Facility Location in Location Facility Location Decisions ... · Facility Location Decisions Chapter 13 Experience teaches that men are so much ... The COG method involves • Determining

Facility Location Decisions

Chapter 13

Experience teaches that men are so much governed by what they are accustomed to see and practice, that the simplest and most obvious improvements in the most ordinary occupations are adopted with hesitation, reluctance, and by slow graduations. Alexander Hamilton, 1791

Thursday, 10 November, 11

Facility Location in Location Strategy

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Transport Strategy• Transport fundamentals• Transport decisionsCustomer

service goals• The product• Logistics service• Ord. proc. & info. sys.

Inventory Strategy• Forecasting• Inventory decisions• Purchasing and supply

scheduling decisions• Storage fundamentals• Storage decisions

Location Strategy• Location decisions• The network planning process

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Transport Strategy• Transport fundamentals• Transport decisionsCustomer

service goals• The product• Logistics service• Ord. proc. & info. sys.

Inventory Strategy• Forecasting• Inventory decisions• Purchasing and supply

scheduling decisions• Storage fundamentals• Storage decisions

Location Strategy• Location decisions• The network planning process


Location OverviewO que é localizado?• “Fontes” − Fábricas− Distribuidores− Portos

• Pontos Intermediários− CD− Terminais− Serviços Públicos (bombeiros, policia, saúde)− Centros de Serviço

• Distribuição− Varejo− Consumidores / Usuários


Location Overview (Cont’d)Questões Chave• Quantas facilidades devm ser localizadas?• Onde devem ser localizadas?• Qual o tamanho ideal?

Porque localização é importante?

• Fornece a estrutura da rede logística• Afeta significantemente os custos logísticos• Impacta o nível de serviço ao cliente


Methods of Solution• Single warehouse location

– Graphic– Grid, or center-of-gravity approach

• Multiple warehouse location– Simulation– Optimization– Heuristics

Location Overview


Nature of Location AnalysisManufacturing (plants & warehouses)Decisions are driven by economics. Relevant costs such as transportation, inventory carrying, labor, and taxes are traded off against each other to find good locations.RetailDecisions are driven by revenue. Traffic flow and resulting revenue are primary location factors, cost is considered after revenue.ServiceDecisions are driven by service factors. Response time, accessibility, and availability are key dimensions for locating in the service industry.


Some Location Theory/PracticeEarly economic analysis

• Bid rent curves• Weber’s isodapanes• Weber’s classification of industries• Hoover’s tapered transport rates• Agglomeration

Mathematical approaches• Light analysis

-Chart, compass, ruler techniques-Spreadsheets-Checklists

• Continuous location methods• Mathematical programming


Bid Rent Curve


Weber’s Classification of Industries


Hoover’s Transport Curves


CR (2004) Prentice Hall, Inc.

Method appraisal• A continuous location method• Locates on the basis of transportation costs alone

The COG method involves• Determining the volumes by source and destination point• Determining the transportation costs based on $/unit/mi.• Overlaying a grid to determine the coordinates of source and/or destination points• Finding the weighted center of gravity for the graph

COG Method


COG Method (Cont’d)

where Vi = volume fluindo do e/ou para o ponto i Ri = custo unitário do transporte de Vi para o ponto iXi,Yi = coordenadas do ponto i = coordenadas do ponto a ser localizado


COG Method (Cont’d)Example Suppose a regional medical warehouse is to be established to serve several Veterans Administration hospitals throughout the country. The supplies originate at S1 and S2 and are destined for hospitals at H1 through H4. The relative locations are shown on the map grid. Other data are: Note rate is a

per mile costPointi

Prod-ucts Location

Annualvolume,

cwt.

