victor Araman EOQ Adjusted – Costs of Emissions Cost of reducing emissions Inventory Management – Victor Araman 17 . Out of Stock At Supermarkets Inventory Management .Victor Araman Receive order 18 .Victor Araman EOQ Adjusted – Demand Uncertainty Frequency Service Level P(Stockout) Inventory Level Q SS Avg dLT ROP dLT ROP Avg dLT SS Safety Stock Time Lead Time Place order Inventory Management . Victor Araman Safety Stock Computation Leadtime demand is a normal distribution with an average and standard deviation Decide on your TARGET Service Level – Likelihood that leadtime demand is smaller than ROP is a service level – Example: SL = 99% means that you leave a 1% chance of stock-out during any cycle Find the corresponding level of inventory: ROP – ROP = Avg dLT + Safety Stock Normal Service Level Avg dLT ROP Using Excel the ROP is ROP = NORMINV(SL. stdev) Leadtime Demand Inventory Management .Probability of stockout – Higher service level means more safety stock – More safety stock means higher ROP – ROP = Avg of leadtime demand + safety stock Inventory Management .Service Level & Safety Stock How much & when to order ? Uncertain demand (and possibly uncertain lead time) – Lead Time Demand: Demand during leadtime – Leadtime demand follows normal distribution (forecasting) – Continuous replenishment What is a service level? What is the differ – What is the difference between a service level and a fill rate? How is the service level linked to the Safety Stock? – Service level = 1 .Victor Araman 19 . Avg dLT. Management wants a 97% service level. the daily demand for CD-ROM drives averages 10 units (normally distributed). What safety stock should be carried? What is the appropriate reorder point? Inventory Management . The lead-time is exactly 5 days. What safety stock should be carried for a 90% service level? What is the appropriate reorder point? Based on available information.Probabilistic Model: Examples Demand during lead-time for one brand of TV is normally distributed with a mean of 36 TVs and a standard deviation of 15 TVs. with a standard deviation of 1 drive.Victor Araman Agenda A First Look at Inventory Management – Motivation Continuous Replenishment Model – Economic Order Quantity (EOQ) – EOQ variants Periodic Review Model – News Vendor – LL Bean (see other slides) Supply Chain Inventory Inventory Management – Victor Araman 20 . Inventory Management: The Newsvendor model Demand Uncertainty Fixed Price Single Order Too many? Inventory Management – Victor Araman Selling Newspapers… Economic parameters – buy at w = € 1 – sell at r = € 1.05 Random demand – a distribution is available (with an average 300 and a standard deviation 100 units) The too much/too little problem Order too much and there is a loss due to unsold newspapers Order too little and you lose potential sales (and profits) Inventory Management – Victor Araman 21 .5 – salvage at s = € 0. Market Uncertainty & Ex-Ante Bet There are consequences of getting this bet wrong The expected profit maximization balances the “too much too little” costs Inventory Management – Victor Araman Brief Comparative Analysis EOQ Long lifecycle products with stationary demand No demand uncertainty Tradeoff between setup and holding costs. holding or disposal costs) – excess demand (stockout costs) Examples – fashion clothing | toys | computer games | music albums | books. driven by the frequency of ordering The “Newsvendor” model Short lifecycle products – One shot items – can be stocked only once at the beginning of the selling season) Considerable demand uncertainty Tradeoff between – costs of excess leftover inventory (overstocking. consumer electronics Inventory Management – Victor Araman 22 . 