Facility Location

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Facility Location

• Inventory Management
• Dr. Ron Tibben-Lembke

2
Location Decisions

• Long-term decisions
• Difficult to reverse
• Affect fixed variable costs
• Transportation costs (25 of price)
• Other costs taxes, wages, rent
• Objective maximize benefit of location to firm

3
What factors should we consider?

• Skilled workforce
• Environmental laws / cost of compliance
• Cost of utilities, labor, taxes
• Suppliers close by fast cheap access
• Customers close by
• Competitors close by? Skilled labor pool
• International - control issues?

4
Service Facilities Traffic focus

• Revenue changes a huge amount, depending on the
  location.
• Old Navy in Stead because of cheap land?
• Location, location, location you need traffic
• Make it convenient!
• vitamins need enough, but it has to be the right
  kind
• people who would want to buy your products when
  they are there.
• Cost probably doesnt change nearly as much, by
  location
• All malls have high rent

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Wal-Mart
Toys Party
Office Max
WinCo
6

• I-80 McCarran sounds great.
• Kmart Sins
• Cant see from anywhere
• - see where were going
• Very circuitous entry
• feels inconvenient, no matter
• how long it actually takes

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Cost Focus

• Revenue does not vary much, depending on the
  location.
• Customers dont care if your warehouse is in
  Sparks or Sacramento
• Location is a major cost driver
• Impacts shipping, labor, production costs
• Varies greatly by location

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Cost Minimization

• Identify the costs that will vary most with the
  location you choose.
• Transportation, taxes, labor,
• Facility construction cost, utilities
• Other considerations
• Proximity of services, suppliers
• Quality of life
• Government incentives

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Cost Focus Process Overview

• Identify general region to locate in
• Usually based on mostly on transp. costs
• Identify a list of candidate cities
• Choose cities with good transp. Access
• Estimate labor cost availability, facilities
  costs
• Select metro area, identify candidate properties.
• Find cost of building or leasing individual
  properties

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Case StudyImporting from China to E. Coast
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Customer Location
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More detail on East Coast possibilities
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Interstate Detail
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China to U.S. Container Rates
NY / NJ 3,600 36 days
Wilmington DE 3,950 36 days (door)
Norfolk 3,600 34 days
Charleston 3,600 35 days
Atlanta 3,200 37 days (door)
New Orleans 3,200 36 days
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Allentown
575
305
428
DrayageRates North
Elizabeth, NJ
850
295
Harrisburg
343
350
Philadelphia
305
265
850
375
Wilmington
656
825
Baltimore
305
750
375
750
780
950
1125
725
950
888
Roanoke
750
Norfolk
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China to Long Beach
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Landbridge Data
Columbus 3000, 21days
Cincinnati 2925, 21d
Louisville 3050, 20d
Murray 3350, 22d
Nashville 3300, 22d
Memphis 2900, 18.5d
Atlanta 3300, 23d
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Interstate Access
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Distribution Center Location

• Minimize demand-weighted distance distance to
  each customer times the volume of shipments to
  the customer
• How many to build?
• Where to build?

20
Case Study Retailer

• Location of a 5th returns processing facility
• Addresses of 2125 Continental U.S. stores
• Location of 4 Return Goods Processing Centers
• List of all return shipments from each store,
  including pounds and pallets
• Calculated actual highway distances from every
  store to its DC

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Local Streets
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Transportation Cost Approx.

• Current Pallets 205,254
• Current Pallet Miles 77.9m
• Cost / pallet-mile 11.68 cents
• Pallet-Mile 1 pallet traveling 1 mile
• Minimize average distance traveled

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Solution Software

• Some locations must have a facility
• Considers adding a facility at every existing
  store
• We wont really build next to a store, but thats
  ok
• Finds one best facility to add
• Finds second best facility to add
• Reconsider first added facility, then second,
  etc.
• Improvement heuristics, optimal methods

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Current RCs
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Dallas Realignment
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Close 1 existing RDC
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Location Methods

• Minimize demand-weighted distance
• Center of Gravity minimizing demand-weighted
  distances of one facility
• Ardalan minimize transportation of multiple
  facilities, but must locate by customers
• (P-Median Problem, Maximum Covering)
• Factor Weighting consider qualitative factors
• Break-even Consider fixed variable costs

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Center of Gravity

• Compute X and Y coordinates separately
• dix is the X coordinate of location i.
• diy is the Y coordinate of i.
• Wi is the X demand at i.
• CX and CY are the coordinates of the DC.

