SC Design Facility Location Sections 4.1, 4.2 Chapter 5 and 6

Transcription

1 SC Desgn Faclty Locaton Sectons 4., 4.2 Chapter 5 and 6

2 Outlne Frequency decomposton of actvtes A strategc framework for faclty locaton Mult-echelon networks Analytcal methods for locaton 2

3 Frequency Decomposton SCs are enormous It s hard to make all decsons at once Integraton by smart decomposton Frequency decomposton yelds several sets of decsons such that each set s ntegrated wthn tself 3

4 Frequency Decomposton Low frequency actvty, ~ once a year, hgh fed cost Capacty epanson budget Moderate frequency actvty, ~ once a month Specfc machnes to purchase Hgh frequency actvty, ~ once a day, low fed cost What to produce 4

5 The Cost-Response Tme Fronter H Local FG M Regonal FG 7-Eleven Regonal Cost Local WIP Central FG Central Central WIP Sam s Club Central Raw Materal and Custom producton Low Custom producton wth raw materal at supplers Low Response Tme H 5

6 Servce and Number of Facltes Response Tme Number of Facltes 6

7 Where nventory needs to be for a one week order response tme - typcal results --> > DC Customer DC 7

8 Where nventory needs to be for a 5 day order response tme - typcal results --> > 2 DCs Customer DC 8

9 Where nventory needs to be for a 3 day order response tme - typcal results --> > 5 DCs Customer DC 9

10 Where nventory needs to be for a net day order response tme - typcal results --> > 3 DCs Customer DC 0

11 Where nventory needs to be for a same day / net day order response tme - typcal results --> > 26 DCs Customer DC

12 Costs and Number of Facltes Total SC Inventory Costs Faclty costs Transportaton Number of facltes No economes of scale n shpment sze Economes of scale n nbound shppng 2

13 Cost Buld-up as a functon of facltes Total Costs Cost of Operatons Percent Servce Level Wthn Promsed Tme Facltes Inventory Transportaton Labor Number of Facltes 3

14 Network Desgn Decsons Faclty functon: Plant, DC, Warehouse Where to locate functons, e.g. packagng Faclty locaton Capacty allocaton Market and supply allocaton Who serves whom 4

15 Factors Influencng Network Desgn Decsons Strategc Facltes Global Customers Offshore <reduce tarffs> VW plants n Meco Servng Latn Amerca Regonal Customers Server <local-content> Source Suzk s Indan venture Marut Udyog <low-cost> Nke plants n Korea Outpost faclty <Learn local sklls> Facltes n Japan Contrbutor <customzaton> Marut Udyog Lead faclty 5

16 Factors Influencng Network Desgn Decsons Technologcal, avalablty and economes of scale (fed operatonal costs) Macroeconomc, Tarffs, echange rate volatlty, economc volatlty Poltcal, stablty Infrastructure, electrcty, phone lnes, supplers Compettve Negatve eternaltes, see the net slde Postve eternaltes» Nssan n Inda» Toyota Cty» Shoppng Malls» Telecom corrdor Logstcs and faclty costs 6

17 Negatve eternalty: Market Splttng by Hotellng s Model 0 a b a -a-b Suppose customers (preferences) are unformly dstrbuted over [0,] How much does frm at a get, how about frm at b? b If a locates frst, where should b locate? If a estmates how b wll locate n response to a s locaton, where should a locate? 7

18 A Framework for Global Ste Locaton Compettve STRATEGY INTERNAL CONSTRAINTS Captal, growth strategy, estng network PRODUCTION TECHNOLOGIES Cost, Scale/Scope mpact, support requred, fleblty COMPETITIVE ENVIRONMENT PRODUCTION METHODS Skll needs, response tme PHASE I Supply Chan Strategy PHASE II Regonal Faclty Confguraton PHASE III Desrable Stes GLOBAL COMPETITION TARIFFS AND TAX INCENTIVES REGIONAL DEMAND Sze, growth, homogenety, local specfcatons POLITICAL, EXCHANGE RATE AND DEMAND RISK AVAILABLE INFRASTRUCTURE FACTOR COSTS Labor, materals, ste specfc PHASE IV Locaton Choces LOGISTICS COSTS Transport, nventory, coordnaton 8

19 Analytcal Models for SC Desgn Objectve functons» Prvate sector vs. Publc sector. Equty? Demand allocaton» Dstance vs. Prce vs. Qualty Recall Hotellng Demand pattern over a geography» Dscrete vs. Contnuous Feasblty check» Ante vs. Post Dstances» Eucldean vs. Rectlnear» Trangular nequalty 9

20 Network Optmzaton Models Allocatng demand to producton facltes Locatng facltes and allocatng capacty Key Costs: Fed faclty cost Transportaton cost Producton cost Inventory cost Coordnaton cost Whch plants to establsh? How to confgure the network? 20