50 Inventory Management .The Newsvendor Concept Overage cost per unit Co is the (opportunity) cost of one unit of excess inventory (“over” ordering) – What if you had ordered one fewer unit? – Overage cost = Cost – Salvage value = w – s • What if additional cost is required to dispose of a leftover inventory? – Co = € 0.Victor Araman The Newsvendor Order Quantity Q We define the critical ratio CR = 𝐶𝑢 𝐶𝑢 +𝐶𝑜 CR measures the balance of power between marginal costs of shortage and leftover – how worse or better is too little compared to too much Probability Distribution Risk of leftover Risk of shortage Critical Ratio CR Inventory Management – Victor Araman Avg Dmd Q Demand 23 .95 Underage cost per unit Cu is the (opportunity) cost of one unit of lost sales (“under” ordering) – What if you had ordered one additional unit? – Underage cost = Price – Cost = r – w • what if a goodwill cost or penalty cost is incurred in addition to the lost margin? – Cu = € 0. Salvage value = s (Q – D ) Profit = r min{D .D)+ Cu : under-ordering x Expected Lost cost or lost margin Sales Co : over-ordering cost x Expected leftover or the overage cost Profit = r min{D .Expected Profit Penalty cost = p = 0 If Q < D : Revenues = r Q . If Q > D : Revenues = r D . Q} + s (Q – D )+ . Q} + s (Q – D )+ – w Q r x Sales s x Leftover News Boy – Victor F.Q)+ + (w – S) E(Q .w Q Expected Profit Pr (Q) = (r – w) ED – Gr (Q) Risk free profit News Boy – Victor F.w) E(D . Araman Simple manipulations Mismatch Cost 24 . Araman Cost of Demand Uncertainty The mismatch Cost Gr(Q) = (r . Marginal Analysis: Balancing the Risks Ordering one more unit D>Q Q+1 X – Cu X – Cu Prob{D > Q } + Co Prob{D ≤ Q } + (X + Co) x Prob{D ≤ Q } D≤Q X+C o (X – Cu) x Prob{D > Q } Q+1 is better than Q if Co Prob{D ≤ Q } < Cu Prob{D > Q Q 80 X Expected marginal benefit of understocking 70 60 50 40 . Expected gain or loss As more units are ordered the average benefit from ordering one unit decreases (it becomes more likely to be left with inventory) while the average loss of ordering one more unit increases (it becomes less likely to be short in inventory) 30 20 Expected marginal loss of overstocking 10 0 0 800 1600 2400 3200 4000 4800 5600 6400 Inventory Management – Victor Araman Newsvendor Cost Tradeoff Optimal Rule Expected cost of ordering one extra unit = Expected cost of ordering one less unit So.Victor Araman 25 .95+0.345 Inventory Management .5) = 0.5/(0. In the newspaper example: critical ratio = 0. the optimal quantity solves for C0 P(D ≤ Q) = Cu P(D > Q) P{Demand Q} Underage Cost Overage Cost Underage Cost The quantity 𝐶𝑢 𝐶𝑢 +𝐶𝑜 is known as the critical ratio. 300. s) = Norminv(0.Victor Araman Q Demand A Normal Distribution If demand distribution is normal Use Excel s =100 Q* = Norminv(CR.Newsvendor: Optimal Quantity to order Probability Distribution Risk of leftover Risk of shortage Critical Ratio Average Demand Inventory Management .100) CR 0.345. m .345 = 260 m =300 Q Inventory Management – Victor Araman 26 . 10. 200} Suppose Q=120 What is the average lost sales? – If D<=Q : No lost sales = 0 – If D = 130. What is the fraction of demand unmet?) Once lost sales are evaluated the rest follow trivially For normal distribution lost sales is known – tables that provide the values of lost sales – excel functions that give the exact value of lost sales If demand is not normal.e.Financial Performance If seller orders the newsvendor quantity Q* – What should the seller expect in terms of profits ? – What about averages sales? – How many units will be discounted on average (salvage)? – How much money is left on the table? (i. lost sales = D .Q = 20 Average Lost Sales = 10 x P(D=130) + 20 x P(D=140) + … + 80 x P(D=200) Inventory Management – Victor Araman 27 . 20. Harder to get (need simulation) Inventory Management – Victor Araman Average Lost Sales Suppose demand can take one of these values D belongs to {0. lost sales = D .…190.Q= 10 – If D = 140. g. 0) – z x (1 .88 ~ $97 Inventory Management – Victor Araman 28 . 1.4 L(z) = normdist(z.4) = 0.Average Lost Sales for Normal Dist. = (1.63 = 63 Inventory Management – Victor Araman The Rest Indeed Follows Sales + Lost Sales = Demand Avg Sales = Avg Demand – Avg Lost Sales = 300 – 63 = 237units Leftover Inventory + Sales = Q Avg leftover inventory = Q – Avg Sales = 260 – 237=23units Average Profit Price x Avg Sales + Salvage x Avg Leftover Inv. 1)) e. 0.normdist(z.g. z = (260-300)/100 = – 0.63 and Average Lost Sales = 100 x 0.06)*23 = $96. 