Rate,$/cwt/

mi. Xi Yi1 S1 A Seattle 8,000 0.02 0.6 7.32 S2 B Atlanta 10,000 0.02 8.6 3.03 H1 A & B Los

Angeles5,000 0.05 2.0 3.0

4 H2 A & B Dallas 3,000 0.05 5.5 2.45 H3 A & B Chicago 4,000 0.05 7.9 5.56 H4 A & B New York 6,000 0.05 10.6 5.2


COG Method (Cont’d)Map scaling factor, K



Solve the COG equations in table form

i Xi Yi Vi Ri ViRi ViRiXi ViRiYi1 0.6 7.3 8,000 0.02 160 96 1,1682 8.6 3.0 10,000 0.02 200 1,720 6003 2.0 3.0 5,000 0.05 250 500 7504 5.5 2.4 3,000 0.05 150 825 3605 7.9 5.5 4,000 0.05 200 1,580 1,1006 10.6 5.2 6,000 0.05 300 3,180 1,560

1,260 7,901 5,538


COG Method (Cont’d)Now,

X = 7,901/1,260 = 6.27

Y = 5,538/1,260 = 4.40

This is approximately Columbia, MO.

The total cost for this location is found by:

where K is the map scaling factor to convertcoordinates into miles.CR (2004) Prentice Hall, Inc.


COGCOG Method (Cont’d)



2,360,882Total660,4920.056,0005.210.66196,6440.054,0005.57.95160,7330.053,0002.45.54561,7060.055,0003.02.03271,8250.0210,0003.08.62509,4820.028,0007.30.61

TCRiViYiXiiCalculate total cost at COG


Note The center-of-gravity method does not necessarilygive optimal answers, but will give good answers if there area large numbers of points in the problem (>30) and thevolume for any one point is not a high proportion of the totalvolume. However, optimal locations can be found by theexact center of gravity method.

∑∑

∑∑

==

i iii

i iiiin

i iii

i iiiin

/dRV/dYRV

Y,/dRV/dXRV

X

where

22 )Y(Y)X(Xdn

in

ii−+−=

and n is the iteration number.



Solution procedure for exact COG


1) Solve for COG2) Using find di3) Re-solve for using exact formulation4) Use revised to find revised di

5) Repeat steps 3 through 5 until there is no change in

6) Calculate total costs using final coordinates



• A more complex problem that most firms have. • It involves trading off the following costs:

− Transportation inbound to and outbound from the facilities − Storage and handling costs− Inventory carrying costs− Production/purchase costs− Facility fixed costs

• Subject to:− Customer service constraints− Facility capacity restrictions

• Mathematical methods are popular for this type of problemthat:− Search for the best combination of facilities to minimize

costs− Do so within a reasonable computational time− Do not require enormous amounts of data for the analysis

Multiple Location Methods


Location Cost Trade-Offs

Number of warehouses

Cos

t

Production/purchaseand order processing

Inventory carryingand warehousing

Warehousefixed

Inbound andoutboundtransportation

Total cost

00




• A method used commercially- Has good problem scope- Can be implemented on a PC- Running times may be long and memory requirements substantial- Handles fixed costs well- Nonlinear inventory costs are not well

handled

• A linear programming-like solution procedure can be used (MIPROG in LOGWARE)

Mixed Integer Programming


• Less complicated than previous example, butbased on integer programming

• Locates on basis of transportation costs andfacility fixed costs

• Locations are restricted to the node (e.g.,demand) points in the problem

• Method finds the optimal location of M facilities at a time

P-Median Location Method


Example Five incinerators are to be located for toxic chemicalreclamation. The cost to move chemicals from 12 market areas tothe incinerators is $0.0867/cwt./mi. The areas, the chemicalvolume, and fixed costs to operate an incinerator are:

Market

Annualvolume,

cwt.

Fixedoperating

cost, $ Market

Annualvolume,

cwt.

Fixedoperating

cost, $Boston MA 30,000 3,100,000 Chicago IL 240,000 2,900,000New York NY 50,000 3,700,000 Minneapolis MN 140,000 --Atlanta GA 170,000 1,400,000 Phoenix AZ 230,000 1,100,000Baltimore MD 120,000 -- Denver CO 300,000 1,500,000Cincinnati OH 100,000 1,700,000 Los Angeles CA 40,000 2,500,000Memphis TN 90,000 -- Seattle WA 20,000 1,250,000

P-Median (Cont’d)

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The database for this problem is PMED02.DAT inLOGWARE.