21 Demand Allocaton Model: Transportaton Problem Whch market s served by whch plant? Whch supply sources are used by a plant? Gven m demand ponts, j=..m wth demands D j Gven n supply ponts, =..n wth capacty K Send supples from supply ponts to demand ponts j = Quantty shpped from plant ste to customer j Each unt of shpment from supply pont I to demand pont j costs c j Mn s. t. n = m j= j c n = j= j j 0 = m D K j <See Ecel Fle> j j 2

22 Plant Locaton wth Multple Sourcng Whch market s served by whch plant? Whch supply sources are used by a plant? None of the plants are open, a cost of f s pad to open plant At most k plants wll be opened y = f plant s located at ste, 0 otherwse j = Quantty shpped from plant ste to customer j How does cost change as k ncreases? Mn s. t. n = m j= m = y y n = j j f = k D K {0,} y j y + n m c = j= j j 22

23 Plant Locaton wth Sngle Sourcng Whch market s served by whch plant? Whch supply sources are used by a plant? None of the plants are open, a cost of f s pad to open plant Mn s. t. n = f y + n m Dc j = j= j j At most k plants wll be opened y = f plant s located at ste, 0 otherwse j = f market j s suppled by factory, 0 otherwse n = m j= = D j y j j {0,} K y How does cost change as k ncreases? 23

24 24 Gravty Methods for Locaton Ton Mle-Center Soluton Gven n delvery locatons, =..n,, y : Coordnates of delvery locaton d : Dstance to delvery locaton F : Annual tonnage to delvery locaton Locate a warehouse at (,y) + = n y y F y, ) ( ) ( 2 2 Mn <Show Ecel Fle> = = = = = = n n n n d F d F y y d F d F ) ( ) ( 2 2 y y d + =

25 Gravty Methods for Locaton Change the dstance Gven n delvery locatons, =..n, Mn F[ (, y, y : Coordnates of delvery locaton d : Dstance to delvery locaton F : Annual tonnage to delvery locaton Locate a warehouse at (,y) d = ( n F = = = y = n n F = 2 2 ) ( y y) ) 2 + ( y y) 2 ] + n y F F = 25

26 Applchem Demand Allocaton To Meco Canada Venezuela Frankfurt Gary Sunchem Capacty From Meco $ 8 $ 92 $ 36 $ 0 $ 96 $ Canada $ 47 $ 78 $ 35 $ 98 $ 88 $ Venezuela $ 72 $ 06 $ 96 $ 20 $ $ 7 45 Frankfurt $ 5 $ 7 $ 0 $ 59 $ 74 $ Gary, Indana $ 43 $ 77 $ 34 $ 9 $ 7 $ Sunchem $ 222 $ 29 $ 205 $ 45 $ 36 $ 6 50 Demand

27 Applchem Demand Allocaton (982) Capacty 220 Meco 37 Canada 45 Venezuela 470 Frankfurt 85 Gary 50 Sunchem Demand Meco 30 Canada 26 Latn Amerca 60 Europe 200 U.S.A 264 Japan 9 27

28 Applchem Producton Network 982 (wth dutes) Meco Canada Venezuela Frankfurt Gary, Indana Sunchem Meco Canada Latn Amerca Europe U.S.A Japan Annual Cost = $72,96,400 28

29 Applchem Producton Network 982 (wthout dutes) Meco Canada Venezuela Frankfurt Gary Sunchem Meco Canada Latn Amerca Europe U.S.A Japan Annual Cost = 66,328,00 29

30 98 Network. Meco Canada Venezuela Frankfurt Gary Sunchem Meco Canada Latn Amerca Europe U.S.A Japan Annual Cost = $79,598,500 30

31 98 Network (Sunchem Closed) Meco Canada Venezuela Frankfurt Gary Sunchem Meco Canada Latn Amerca Europe U.S.A Japan Annual Cost = $82,246,800 3

32 Cash Flows From Sunchem Plant Year Optmal ($ Mllon) Sunchem Closed Dfference

33 Value of Addng 0. M Pounds Capacty (982) Shadow (dual) prces from LP tells you where to nvest. Locaton Shadow prce Meco $0 Canada $8,300 Venezuela $36,900 Frankfurt $22,300 Gary $25,200 Sunchem $0 Should be evaluated as an opton and prced accordngly. 33

34 Chapter 6 Network Desgn n an Uncertan Envronment 34

35 A tree representaton of uncertanty One way to represent Uncertanty s bnomal tree Up by down by - move wth equal probablty Normal(0, Tσ 2 ) σ 2 = () 2 (0.5) + ( ) 2 (0.5) = <Show Applet> T steps 35

36 Decson tree One column of nodes for each tme perod Each node corresponds to a future state» What s n a state? Prce, demand, nflaton, echange rate, your OPRE 6366 grade Each path corresponds to an evoluton of the states nto the future Transton from one node to another determned by probabltes Peces of optmal paths must be optmal» Fnd shorter and optmal paths startng from perod T and work backwards n tme to perod 0. 36

