Class 6: Inventory Lecture - MIT OpenCourseWare

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Class 6: Inventory LectureDesign Decision:CAPACITY (cf. Class 3)TIMEQUALITYPlanning/Control Decision:INVENTORYCOSTFLEXIBILITY(Oct 2001: 1.16 trillion in US!)Trade-off: Inventory Cost Vs. Service Level2002 - Jérémie Gallien

From the Trenches Too much: Liz Claiborne experiences "unexpected earnings decline as aconsequence of 'higher-than-expected excess inventories'” – Agins,Teri. “Liz Claiborne Seems to Be Losing Its Invisible Armor,” The Wall Street Journal, July 191993. “On Tuesday, the network-equipment giant Cisco provided the grislydetails behind its astonishing 2.25 billion inventory write-off in thethird quarter” – Barrett, Larry. “Cisco’s 2.25 Billion Mea Culpa,”, May 9 2001, (accessed June 3, 2004).Too little: IBM struggles with shortages in ThinkPad line due to ineffectiveinventory management – Hays, Laurie. “IBM to Slash Prices Up to 27% on BusinessPCs,” The Wall Street Journal, August 24 1994. “Since 1990 we have designated the Department of Defense’smanagement of its inventory, including spare parts, as high riskbecause [ ] its management systems and procedures wereineffective.” – US General Accounting Office. “Army Inventory: Parts Shortages AreImpacting Operations and Maintenance Effectiveness,” August 2001.2002 - Jérémie Gallien

Why Inventory Costs Money Cost of (stuck) capitalObsolescenceStorageInsuranceSecurityTheft (Shrinkage)Typical per annuminventory holding cost:2002 - Jérémie Gallien

Financial Inventory MetricsEarnings or P & LCOGSInventory Turns Inventory ValueBalance sheetHolding CostInventory Value x Holding CostInventory Cost / Unit COGSInventory TurnsExample: 10k filings, 2002 ( M)InventoryC.O.G.SWal Mart Stores Inc. 22,749 171,562Kmart Corp. 4,825 26,2582002 - Jérémie Gallien

Why Hold Inventory? How Much?Type of InventoryDecision ToolSafety InventoryNewsboy ModelCycle InventoryEOQ ModelSeasonal InventoryBuildup DiagramSpeculative InventoryFinanceIn-Process/Pipeline InventoryLittle’s LawMarketing/Shelf Inventory (Retail)Experience2002 - Jérémie Gallien

Economic Order Quantity Model Set order size for repetitive ordering process withfixed order cost Trade-off:– Order size too large (too much average inventory) versus– Order size too small (too much ordering cost) Examples:– Ordering/Inventory replenishment policy;– Batch size on machine with setup time 2002 - Jérémie Gallien

Running to the Store a Lot nventory2002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

Vs. Running to the Store a LittleMonTueWedThu FriSatSunMILKMILKMILKMILKMILKMILKMILKInventory2002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

EOQ Model Parameters Q Order Quantity decisionD Demand Rate (units/time)C Purchasing Cost ( /unit)parametersF Fixed Order Cost ( )H Inventory Holding Cost (% p.a.)Assumptions:- constant, deterministic demand- instantaneous replenishment2002 - Jérémie Gallien

EOQ Model DerivationC QD Inventory Cost H ; Order Cost F ;2QDQV F C H Q2 Total CostInventoryQQD2QD3QD4QDtime2002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

EOQ Formula Set first derivative to 0: VDF CH 2 0Q Q2 This yields:Q *2 DFCH2002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

EOQ ExampleA PC assembly operation procures its 128Mb memory chips at 45each (purchase shipment cost) from a foreign vendor; in additioneach order also costs 500 in customs fees. Assuming a constantdemand of 400 chips per week and an inventory holding cost of 45%,how often would you order?2002 - Jérémie Gallien

Newsvendor Model One time decision under uncertainty Trade-off:– Ordering too much (waste, salvage value cost) versus– Ordering too little (excess demand is lost) Examples:––––Restaurant;Fashion;High Tech;Inventory decisions 2002 - Jérémie Gallien

Christmas Tree Problem 100DECEMBER1 2 3 4 5 6 78 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30 312002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