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Center of Gravity Example 1

• You need to decide where to build a new DC for
  Motorola.
• It needs to serve wholesalers in Reno, Dallas,
  and Chicago.
• Locate these cities on an unscientific,
  rectangular grid.
• Grid must maintain relative distances, but X and
  Y grids could be different.

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60
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0 20 40 60 80 100 120 140 160
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Center of Gravity Method

• City Demand
• Reno is at 17, 55 100
• Fort Worth is at 78, 20 90
• Chicago is at 110, 65. 120
• Demand is TL/month

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Center of Gravity
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80
60
40
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0 20 40 60 80 100 120 140 160
34
North Platte
Sharon Springs
Salina KS
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Compromise Solution

• Closest town is Sharon Springs, KN
• Population 872
• 30 miles from I-70.
• Probably not a good choice
• Salina, KN puts us at I-70 and I-35
• North Platte NE is at I-80 and 83.
• Access to Dallas less convenient

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80
60
40
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0 20 40 60 80 100 120 140 160
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Finalizing City

• Go where other warehouses are
• More choice in pre-built buildings
• Cheaper, easier to build a new one
• More trucks to and from town, means more carriers
  there, means cheaper rates.
• Backhaul situation
• Get estimates of inbound, outbound trucking
  costs.
• Provide lists of loads per year to each
  destination, from each source

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Center of Gravity Example 2

• You need to decide where to locate a DC in South
  Dakota
• X Y Demand
• Pierre 78 47 50
• Watertown 150 65 8
• Sioux Falls 160 25 90
• Rapid 12 42 60

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100










80
60
40
20
0
0 20 40 60 80 100 120 140 160
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Center of Gravity
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100
80
60
40
20
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0 20 40 60 80 100 120 140 160
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Ardalan Heuristic

• Need a matrix of distances or costs from each
  customer location to every other location
• Demand at each location
• Weight give higher weight to more important
  customers their pain of traveling a longer
  distance is worth more.
• Only consider locating where customers are
• Identify the one best place to locate at, then
  the second one to add, then the third, etc.

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Ardalan Heuristic

• Minimize weighted distance traveled
• To
• From A B C D Dem. Weight
• A 0 11 8 12 10 1.1
• B 11 0 10 7 8 1.4
• C 8 10 0 9 20 0.7
• D 9.5 7 9 0 12 1.0

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Ardalan Method

• Expected demand at each location.
• Weight represents importance of serving location
  (bigger more important)
• Step 1 Multiply distances weights demand
• A to B 11 1.1 10 121

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Ardalan Method

• Step 2. Add up values in columns
• From A B C D
• A 0 121 88 132
• B 123.2 0 112 78.4
• C 112 140 0 126
• D 114 84 108 0
• 349.2 345 308 336.4

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Ardalan Method

• Choose smallest value as first site.
• From A B C D
• A 0 121 88 132
• B 123.2 0 112 78.4
• C 112 140 0 126
• D 114 84 108 0
• 349.2 345 308 336.4

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Ardalan Method

• 3. If larger, set each cost equal to cost in same
  row in the chosen column
• From A B C D
• A 0 88 88 88
• B 112 0 112 78.4
• C 0 0 0 0
• D 108 84 108 0
• 220 172 308 166.4

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Ardalan Method

• Get rid of previously chosen column.
• Sum, choose smallest sum.
• From A B D
• A 0 88 88
• B 112 0 78.4
• C 0 0 0
• D 108 84 0
• 220 172 166.4

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Ardalan Method

• Repeat 3 4 until enough sites chosen.
• From A B D
• A 0 88 88
• B 78.4 0 78.4
• C 0 0 0
• D 0 0 0
• 78.4 88 166.4

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Ardalan Method

• Repeat 3 4 until enough sites chosen.
• From A B
• A 0 88
• B 78.4 0
• C 0 0
• D 0 0
• 78.4 88

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Ardalan Summary

• What we decided is that if we only want to build
  one location, it should be in C.
• If we want to build two, they should be in C and
  D. If we add a third one, it should be in A.

