Why do we have inventory? Inventory Decisions. Managing Economies of Scale in the Supply Chain: Cycle Inventory. 1. Understanding Inventory.

Transcription

1 -- Chapter Managng Economes of Scale n the Supply Chan: Cycle Inventory Pros: Why do we have nventory? To overcome the tme and space lags between producers and consumers To meet demand/supply uncertanty To acheve producton /transportaton economes/flexblty To take advantage of quantty purchase dscounts To mprove servce level (?) So, the more, the better? Cons: Sgnfcant cost Space, captal, rsk, So, the less, the better? 10-2 Issues: - Overstockng vs. vs. under-stockng -- Supply chan responsveness vs. vs. effcency Understandng Inventory What types of nventory? raw materals WIP, parts, assembly components fnshed goods Where do we hold nventory? Supplers and manufacturers warehouses and dstrbuton centers Retalers Central locaton When to have nventory? How much nventory should be held? Transport Transport Transport Inventory Decsons Inventory decson s affected by Demand characterstcs Lead tme Number of products Objectve (servce level, mn costs, or the both?) Cost structure Goal: Optmal matchng supply and demand 5 R prncple Decson crtera: Tradtonal vew: better tradeoff between customer servce level and nventory nvestment (cost) Recent emphass: ncreasng customer servce AND reducng Supplers Producton Dstrbuton Resellers Customers What to What to make What to shp and nventory nvestment buy and when? and when? when?

2 Cost structure of nventory: Order costs Fxed Varable Mantenance & handlng Is t possble to reduce cost AND mprove servce? It can be acheved through Inventory Costs Inventory carryng costs Captal costs Inventory servce costs Storage space costs Inventory nvestment Insurance Taxes Plant warehouses Publc warehouses Rented warehouses Company-owned warehouses Effectve nventory management How to order? When to order? What to order? How much to order? Supply chan management strateges Obsolescence Inventory rsk costs Damage Plferage Relocaton costs

3 2. The measure of nventory level Example: Cycle Inventory The average nventory that bulds up n the SC when produced or purchased lots are larger than those demanded by customer Lot, or batch sze: quantty that a supply chan stage ether produces or orders at a gven tme lot or batch sze of an order D demand per unt tme Cycle nventory /2 (depends drectly on lot sze) Average flow tme Avg nventory / Avg flow rate Average flow tme from cycle nventory /(2D) unts D 100 unts/day Cycle nventory /2 1000/2 500 Avg nventory level from cycle nventory Avg flow tme /2D 1000/(2)(100) 5 days Cycle nventory adds 5 days to the tme a unt spends n the supply chan Lower cycle nventory s better because: Average flow tme s lower Workng captal requrements are lower Lower nventory holdng costs Role of Cycle Inventory How to decde lot sze? Cycle nventory s held prmarly to take advantage of economes of scale n the supply chan Supply chan costs nfluenced by lot sze: Materal cost C Fxed orderng cost S Holdng cost H hc (h cost of holdng $1 n nventory for one year) Prmary role of cycle nventory s to allow dfferent stages to purchase product n lot szes that mnmze the sum of materal, orderng, and holdng costs Ideally, cycle nventory decsons should consder costs across the entre supply chan, but n practce, each stage generally makes ts own supply chan decsons ncreases total cycle nventory and total costs n the supply chan Lot szng for a sngle product -- EO Aggregatng multple products n a sngle order Lot szng wth multple products or customers Lots are ordered and delvered ndependently for each product Lots are ordered and delvered jontly for all products Lots are ordered and delvered jontly for a subset of products 10-14

