Class 6: Inventory Lecture - MIT OpenCourseWare
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,” News.com, May 9 2001,http://cnet.news.com (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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Partial Di erential Equations MSO-203-B T. Muthukumar tmk@iitk.ac.in November 14, 2019 T. Muthukumar tmk@iitk.ac.in Partial Di erential EquationsMSO-203-B November 14, 2019 1/193 1 First Week Lecture One Lecture Two Lecture Three Lecture Four 2 Second Week Lecture Five Lecture Six 3 Third Week Lecture Seven Lecture Eight 4 Fourth Week Lecture .
An inventory valuation method that assumes the most recent products added to your inventory are the ones to be sold first. Average inventory cost . An inventory valuation method that bases its figure on the average cost of items throughout an accounting period. Average inventory . The average inventory on-hand over a given time period,
property inventory system. The PCO will also prepare annual inventory control printouts and furnish them to all ODOC facilities/units. III. Inventory Control Officers and Agents Each facility/unit will designate an inventory control officer (ICO) who may designate one or more inventory control agents (ICA) to maintain inventory records
Anatomi dan Fisiologi a. Anatomi Tulang Tulang terdiri dari sel-sel yang berada pada ba intra-seluler. Tulang berasal dari embrionic hyaline cartilage yang mana melalui proses “ Osteogenesis ” menjadi tulang. Proses ini dilakukan oleh sel-sel yang disebut “ Osteoblast”. Proses mengerasnya tulang akibat penimbunan garam kalsium. Ada 206 tulang dalam tubuh manusia, Tulang dapat .