Ordering Too Many 5DECEMBER1 2 3 4 5 6 78 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30 312002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

Versus Ordering Too FewSold OutDECEMBER1 2 3 4 5 6 78 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30 312002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

Newsvendor Model Parameters q Order Quantitydecision c Unit Cost r Unit Revenue b Unit Salvage Valueparameters(r c b) d Demand (unknown)random variable2002 - Jérémie Gallien

Newsboy ObjectiveIF d q(demand quantity ordered)IF q d(quantity ordered demand)Opportunity cost:(r – c) x (d – q)Disposal cost:(c – b) x (q – d)Objective:minimize expected opportunity disposal cost2002 - Jérémie Gallien

Model Derivation IF d q(demand order qty)Profit:q (r c )Incremental Analysis:Δ Profit:EAP: IF d q(demand order qty)d (r c ) (q d ) (b c )q q 1:r-cb-cP(d q ) (r-c ) P(d q ) (b-c )As long as the Expected Additional Profit [EAP] ispositive, it is lucrative to increase q to q 1 !!!2002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

Newsvendor Formular cr cuP(d q *) r b (r c ) (c b )u o123 123cost ofunder stockingcost ofover stockingRemark: If d is Normal(µ,σ),r c αr bq* µ k.σ withq*α 95%α 99%α 99.9% k 1.64k 2.32k 3.09Demand Distribution2002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

Newsvendor ExampleBased on forecasts and marketing studies you are expecting a totallifecycle demand N(60,000;20,000) for a new product due to launch inthe future. The product has a gross margin of 750 and aliquidation/disposal cost (for unsold inventory) of 250. Because of longlead-times you must commit orders to supplier for the entire productlife-cycle now. How much should you order?2002 - Jérémie Gallien

Continuous Review System“order Q whenever inventory reaches R”Order Quantity QEDDLTEDDLTEDDLTDDLT1Reorder Level ROrder Quantity Q Lead Time Expected Demand During Lead Time (Actual) Demand During Lead TimeDDLT2LTEDDLTDDLTInventorySafety StockOrder 1placedLT 1Order 1receivedLT 2Time2002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

(R,Q) Parameters“order Q whenever inventory reaches R” Set Q as the EOQ solution Set R as the newsboy solution:P(DDLT R) αwhere α is a desired service level (e.g. 95%)Example (cont’d): if weekly demand for 128Mb chips is in fact N(400,80)and delivery time is 2 weeks, for a 95% service level:2002 - Jérémie Gallien

Periodic Review System“order back to S every T time units”TTTQ3Q1SQ2LT 2DDLT2DDLT1U1LT 1Safety StockLT Lead TimeT Cycle Time orReview PeriodDDLT ActualDemand During LeadTimeQi Order SizeS Order Up ToLevelOrder 1 Order 1placed received2002 - Jérémie GallienSlide courtesy of Prof. Thomas Roemer, MIT.

(S,T) Parameters“order back to S every T time units” Set T as the EOQ solution divided by the demand rate Set S as the newsboy solution:P(DDLTRP S) αwhere:- α is the desired service level (e.g. 95%)- DDLTRP Demand During Lead-Time andReview Period2002 - Jérémie Gallien

Safety Stock Formula Under periodic and review systems, safety stock SS(under normally distributed demand) is given by:SS k σfractile dependingon service level, e.g.95% k 1.6499% k 2.3299.9% k 3.09standard deviationof DDLT or DDLTRP2002 - Jérémie Gallien

Class 6 Wrap-Up1. Financial inventory metrics: inventory turns,per unit inventory cost2. Functions of inventory: seasonal, cyclical,safety, speculative, pipeline, shelf3. EOQ & newsboy models4. Continuous and discrete replenishmentpolicies, safety stock formula2002 - Jérémie Gallien

Balance sheet Inventory Cost / Unit Inventory Value x Holding Cost Inventory Turns Inventory Value Inventory Turns Wal Mart Stores Inc. Kmart Corp. . Restaurant; High Tech; Inventory decisions 1 Christmas Tree Problem 100 8 15 22 29 2 9 16 23 30 3 10 17 24 31 4 11 18 25 5 12 19 26 6 13 20 27 7 14 21 28

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