4 EO: Optmal lot sze and reorder nterval H T TC Order cost + Holdng Cost + Purchasng Cost (R/)S + (/2)hC + CR Mn TC EO model: n hc 2 DS H 2 S DH D DhC 2 S d( TC) DS hc + d D -- Annual demand S -- Setup or Order Cost C -- Cost per unt h -- Holdng cost per year as a fracton of product cost H -- Holdng cost per unt per year -- Lot Sze, order quantty T -- Reorder nterval n orderng frequency uestons answered : Optmal order quantty - The most economc order quantty (EO) Mn TC EO model How much to order? When to order? Annual cost (dollars) Lowe st total cos t (EO) Total cost Sze of order Inventory carryng cost Orderng cost Example 10.1 The Deskpro computer at Best Buy, Demand, D 12,000 computers per year Unt cost, C $500 Holdng cost, h 0.2 Fxed cost, S $4,000/order By EO model: The optmal Cycle Inventory Flow tme 12 2d Re cord nt erval : order quantty : T unts mth / yr 2S DH See Excel fle (Text Web) DS H 0.49 mths mths unts days Assumptons under the smple EO model A contnuous, constant, and known rate of demand. A constant and known replenshment cycle or lead tme. A constant purchase prce that s ndependent of the order quantty or tme. A constant transportaton cost that s ndependent of the order quantty or tme. The satsfacton of all demand (no stockouts are permtted). Only one tem n nventory, or at least no nteracton among tems. No lmt on captal avalablty Removng some of the assumptons -- Varatons of EO: -EO wth backlog - EO wth quantty dscount - EO wth contnues replenshment - Stochastc nventory models

5 ueston: Can we further reduce the TC by reducng? If lot sze reduce to 200 unts, Annual nventory cost (D/)S + (/2)hC $250,000 whch s hgher than TC$97980 when 980 unts (Example 10.2) To make t economcally feasble to reduce lot sze, the fxed cost assocated wth each lot would have to be reduced If desred lot sze 200 unts, The desred orderng cost, S hc 2 /2d $ The store manager would have to reduce the orderng cost per lot from $4000 to $ Total cost for a lot sze of 200 to be optmal. Observaton: (< ) Fxed cost TC Annual cost (dollars) Lowe s t total co s t (EO) Inventory carryng cost Orderng cost Key Ponts from lot szng by EO In decdng the optmal lot sze, the trade off s between order (setup) cost and holdng cost. If demand ncreases by a factor of k, t s optmal to ncrease batch sze by a factor of (k 1/2 ) and produce (order) a factor of (k 1/2 ) as often. Flow tme attrbuted to cycle nventory should decrease by a factor of (K 1/2 ). If lot sze s to be reduced, one has to reduce fxed order cost. To reduce lot sze by a factor of (k), order cost has to be reduced by a factor of (k 2 ). Sze of order Strateges to mprove SC performance whle lowerng cycle nventory 1) Aggregaton (across products, supply ponts, delvery ponts ) 2) Lot szng wth aggregaton strateges 3) uantty dscounts 4) Short term dscountng: trade promotons Successful cases Wal-Mart: 3 day replenshment cycle 7-11 Japan: Multple daly replenshment Aggregatng Multple Products n a Sngle Order Transportaton s a sgnfcant contrbutor to the fxed cost per order Can possbly combne shpments of dfferent products from the same suppler same overall fxed cost shared over more than one product effectve fxed cost s reduced for each product lot sze for each product can be reduced Can also have a sngle delvery comng from multple supplers or a sngle truck delverng to multple retalers Aggregatng across products, retalers, or supplers n a sngle order allows for a reducton n lot sze for ndvdual products because fxed orderng and transportaton costs are now spread across multple products, retalers, or supplers