37 Evaluatng Faclty Investments: AM Tres. Secton 6.5 of Chopra. Plant US 00,000 Meco 50,000 Dedcated Plant Fleble Plant Fed Cost Varable Cost Fed Cost Varable Cost $ M $5 $. M $5 /year. /tre /year /tre 4 M pesos / 0 pesos 4.4 M pesos 0 pesos year /tre /year /tre U.S. Demand = 00,000; Meco demand = 50,000. US$ = 9 pesos Demand goes up or down by 20 percent wth probablty 0.5 and echange rate goes up or down by 25 per cent wth probablty

38 AM Tres Perod 0 Perod Perod 2 RU=00 RM=50 E=9 RU=20 RM = 60 E=.25 RU=20 RM = 60 E=6.75 RU=20 RM = 40 E=.25 RU=20 RM = 40 E=6.75 RU=80 RM = 60 E=.25 RU=80 RM = 60 E=6.75 RU=80 RM = 40 E=.25 RU=80 RM = 40 E=6.75 RU=44 RM = 72 E=4.06 RU=44 RM = 72 E=8.44 RU=44 RM = 48 E=4.06 RU=44 RM = 48 E=8.44 RU=96 RM = 72 E=4.06 RU=96 RM = 72 E=8.44 RU=96 RM = 48 E=4.06 RU=96 RM = 48 E=

39 AM Tres Four possble capacty scenaros: Both dedcated Both fleble U.S. fleble, Meco dedcated U.S. dedcated, Meco fleble For each node solve the demand allocaton model. Plants U.S. Meco Markets U.S. Meco 39

40 AM Tres: Demand Allocaton for RU = 44; RM = 72, E = 4.06 Source Destnaton j Varable cost Shppng cost E Sale prce Margn($) m j U.S. U.S. $ $30 $5 U.S. Meco $5 $ pesos $. Meco U.S. 0 pesos $ 4.06 $30 $2.2 Meco Meco 0 pesos pesos $9.2 Ma = j= n m j j j n 0 = j= m D K j m j j such that Compare ths formulaton to the Transportaton problem. 40

41 AM Tres: Demand Allocaton for RU = 44; RM = 72, E = 4.06 Plants Markets U.S. Meco 00,000 6,000 44,000 U.S. Meco Proft =Revenue-Cost The computatons n the book go beyond my understandng now. Proft wthout fed costs=objectve value of optmzaton=$,38,000 The number assocated wth Node (RU=44,RM=72,E=4.06) must be $,38,000. Fed costs should not be deducted now. They are ncurred n year 0 so must be deducted n year 0. 4

42 Faclty Decson at AM Tres Make proft computatons for the frst year nodes one by one: Compute the proft for a node and add to that (0.9)(/8)(Sum of the profts of all 8 nodes connected to the current one) Plant Confguraton NPV Unted States Meco Dedcated Dedcated $,629,39 Fleble Dedcated $,54,322 Dedcated Fleble $,722,447 Fleble Fleble $,529,758 42

43 Capacty Investment Strateges Sngle sourcng Hedgng Strategy Rsk management? Match revenue and cost eposure Fleble Strategy Ecess total capacty n multple plants Fleble technologes More wll be sad n aggregate plannng chapter 43

44 Summary Frequency decomposton Factors nfluencng faclty decsons A strategc framework for faclty locaton Gravty methods for locaton Network-LP-IP optmzaton models Value capacty as a real opton 44

45 Locaton Allocaton Decsons Plants 2 Warehouses Markets Whch plants to establsh? Whch warehouses to establsh? How to confgure the network? 45

46 p-medan Model Inputs: A set of feasble plant locatons, ndeed by j A set of markets, ndeed by Mn s. t. D j d j j D demand of market No capacty lmtatons for plants At most p plants are to be opened d j dstance between market and plant j y j = f plant s located at ste j, 0 otherwse j = f market s suppled from plant ste j, 0 otherwse j, j j j, y = y j j y p for all, j for all j j {0,} for all, j 46

47 p-center Model Replace the objectve functon n p-medan problem wth Mn Ma {d j j : s a market assgned to plant j} We are mnmzng mamum dstance between a market and a plant Or say mnmzng mamum dstance between fre statons and all the houses served by those fre statons. An eample wth p=3 statons and 9 houses: 47

48 p-coverng Model = f demand pont s covered, 0 otherwse y j = f faclty j s opened, 0 otherwse N facltes assocated wth demand pont If j s n N, j can serve Can you read constrant (*) n Englsh? Ma s. t. j N j, y y j y j = p j D for all (*) {0,} for all, j 48

49 Other Models p-choce Models Crtera to choose the server: dstance, prce? Models wth multple decson makers Franchse model 49