AnswerNo. Facility name Volume Assigned

node numbers 1 New York NY 200,000 1 2 4 2 Atlanta GA 260,000 3 6 3 Chicago IL 480,000 5 7 8 4 Phoenix AZ 270,000 9 11 5 Denver CO 320,000 10 12 Total 1,530,000

Total cost: $24,739,040.00and graphically shown…

P-Median (Cont’d)


P-Median (Cont’d)

Repeating the analysis for a different number of incinerators can find the optimal number of incinerators as well.

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Selective Evaluation Using COG

Note : Inventorycosts and fixedcosts increase withmore warehouses

User selects the locations or the number of locations to be evaluated. Analysis is repeateduntil the optimum is found. Inventory value can be easily added as in the following examplewhere I NT = $6, ,000 000 . At 25% per year, the inventory carrying cost is CC = 0.25 I T .

Number ofWarehouses

TransportationCost, $

FixedCost, $

InventoryCost, $

TotalCost, $

1 41,409,628 2,000,000 1,500,000 44,909,6282 25,989,764 4,000,000 2,121,320 32,111,0843 16,586,090 6,000,000 2,598,076 25,184,1664 11,368,330 8,000,000 3,000,000 22,368,3305 9,418,329 10,000,000 3,354,102 22,772,4316 8,032,399 12,000,000 3,674,235 23,706,6347 7,478,425 14,000,000 3,968,627 25,447,0528 2,260,661 16,000,000 4,242,641 22,503,3029 948,686 18,000,000 4,500,000 23,448,686

10 0 20,000,000 4,743,416 24,743,416

Note : Transport cost declinewith more warehouses

Example

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Shows effect of inventory policy on location. Presence of local optima make it difficult to find the optimum solution in complex problems.

Total Cost Curve for Selective Evaluation Example

0

12,500,000

25,000,000

37,500,000

50,000,000

Total cost, $

1 2 3 4 5 6 7 8 9 10

Number of warehouses

Local optimumOptimum


Location by Simulation


•Can include more variables than typical algorithmic methods

•Cost representations can be precise so problem can be more accurately described than with most algorithmic methods

•Mathematical optimization usually is not guaranteed, although heuristics can be included to guide solution process toward satisfactory solutions

•Data requirements can be extensive

•Has limited use in practice


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Commercial Models for Location

Features

•Includes most relevant location costs

•Constrains to specified capacity and customer service levels

•Replicates the cost of specified designs

•Handles multiple locations over multiple echelons

•Handles multiple product categories

•Searches for the best network design




Com

mer

cial

Mod

els

(Con

t’d)

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Commercial Models (Cont’d)

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Dynamic Location

Retail Location

Methods

• The general long-range nature of the location problem- Network configurations are not implemented immediately- There are fixed charges associated with moving to a new

configuration

• We seek to find a set of network configurations that minimizes the presentvalue over the planning horizon

• Contrasts with plant and warehouse location.- Revenue rather than cost driven- Factors other than costs such as parking, nearness to competitive

outlets, and nearness to customers are dominant

• Weighted checklist - Good where many subjective factors are involved - Quantifies the comparison among alternate locations



A Hypothetical Weighted Factor Checklist for a Retail Location Example

(1)FactorWeight

(1 to 10)a Location Factors

(2)

Factor Score(1 to 10)b

(3)=(1)×(2)

WeightedScore

8 Proximity to competing stores 5 405 Space rent/lease

considerations 3 158 Parking space 10 807 Proximity to complementary

stores 8 566 Modernity of store space 9 549 Customer accessibility 8 723 Local taxes 2 63 Community service 4 128 Proximity to major

transportation arteries 7 56 Total index 391

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Documents

Facility Location in Location Facility Location Decisions ... · Facility Location Decisions Chapter 13 Experience teaches that men are so much ... The COG method involves • Determining