6 Example: Aggregatng Multple Products n a Sngle Order Suppose there are 4 computer products n the prevous example: Deskpro, Ltepro, Medpro, and Heavpro. Assume demand for each s 1000 unts per month If each product s ordered separately: 980 unts for each product Total cycle nventory 4(/2) (4)(980)/ unts Aggregate orders of all four products: Combned 1960 unts For each product: 1960/4 490 Cycle nventory for each product s reduced to 490/2 245 Total cycle nventory 1960/2 980 unts Average flow tme, nventory holdng costs wll be reduced Lot Szng wth Aggregaton Strategy Why? In practce, the fxed orderng cost s dependent at least n part on the varety assocated wth an order of multple models A porton of the cost s related to transportaton (ndependent of varety) A porton of the cost s related to loadng and recevng (not ndependent of varety) Aggregatng across products, retalers, or supplers n a sngle order allows for a reducton n lot sze for ndvdual products because fxed orderng and transportaton costs are now spread across multple products, retalers, or supplers. Servce? How? -- Three scenaros: Lots are ordered and delvered ndependently for each product Lots are ordered and delvered jontly for all three models Lots are ordered and delvered jontly for a selected subset of models Example 10.3 Best Buy The Deskpro computer at Best Buy, three models, Demand per year: D L 12,000; D M 1,200; D H 120 Product specfc order cost: s L s M s H $1,000 Unt cost: C L C M C H $500 Common transportaton cost: S $4,000 Holdng cost: h 0.2 Delvery optons: No Aggregaton: Each product ordered separately Complete Aggregaton: All products delvered on each truck Talored Aggregaton: Selected subsets of products on each truck Opton 1: No Aggregaton - Order each product ndependently Example 10.3 Ltepro Medpro Heavypro Demand per year 12,000 1, Fxed cost / order $5,000 $5,000 $5,000 Optmal order sze () 1, Cycle nventory (/2) Order frequency (n) 11.0 / year 3.5 / year 1.1 / year Annual cost (TC) $109,544 $34,642 $10,954 Total cost $155,

7 Opton 2: Complete Aggregaton: Order all products jontly Opton 3: Talored Aggregaton: Orderng Selected Subsets The combned fxed order cost: S S + S L + S M + S H TC {Annual Order Cost}+{Annual Holdng Cost} d ( TC ) (mn TC 0 n ) n dn ( DhC ) The optmal orderng frequency, n 2 S Ltepro Medpro Heavypro Example 10.4 Demand per 12,000 1, year Order 9.75/year 9.75/year 9.75/year frequency n Optmal 1, order sze Cycle nventory( /2) Annual holdng cost $61,512 $6,151 $615 ns + DhC 2n Annual order cost 9.75 $7,000 $68,250 Annual total cost $136, Dscusson: An heurstc procedure for talored aggregaton: Step 1: Identfy most frequently ordered product n hc D, 2 ( S + S ) n max { n } Step 2: Identfy frequency of other products as a multple hcd n n, m, m 2S n Step 3: Recalculate orderng frequency of most frequently ordered product hc h n S, Fxed cos t per order S + 2 ( S + m ) Step 4: Identfy orderng frequency of all products n m for product m ( closest nt eger) S m Talored Aggregaton: Order selected subsets Example 10.5 Ltepro Medpro Heavypro Demand per 12,000 1, year Order 10.8/year 5.4/year 2.16/year frequency n Optmal 1, order sze Cycle nventory Annual holdng cost $55,556 $11,111 $2,778 Annual order cost $61,560 Total annual cost $131,

8 No Aggregaton Complete Aggregaton Talored Aggregaton Product specfc order cost $1000 Total cost Cycle Inv. Aggregaton reduces the total cost AND cycle nventory! Product specfc order cost $3000 $155, $183,564 $136, $186,097 $131, $165,233 Impact of product specfc order cost A Lessons From Aggregaton Aggregaton allows frm to lower lot sze wthout ncreasng cost A key to reduce lot sze wthout ncreasng costs s to reduce the fxed cost assocated wth each lot, whch can be acheved by reducng the fxed cost tself or by aggregatng across multple products, customers or supplers. Complete aggregaton s effectve f product specfc fxed cost s a small fracton of jont fxed cost Talored aggregaton s effectve f product specfc fxed cost s large fracton of jont fxed cost Talored aggregaton can also be used when a sngle truck makes delveres to multple customers, some large and some small Strategy 3: uantty Dscounts Commonly used n B2B transactons Types of uantty Dscount Lot sze based (based on the quantty ordered n a sngle lot) All unts Margnal unt Volume based (based on the total quantty purchased over a gven perod) uestons: How should buyer react? How to determne approprate dscountng schemes? What s the mpact of quantty dscounts on the supply Chan? How to use the D strategy to mprove SC performance? Example 10.6 [Revew yourself!!!] Drugs Onlne (DO) an onlne retaler of prescrpton drugs and health supplements D 120,000/yr. S $100/lot, h 0.2 Order quantty 0-5, ,000 Over 10,000 $3.00 $2.96 $2.92 The manager wants to know how many bottles to order n each lot? By usng the EO model wth quantty dscount, 10,001 unts (wth the unt prce $2.96) Unt Prce