0. Available information – Demand (D) is Normal with avg: ED = 300 and stdev sD = 100 – Assuming the previous economic parameters – then CR = 0.5-1)*237-(1-0.325 and Q = 260 Formula for Average Loss Sales sD x L(z) – s is the standard deviation (given) – z = (Q – ED) / sD e. L(-0. – Cost * Q = (Price – Cost) x Avg Sales – (Cost – Salvage) x Avg Leftover Inv. 1. Victor Araman Yield Management “Yield Management: term used in many service industries to describe techniques to allocate limited resources. among a variety of customers.Chicago Wednesday to Friday 1400 1200 1000 US$ US$ 800 600 400 200 0 August September October 1400 1200 1000 800 600 400 200 0 August September October Fare: New York . or by firms with services that cannot be stored at all. – By adjusting this allocation a firm can optimize the total revenue or "yield“ on the investment in capacity – Since these techniques are used by firms with extremely perishable goods. these concepts and tools are often called perishable asset revenue management. such as business or leisure travelers.Chicago Thursday to Saturday Wednesday-Friday fares are 15-20% higher than Thursday-Saturday fares! Inventory Management .Yield Management in Action Fare: New York . – American Airlines credits yield management techniques for a revenue increase of $500 million/year and Delta Airlines uses similar systems to generate additional revenues of $300 million per year. such as airplane seats or hotel rooms.” Inventory Management .Victor Araman 29 . with relatively small increases in capacity and costs Broadcasting companies use yield management to determine how much inventory (advertising slots) to sell now to the "upfront market" and how much to reserve and perhaps sell later at a higher price to the "scatter market’’ The core logic is similar to the newsvendor model Inventory Management .Victor Araman Agenda A First Look at Inventory Management – Motivation Continuous Replenishment Model – Economic Order Quantity (EOQ) – EOQ variants Periodic Review Model – News Vendor – LL Bean (see other slides) Supply Chain Inventory Inventory Management – Victor Araman 30 .Yield Management “Marriott Hotels credits its yield management system for additional revenues of $100 million per year. m is the production unit cost incurred by the manufacturer and Q* is the optimal quantity ordered by the retailer News Boy – Victor F. Q Retailer r. D End consumer The manufacturer’s profit is given by Pm = (w – m) Q* where.A Simple Supply Chain m Manufacturer w. Araman Supply Chain Inventory Insights Double marginalization effect Postponement strategies Risk sharing and supply chain maximum value Refer to Newsvendor Problems Inventory Management – Victor Araman 31 . q} + S (q .x) min{D. sD) – P(D ≤ q) = CF – q*= norminv(CF. Q} + s (Q – D )+ . sD) Profit Manufacturer (w – m) Q* Inventory Management – Victor Araman Profit Manufacturer E (c . q}] – c q News Boy – Victor F.Supply Contracts: Real Options Retailer buys q “call” options at unit cost c – Call option: right to buy one unit at the exercise price x – Options bought ahead of season.m)q + x min{D. solution must be given by Critical Ratio – ku = r – x – c | ko = c – CF = 𝑘𝑢 𝑘𝑢 +𝑘𝑜 Solution given by Critical Ratio – Cu = r – w | Co = w – s – CR = 𝐶𝑢 𝐶𝑢 +𝐶𝑜 – P(D ≤ Q) = CR – Q*= norminv(CF. Avg D.w Q Newsvendor with Options Max Profit (r . q} – c q Set r→r–x |w→c|s→0 By analogy. Araman Comparing to Original Newsvendor Standard Newsvendor Max Expected Profit r min{D .D)+ 32 . but exercised after demand is observed – Induce the retailer to buy more units at the expense of sharing the risk (demand uncertainty) Retailer’s Expected profit pr(q) = E[(R .x) min{D. Avg D. M) q + x min{D.D)+] Net revenues from Revenues from exercised options selling q options Revenues from nonexercised options See notes for an Excel formulation of this profit under normal demand! News Boy – Victor F.q)+] + c E[ (q . q}] – c q Re-writing the profit pr(q) = (R .x .D)+] – ku = R . Araman 33 .x .x) min{D. Araman Manufacturer’s Expected Profit Expected profit Sales Leftover pm(q) = E[(c .c : opportunity cost (too few options) – k0 = c : opportunity cost (too many options) gr(q*) = s (ku + k0) Normdist(Normsinv(ku /(ku + k0)).Retailer’s Expected Profit Retailer’s Expected profit pr(q) = E[(R .c) ED – gr(q) gr(q) = (R .1.0. q} + S (q .false) News Boy – Victor F.x .c) E[(D . Commonly used for One Shot Items – Critical Ratio measures the imbalance between too much and too little Supply Chain Inventory Inventory Management – Victor Araman 34 . Simple and Commonly used model – Tradeoff between setup and holding costs Newsvendor.Key Learnings Inventory is the result of the imbalance between Supply and Demand It serves as a buffer to – – – – Smooth seasonality Reduce risk/cost of stockouts Alleviate production scheduling Take advantage of economies of scale Inventory is not free EOQ.