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Ardalan Summary

• Assumes that we have to locate in the same city
  as one of our customers, which is not always the
  case.
• However, it can be used to find more than one
  location.
• Center of Gravity does not try to locate in the
  same city as one of the customers, but can only
  set one site.
• If we choose the same sites as customers A and X,
  we obviously dont really have to put the
  warehouses in those exact cities.

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P-Median Problem

• Minimize average weighted distance to customers,
  when locating P facilities, where Pgt1.
• Can consider 100s of locations.
• Complex to solve there is software for this.

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Maximum Covering Problem

• A facility can cover a customer if the customer
  is within X miles of the facility.
• Try to find the best location, and minimum number
  of facilities to cover all demands.
• Cover a table with plates.
• Math also very hard.

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Comparison of Results
(Using Distances of 150, 200, 250,250)
Demand Covered
Number of Facilities
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Solving large problems
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Incremental or clean-slate apprach

• Take into account existing facilities
• What is the best location to add, given the
  existing facilities?
• What is the best to add, if we were to close down
  one of the current facilities?
• Unfortunately, only P-Median or Maximum Covering
  can deal with these.

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Factor Rating Method

• Most widely used method?
• Useful for service or industrial facilities can
  include intangible, qualitative factors
• List relevant factors, assign a weight
• Develop a scale for each factor
• Score each factor using the scale
• Multiply scores by weights, add up
• Choose location with highest total score
• Kind of like Miss America

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Factor Rating Example

• We need to decide where to build a new coffee
  roasting plant. There are two possible
  locations Dallas, and Denver.
• We consider the following factors
• Transp annual trucking costs in k
• Lease annual costs in k
• Labor availability scale 1-10, unemployment,
  related industries
• Quality of life scale 1-10 outdoor activities,
  cultural, sports, education

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Factor Rating Example

• Using a scoring system we developed, we have the
  following.
• Factor Weight TX CO
• Transportation 0.5 900 1,023
• Plant Lease Cost 0.3 45 39
• Labor availability 0.2 10 8
• Quality of Life 0.1 7 9.5

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Normalizing Scores

• All factors must be scored on the same scale,
  like 1-10, or 0-1.0, etc.
• Costs need to be re-scaled
• Lowest cost site gets a 10.
• More expensive site gets 39/45 10 or 900/1,023
  10

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Factor Rating Example

• TX CO
• Factor Wt Raw Wtd Raw Wtd
• Tr 0.4 10 4.00 8.80 3.52
• Plant 0.3 8.7 2.61 10 3.00
• Labor 0.2 10 2.00 8 1.60
• Q Life 0.1 7 0.70 9.5 0.95
• TOTAL 9.31 9.07
• TX is best

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Possible Approach

• Use Ardalan to find out which general regions to
  locate in (state / county).
• Use factor weighting to choose city.
• Ardalan has disadvantage of choosing weights --
  difficult to set levels.

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Break-Even Analysis

• Determine fixed and variable costs for each
  location
• Fixed cost how much it would cost to open a
  facility there
• Variable cost how much total costs would
  increase as production increases
• Transportation costs
• Labor costs
• Taxes
• Increased construction costs

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Locating Service Facilities

• Using Linear Regression
• Collect data about your current facilities
• Use regression to determine which variables have
  a significant impact on profits
• Choose new facilities which have these
  characteristics

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Method Comparison

• Center of gravity minimizes average distance for
  one facility only.
• Ardalan Minimizes weighted distances for more
  than one facility.
• Breakeven fixed variable costs.
• Factor weighting considers many other important
  aspects of location, but does not minimize
  distance.

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Transportation Method

• You have 3 DCs, and need to deliver product to 4
  customers.
• Find cheapest way to satisfy all demand

D 2
A 10
E 4
B 10
F 12
C 10
G 11
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Solving Transportation Problems

• Trial and Error
• Linear Programming ooh, whats that?!
• Tell me more!

D E F G
A 10 9 8 7
B 10 11 4 5
C 8 7 4 8