9 The Method for All-Unt uantty Dscounts Evaluate EO for prce n range q to q If q EO < q +1, D evaluate cost of orderng EO TC S hc DC If EO < q, D evaluate cost of orderng q q TC S hc DC q If EO q +1, D q+ 1 evaluate cost of orderng q +1 TC S + hc + DC q Evaluate mnmum cost over all prce ranges Impacts of uantty Dscounts (recallng the beer game ) uantty dscounts encourage large order quanttes and lead a sgnfcant buldup of cycle nventory Retalers are encouraged to ncrease the sze of ther orders Average nventory (cycle nventory) n the supply chan s ncreased Average flow tme s ncreased So, why quantty dscount? uantty dscount can be valuable n a SC to mprove chan coordnaton and reduce the total chan cost But How? Coordnaton for Commodty Products Commodty product the market sets the prce and the frms objectve s to lower costs DO makes ts lot szng decsons (of vtamns) based on ts own costs Suppler -- Manufacturer Suppler sde S S $250, h S 0.2, C S $2 Suppler cost (120,000/6324)x250 +(6324/2)x2x0.2 $6,009 Retaler -- DO Retal sde: D 120,000 bottles/yr S R $100/order, h R 0.2, C R $3/bottle Retaler s optmal lot sze: 6,324 Retaler cost $3,795 Supply chan cost $9,804 Customers p & D If Do s s Order Sze 9165 unts Suppler -- Manufacturer Suppler Cost ( $6,009 - $902) $5,107 Retaler -- DO Retaler cost ( $3,795 + $264) $4,059 Supply chan cost $9165 ( $9,804 - $638) Customers Observaton: If DO order 9165, the total chan saves $638 and the suppler saves $902, but retaler pays $624 more! ueston: How to convnce DO to take the order sze of 9165? 10-39

10 Use uantty Dscount Strategy to acheve the Chan Coordnaton and the Chan Cost Reducton The SC Soluton: - The suppler offer lot sze-based quantty dscounts ncentve < 9165, $3 > 9165, $ The resulted optmal order sze at DO: 9165, by usng EO model wth quantty dscount The manufacturer returns $264 ($ ) to DO as materal cost reducton to make t optmal for DO to order 9165 bottles Passng some fxed cost to retaler (enough that he rases order sze from 6324 to 9165) After all Retaler cost $4, $3795 (no change); Suppler cost $5, (save $639); Supply chan cost $9,165 (save $639). Key pont: For commodty products for whch prce s set by the market, manufacturers can use lot sze-based quantty dscounts to acheve coordnaton n the supply chan and decrease supply chan cost. Lot sze-based dscounts, however, ncrease cycle nventory n the supply chan uantty Dscounts When Frm has Market Power A new vtamn Vtaherb, no compettors The sale prce at DO wll nfluence demand The demand curve s gven by 360,000-60,000p Producton cost at the manufacturer C s $2/bottle Manufacturer needs to decde the prce to charge Do, p R,,and DO needs to decde the prce to charge customers, p. IF the two stages make the prcng decson ndependently Manufacturer DO Customer C s $2 p R? p? (D360-60p) Prof M p R (360-60p)-(360-60p)C S p R (360-60p)-(360-60p)x$2 ()p R [360-60(3+0.5p R )] (3+0.5p R ) -30p R p R -360 d(prof M )/d(p R )-60p R p R $4, Prof M 120,000, Prof R p(360-60p)-(360-60p)p R d(prof R )/d(p) p+60p R 0 P (360+60p R )/ p R () P 3+0.5p R 3+0.5x4$5, Prof R $60,000, Total Chan Proft $180,000, Demand 60,000 Manufacturer DO Customer C s $2 p R? p? (D360-60p) IF the two stages coordnate the prcng decsons pp R $4, then Prof R $60,000, Prof M 180,000, and Total Chan Proft $240,000 (ncreased by $60,000), Demand120,

11 ueston: How can the manufacturer acheve the coordnated soluton and maxmze supply chan proft? Desgn a volume dscount scheme (see the text page 161 for detal, f nterested.) that acheves the coordnated soluton. < 120,000, $4 > 120,000, $3.5 Followng ths dscount scheme, the DO s optmal order 120,000 and p$4 Desgn a two-part tarff that acheves the coordnated soluton. Ask DO (1) a up-front cost of $180,000, and (2) p R $2 Key Pont When products for whch the frm has market power, twopart tarffs or volume-based quantty dscounts can be used to acheve coordnaton n supply chan and maxmze supply chan proft Lessons From Dscountng Schemes Lot sze based dscounts ncrease lot sze and cycle nventory n the supply chan Lot sze based dscounts are justfed to acheve coordnaton for commodty products Volume based dscounts wth some fxed cost passed on to retaler are more effectve n general When products for whch the frm has market power, the approaches of volume-based quantty dscounts or two-part tarffs can be used to acheve coordnaton n supply chan and maxmze supply chan proft Strategy 4: Short Term Dscountng Impact of a trade promoton Goal to nfluence retalers to act n a way that helps the manufacturer acheve ts objectve Induce retalers to use prce dscounts Shft nventory from the manufacturer to the retaler and the customer Defend a brand aganst competton uestons What s the mpact of a trade promoton on the behavor of the retaler and the performance of the supply chan? How should a retaler react to a trade promoton a manufacturer offers? A manufacturer lowers the prce of a product Manufacturer sales nventory Retaler DO forward buy nventory future cost Sze of forward buy? How should the retal react? End Customer no n purchase Supply Chan purchase sales cycle nventory flow tme demand varablty Proft

12 Forward buy of the retaler Short Term Dscounts: Forward buyng : Normal order quantty C: Normal unt cost d: Short term dscount R: Annual demand h: Cost of holdng $1 per year d : Short term order quantty 2RS hc d dr C + ( C - d) h C - d Forward buy d Example 10.8 Normal order sze, 6,324 bottles Normal cost, C $3 per bottle Dscount per tube, d $0.15 Annual demand, R 120,000 Holdng cost, h 0.2 Before promoton: Cycle nventory /2 6324/ bottles Average flow tme /2R 6234 /(2x120000) mths ( 9 days) Promoton: d Forward buy d bottles After promoton: (Opt. Buy for Retaler) Cycle nventory d / / bottles ( 6 tmes) Average flow tme d /2R mths( 5 tmes) Promoton pass through to consumers Key pont: Trade promotons lead to a sgnfcant ncrease n lot sze and cycle nventory because of forward buyng by the retaler. Ths generally results n reduced supply chan profts unless the trade promoton reduces demand fluctuaton It may be optmal to the retaler to pass through some (not entre) of the dscount to the end customer Demand at retaler DO: 300,000-60,000p Normal suppler prce, P R $3.00 Max Prof R p(300,000-60,000p)-(300,000-60,000p)p R 300, ,000p + 60,000P R 0 p (300, ,000P R ) / 120,000 Optmal retal prce: p $4.00 Customer demand: R R 300,000 60,000p 60,000 Promoton dscount $0.15, thus P R $2.85Optmal retal prce: p $3.925 Customer demand: D 64, Retaler passes through half the promoton dscount and demand ncreases by 7.5% 10-51

13 Key pont: Faced wth a short-term dscount, t s optmal for retalers to pass through only a fracton of the dscount to the customer, keepng the rest for themselves. Smultaneously, t s optmal for the retaler to ncrease the purchase lot sze and forward buy for future perod. Ths lead to an ncrease of cycle nventory n the supply chan as the result of a trade promoton wthout a sgnfcant ncrease n customer demand. Summary of Learnng Objectves How are the approprate costs balanced to choose the optmal amount of cycle nventory n the supply chan? What are the effects of quantty dscounts on lot sze and cycle nventory? What are approprate dscountng schemes for the supply chan, takng nto account cycle nventory? What are the effects of trade promotons on lot sze and cycle nventory? What are manageral levers that can reduce lot sze and cycle nventory wthout ncreasng costs?